Dujella (2001)
y2 + xy = x3 - 3531474678706925407855636725500x
+ 2548317483638211729406118411284184511350250000
Torsion points:
O, [1274439983611000, -10844671977181029885500],
[1274439983611000, 10844670702741046274500],
[3065408298441400, -143274960258979544075900],
[1015090784251000, 3083677033796969474500],
[3065408298441400, 143274957193571245634500],
[-1394032294922720, -69009042015707100679100],
[1015090784251000, -3083678048887753725500],
[-1394032294922720, 69009043409739395601820],
[1127778195451000, -563889097725500],
[594696310843000, -25660963243264393725500],
[594696310843000, 25660962648568082882500]
Independent points of infinite order:
P1 = [653077684402600, 22815227981543767634500]
P2 = [387988257149950, 35164648909774644352000]
P3 = [-122360938910600, -54576551943239873123900]
Rathbun (2003)
y2 + xy + y = x3 - x2 - 42403753582533569425032932x
+ 106274144228004532427905140464314177031
Torsion points:
O, [3949439151061, -637753076434512851],
[3949439151061, 637749126995361789],
[7083012434121, 12699443003830818709],
[7083012434121, -12699450086843252831],
[24338879236581, -116155532752313973731],
[24338879236581, 116155508413434737149],
[3810348040551, 150277207446517339],
[3810348040551, -150281017794557891],
[3783754333125, -1891877166563],
[4523103356109, 2648267198106062149],
[4523103356109, -2648271721209418259]
Independent points of infinite order:
P1 = [-2362419518979, -13901972586915491891]
P2 = [3799863365181, 108421510951850869]
P3 = [150735264213265861/39601, 1061927645729427513662011/7880599]
Dujella (2005)
y2 + xy = x3 - 2749906390198370341509293334209840x
+ 55466178854972875780766488008304927128432629217600
Torsion points:
O, [31420484588834050, 287336012793397607524690],
[266957216193740110, 135448784453007283156499260],
[266957216193740110, -135448784719964499350239370],
[31420484588834050, -287336044213882196358740],
[123679053960469759/4, -123679053960469759/8],
[41791236833506912, -3678708652511979390642728],
[41791236833506912, 3678708610720742557135816],
[33725894220200140, 1041235331411183023028260],
[33725894220200140, -1041235365137077243228400],
[73037877015264820, 15628234291578001012953520],
[73037877015264820, -15628234364615878028218340]
Independent points of infinite order:
P1 = [73784354156646366730/529, 594241457820513097886291335220/12167]
P2 = [60144856268790422189935/1887876, 1141071830679487618687810353102115/2593941624]
P3 = [3552098403757232539032020629388404135052178564757/58516568589495224148143093136,
6694641428972566918439666396394037247085348777952632438240290882936757319/14155273884622832540273334842956193130264384]
Dujella (2005)
y2 + xy = x3 - 544753256053055692212823356675x
+ 154756127532691562955214620687209364995464257
Torsion points:
O, [414051058105542, -429728214720413621727],
[414051058105542, 429727800669355516185],
[-104828500368306, -14515847581328282939607],
[520422194097234, 3493594560247399589553],
[425907554236164, -7579389181556251917],
[425907554236164, 7578963274002015753],
[427747122834174, -57918611760265920807],
[427747122834174, 57918184013143086633],
[-104828500368306, 14515847686156783307913],
[520422194097234, -3493595080669593686787],
[426184812828398, -213092406414199]
Independent points of infinite order:
P1 = [780769614212874, 14331343729279998511233]
P2 = [4521513405555635346/10609, 1468974979278800313313851/1092727]
P3 = [27275829940946961/64, 33921871382353791771/512]
Dujella (2005)
y2 + xy + y = x3 - x2 - 30148261392223353627371003927x
+ 2014844441907862958757753840141478478229551
Torsion points:
O, [400989732863979/4, -400989732863983/8],
[108065007276051, -137333441385063636626],
[100250789804991, 68296927715723794],
[100250789804991, -68397178505528786],
[100865662107651, 10743244388165530174],
[100865662107651, -10743345253827637826],
[100296323953651, -858926643724061826],
[100296323953651, 858826347400108174],
[214115101526151, 2318579731663276168174],
[108065007276051, 137333333320056360574],
[214115101526151, -2318579945778377694326]
Independent points of infinite order:
P1 = [-31311304698849, -1711177446268609231826]
P2 = [96338846451692761/961, 836312116873900619334/29791]
P3 = [2669219409992988726489/26697889, 641143066243358068774175453812/137947992463]
Dujella (2005)
y2 + xy = x3 + 22560435880391339052664320x
+ 540479833226131711454100721381679986752
Torsion points:
O, [-28907392053249/4, 28907392053249/8],
[17309447381844, -78212492727413237172],
[6161297209344, 30222074629490270328],
[6161297209344, -30222080790787479672],
[-4939557780606, 17564735458834410978],
[-4939557780606, -17564730519276630372],
[78347396844, -23286216253277604672],
[78347396844, 23286216174930207828],
[71137685678094, 601782847258764582828],
[17309447381844, 78212475417965855328],
[71137685678094, -601782918396450260922]
Independent points of infinite order:
P1 = [27661635621054/25, 2975936714042472539982/125]
P2 = [-30480638069423246996886/10538870281, -22977209079062848462558645281998988/1081909884177179]
P3 = [2342634032664396968144502/246441752041, 4914829306144468018253376552120162012/122340832523961589]
Dujella (2005)
y2 + xy = x3 - 158650177283083359834494480x
+ 2975550938225630369228434206177421574400
Torsion points:
O, [-17999082908640, 8999541454320],
[10518469219360, 49704505375726286320],
[10518469219360, -49704515894195505680],
[718654051360, -53496799368832305680],
[718654051360, 53496798650178254320],
[25449053001760, 124178257282337486320],
[25449053001760, -124178282731390488080],
[99663668791360, -988487709600951045680],
[-11087373233120, 58065447864617186800],
[-11087373233120, -58065436777243953680],
[99663668791360, 988487609937282254320]
Independent points of infinite order:
P1 = [-4105870339040, -59646712275238603280]
P2 = [-267836029357173601436/148962025, -103726188450608036179294356769472/1818081515125]
P3 = [133016718858542220264841/13732089856, 77969116235657583184190111640177403/1609181217685504]
Dujella (2005)
y2 + xy = x3 - 219359669833758885305830876x
+ 1286567133009306197242813828876596893456
Torsion points:
O, [-17156609797576, 8578304898788],
[8605535093816, 6012043045174375652],
[8605535093816, -6012051650709469468],
[12014536867448, -19630335345016356700],
[5594916463160, -15310335249016002844],
[5594916463160, 15310329654099539684],
[12014536867448, 19630323330479489252],
[35959817802296, 199745768711168751332],
[-4661640926464, 46987676382281094812],
[-4661640926464, -46987671720640168348],
[35959817802296, -199745804670986553628]
Independent points of infinite order:
P1 = [4442580116024, 19993128808201418468]
P2 = [1656679641417799046621/58920976, 59568747670299126557401049930797/452277411776]
P3 = [1725727552726593845180/40921609, 67776793894365801559370503451408/261775532773]
Dujella (2005)
y2 + xy = x3 - 9133867357763769559583815213550x
+ 5898928970001153735077443080836755542607104132
Torsion points:
O, [6018765955455292, 411044261970404398951810],
[6018765955455292, -411044267989170354407102],
[13006303621278604, 1444748609279946368756098],
[2859820245261304, 56275708200304092817798],
[51510907202062204, 11671036106346297636716098],
[13006303621278604, -1444748622286249990034702],
[51510907202062204, -11671036157857204838778302],
[2859820245261304, -56275711060124338079102],
[3734051322977404, -154457106474108664679102],
[3734051322977404, 154457102740057341701698],
[2624096533089148, -1312048266544574]
Independent points of infinite order:
P1 = [14959825090199404, 1793658926931564245232898]
P2 = [13604743038585244/25, 4126003470854275880537018/125]
P3 = [6644336613293251639/11236, 31611555359367832743520074553/1191016]
Dujella (2005)
y2 + xy + y = x3 - x2 - 9215871878203448910011960927x
+ 3132784212945409487749240767092972677236551
Torsion points:
O, [2266789295251, -1764059359756380529226],
[2266789295251, 1764059357489591233974],
[273292275684051, -4585411093846472703626],
[273292275684051, 4585410820554197019574],
[-107886460854549, 1694493724656237290974],
[1091432002888851, -35961286439178261975626],
[1091432002888851, 35961285347746259086774],
[-107886460854549, -1694493616769776436426],
[-167192786721645, 83596393360822],
[106018508647059, -1829582305588943946314],
[106018508647059, 1829582199570435299254]
Independent points of infinite order:
P1 = [8103305093885315790099, 729446233182561054772360338776374]
P2 = [602924037077155131/4489, 624972662127733061798180482/300763]
P3 = [1744028880689541771/32041, 9584057808531429135638592146/5735339]
Dujella (2006)
y2 + xy = x3 - 419501639045238763836050631283075x
+ 2842433978740985435656965438988809420534955137857
Torsion points:
O, [15280003964885998, -7640001982442999],
[32041087594996454, -4721814121142123806722727],
[32041087594996454, 4721814089101036211726273],
[20633986913165054, -1723832407365937114549927],
[20633986913165054, 1723832386731950201384873],
[67751953758050354, -16894496684982573665393827],
[67751953758050354, 16894496617230619907343473],
[266612794441924814, -137267878651995369219102967],
[266612794441924814, 137267878385382574777178153],
[16397780614412444, -610484732643315001783207],
[16397780614412444, 610484716245534387370763]
Independent points of infinite order:
P1 = [7391627213243949534014/5041, 635430280639231056930566876695903/357911]
P2 = [-11492940893095368447922/2621161, -9099177759745133453369235004195661/4243659659]
P3 = [4841997678760797168146/1181569, 1402347733236885753428847389817359/1284365503]
Dujella (2006)
y2 + xy + y = x3 - x2 - 28985104452130882509175487233531337957x
+ 59921356539427696596164876188354027506205686554765141789
Torsion points:
O, [3651152795119494847, 1662986857570957126609932576],
[3651152795119494847, -1662986861222109921729427424],
[8782152793874634447, 21970522995384033024940516576],
[8782152793874634447, -21970523004166185818815151024],
[3309578934774774207, 493678522022701793723389216],
[32904682304380597347, 186367034048683491472415932576],
[3309578934774774207, -493678525332280728498163424],
[32904682304380597347, -186367034081588173776796529924],
[3230974516744934847, -1615487258372467424],
[4758221887485710847, 5452811747640785401470316576],
[4758221887485710847, -5452811752399007288956027424]
Independent points of infinite order:
P1 = [-10543311142752797952977/2809, -1602320865955063056498930617389248/148877]
P2 = [1606865090778489209909163/643204, 908516131702919245032823814295695833/515849608]
P3 = [353665470395466543812407/3481, 210034590359020423868011773487336304/205379]
Dujella (2006)
y2 + xy = x3 - 12100574837935299530348826728260x
+ 12237572864806256968480175273606363024430659600
Torsion points:
O, [2772476200570120, -1386238100285060],
[-3295306219008760, 127784195496456861604220],
[3842969899130120, 149966702617722629314940],
[3842969899130120, -149966706460692528445060],
[13010087150536520, 1434198792223256836738940],
[13010087150536520, -1434198805233343987275460],
[-538006847301880, -136352624077201499005060],
[-538006847301880, 136352624615208346306940],
[966330684395120, 38036440641246600514940],
[966330684395120, -38036441607577284910060],
[-3295306219008760, -127784192201150642595460]
Independent points of infinite order:
P1 = [715311048928520, 62832325043940702812540]
P2 = [4688829778331574920/5041, 15130264521562227770953890340/357911]
P3 = [-1518113548462185968620/413449, -22501528578210137585583106507420/265847707]
Dujella (2006)
y2 + xy = x3 - 2898719924159689672493727108121575x
+ 135465904775206154649829932775967333485406858566857
Torsion points:
O, [325557810097921494, -183567289230913083625448187],
[-40159301178304236, 13678771029158366716162983],
[325557810097921494, 183567288905355273527526693],
[-40159301178304236, -13678770988999065537858747],
[-69605438424085002, 34802719212042501],
[85345094942319354, 22576751709767665170944973],
[38264998909169454, 8976323811214603518595773],
[38264998909169454, -8976323849479602427765227],
[5489696763042054, 10941583663357555541582373],
[5489696763042054, -10941583668847252304624427],
[85345094942319354, -22576751795112760113264327]
Independent points of infinite order:
P1 = [312478285885728323398984/20331081, 891372470800631146775985590806499137/91672844229]
P2 = [-365591976012736879480266/6964321, -219757836652216377949711102115549013/18378843119]
P3 = [173887182765009051548902833320608852006/2028436793609970545649,
2077126625621878693674376952742524413189021026057176496499/91357081970434542129190434409143]
Dujella (2006)
y2 + xy = x3 - 338842502244755458889373539201900x
+ 2400433946203319241463771173720705835728491610000
Torsion points:
O, [8224205880275800, 412296836589876852918100],
[8224205880275800, -412296844814082733193900],
[11311280024723800, 122122363063855976118100],
[11311280024723800, -122122374375136000841900],
[10433358694499680, 29859082057172159852500],
[10433358694499680, -29859092490530854352180],
[-10700125187436200, -2191119603529049444681900],
[21401369316770200, 2225076575115724162038100],
[10725330223763800, -5362665111881900],
[-10700125187436200, 2191119614229174632118100],
[21401369316770200, -2225076596517093478808300]
Independent points of infinite order:
P1 = [1924595164951493800/169, 299411494158994155315705700/2197]
P2 = [44356478398809009987521200/4020447649, 18011915829001421589547429727070383300/254924524080143]
P3 = [-60834986883421829525045/4024036, -16280701977703711753820327838846355/8072216216]
Dujella (2006)
y2 + xy = x3 - 20150477240107808836826538345040x
+ 34815737557101743437756926816460813616604276992
Torsion points:
O, [10375979966307071/4, -10375979966307071/8],
[3702398032549424, 104700529714818937850288],
[2585148442007924, 538773887846173436288],
[2585148442007924, -538776472994615444212],
[-1470053775513076, 247509901706767610412788],
[2404382732299424, 16314104099000758850288],
[2404382732299424, -16314106503383491149712],
[2626431576049424, 3063981291426790100288],
[2626431576049424, -3063983917858366149712],
[3702398032549424, -104700533417216970399712],
[-1470053775513076, -247509900236713834899712]
Independent points of infinite order:
P1 = [1972348587100424, 52390091110567913666288]
P2 = [8178147094873808, 645750520428306248948096]
P3 = [2619223988585024, 2424119743314179939888]
Dujella (2006)
y2 + xy + y = x3 - 868617475475590577770073244067064308738x
+ 9853509687915893717709967127954972326559957860978482738788
Torsion points:
O, [68071625472346602391/4, -68071625472346602395/8],
[20638706348058851104, -26787191090538055901913427765],
[-3885409802381029871, -114759700262772189455696153815],
[-3885409802381029871, 114759700266657599258077183685],
[17007863177733985609, 55137344113910182013481065],
[16559718651858959629, 3244323117410296952044225685],
[16559718651858959629, -3244323133970015603903185315],
[17075886920578688254, -428948347891609698488249440],
[17075886920578688254, 428948330815722777909561185],
[20638706348058851104, 26787191069899349553854576660],
[17007863177733985609, -55137361121773359747466675]
Independent points of infinite order:
P1 = [-5983496402447887271, -121805815613180573735493121015]
P2 = [104958357303792405325744/6561, 3828625420116013232678067687033835/531441]
P3 = [1461648129215502583244578/85849, 1750209831824844856635461324047864/25153757]
Dujella (2006)
y2 + xy = x3 - 68021331721440342043360469918787419160x
+ 215696772000462640161957242587564687720033649820510137472
Torsion points:
O, [5397798570415242684, -2408904798642801210479837592],
[5397798570415242684, 2408904793245002640064594908],
[12153969825844602084, 34414235639779085451893276808],
[12153969825844602084, -34414235651933055277737878892],
[44862647114246521434, 295731644012442268294298479908],
[4981705649351651094, 683708498908759325990563638],
[4981705649351651094, -683708503890464975342214732],
[44862647114246521434, -295731644057304915408545001342],
[19557161461848170111/4, -19557161461848170111/8],
[6811307303982491184, 8269566933155439975033315408],
[6811307303982491184, -8269566939966747279015806592]
Independent points of infinite order:
P1 = [14575494010476129060367716/208849, 55273966457396443193409152850387267144/95443993]
P2 = [115214461852502044824709899062658668784/428144536145727025,
1236114877222581145470541885757040423676040744716987207008/280146763241397326508403625]
P3 = [122582728908014079548120915450201911208467381591956/22875432112504881491630254041889,
246343789943043497877590498307098657481233211911099328958717489404170465736/109409229562905869044923830471149407860894335537]
Rathbun (2006)
y2 + xy + y = x3 - 13184052888052858947123730529816438x
+ 582635712328002480125681053265241197284010770898156
Torsion points:
O, [53979397709044437, 5315290931961551202588139],
[53979397709044437, -5315290985940948911632577],
[123808259217644820, 29122742346244012205204692],
[-61547579122669185, 34072475570847678719338447],
[-61547579122669185, -34072475509300099596669263],
[69530250649753530, -1444344478243259976486968],
[69530250649753530, 1444344408713009326733437],
[65436531121523835, 335111065962187380066337],
[123808259217644820, -29122742470052271422849513],
[65436531121523835, -335111131398718501590173],
[266791424900454999/4, -266791424900455003/8]
Independent points of infinite order:
P1 = [90384746400968192361360328555/1336007716164, 897577688726615740032241908568123624889119/1544235206789888712]
P2 = [5194037464987746565160308795312282211469/14136612543324455251600,
357890888974640615009464252738899134950792285088850637338473/1680807713727727128454398565064000]
P3 = [25315097007289109238836003792386778850464435119191808966978179/67305120162324746814009074154208405738502884,
122020568131660973354622647108007440276222360507901519912064475576554751681846368867852894163/
552169171896806235106910575539974491358724841536453411402404130152]
Rathbun (2006)
y2 + xy = x3 - 274487462300394921534982610x
+ 8088165170962729493476703355273008384772
Torsion points:
O, [786763298884, -88728211878456903842],
[786763298884, 88728211091693604958],
[36027584329684, 212043314932521334558],
[36027584329684, -212043350960105664242],
[-15338133382856, -93219447101428582562],
[141872093555524, -1680685557543462583202],
[141872093555524, 1680685415671369027678],
[-15338133382856, 93219462439561965418],
[-24569859508412, 12284929754206],
[14628948209284, -84872775799733012642],
[14628948209284, 84872761170784803358]
Independent points of infinite order:
P1 = [-24311216384816, -19811691453480548942]
P2 = [-15070131646150604/1369, -5008197199111335645906026/50653]
P3 = [705215952375034860586312/1155388081, 592012483604921369994927537680303830/39272796261271]
Rathbun (2006)
y2 + xy = x3 - 1819834111904825898485099130x
+ 36464739063950913898627050323570640110052
Torsion points:
O, [-50427617434732, 25213808717366],
[-22719911828376, -257066747522485830282],
[159225241270164, -1945118944501345030602],
[25789176571092, -81759558919294827210],
[25789176571092, 81759533130118256118],
[9991040992404, -138852504279657705162],
[9991040992404, 138852494288616712758],
[45718173282084, -220959635075228459802],
[45718173282084, 220959589357055177718],
[-22719911828376, 257066770242397658658],
[159225241270164, 1945118785276103760438]
Independent points of infinite order:
P1 = [66213461028264, 454160472058754746998]
P2 = [1587940304415908270265812/29276236609, 1562767158626484667223838196910026442/5009251912509727]
P3 = [869862688746765817528419089891604/39023947629422672401,
20359774603347126439674023407668725020624896107142/243779285717628367403603862649]
Rathbun (2006)
y2 + xy = x3 - 150145048140178517153801000309900x
+ 708132674328288274802558689001094787606855866000
Torsion points:
O, [7082834741308312, -1216538809755432014348],
[7082834741308312, 1216531726920690706036],
[28297949778977599/4, -28297949778977599/8],
[11381181412749820, -688130630876604282809120],
[7256110518318760, -26572563560271495844700],
[7074503623595380, -2588620594751750300],
[7074871081903240, 56124911416713372100],
[7074871081903240, -56131986287795275340],
[7074503623595380, 2581546091128154920],
[11381181412749820, 688130619495422870059300],
[7256110518318760, 26572556304160977525940]
Independent points of infinite order:
P1 = [7074516502890160, 4462478656126774300]
P2 = [241373074549563134920630/34093921, 149827776692939276135994687998800/199074404719]
P3 = [185127187288289383833767110072395720581670647104/5726989937074837140728970316225,
74605920777708357689413270978804458760917255522432802195712214187768972/13705334196483916923894064983118061390055486625]
Rathbun (2006)
y2 + xy = x3 - 221258093304676096682976578348180x
+ 1260872658744531513722247229469983431998017036752
Torsion points:
O, [10484318546361844, 305905910085201245235328],
[10484318546361844, -305905920569519791597172],
[36247706201346751/4, -36247706201346751/8],
[26706461373753244, -3794711731899254068846472],
[26706461373753244, 3794711705192792695093228],
[101213837792233054, 31870447620971059946514088],
[9334275162190594, 94190903210316884539078],
[101213837792233054, -31870447722184897738747142],
[9334275162190594, -94190912544592046729672],
[14071661583890344, -966310884792522268864172],
[14071661583890344, 966310870720860684973828]
Independent points of infinite order:
P1 = [24812545935418208256643426/8567329, 123595106267800227822896225069654031674/25076571983]
P2 = [29144405764786543092556/3115225, 542507884099447715383123143294076/5498372125]
P3 = [140432675602539967608523423127924884107710649546604/21475240824540111420624097394641,
1664183197655907429586124470053790662755438999627957236843578958769830563892/99519243052963578656297728506926773490173758439]
Rathbun (2006)
y2 + xy + y = x3 - 249330946882044475428580013580758x
+ 1515347918712754017203406150167416224963014315468
Torsion points:
O, [36474550258924631/4, -36474550258924635/8],
[9166770807016314, 8315975397421588093405],
[9166770807016314, -8315984564192395109720],
[11564062455012564, 422496037839337988617780],
[11564062455012564, -422496049403400443630345],
[-3068234222216961, 1500489627529603740929455],
[9108979119906939, 1189176435952227155905],
[-3068234222216961, -1500489624461369518712495],
[9108979119906939, -1189185544931347062845],
[8775554151063189, 56028516985571334062155],
[8775554151063189, -56028525761125485125345]
Independent points of infinite order:
P1 = [13850973513067094880333256/1518894729, 14766129258045746197572248327496535/59195884273317]
P2 = [897892028562265414636152006121764/236395268272801,
26904964721442238150016645680365679506114767876905/3634612945379824567951]
P3 = [59453180149118915360908445178129422207469391305162294984132371722104603515166/
5907756461074999256518274331398892773912765529096427171280569,
2287666364227365889778911431207730336413488628456129703792796466736929125480102481276521215153410551854548653154160/
14359320059678889418929274438350373394687949046650197762118412205574875618000819299460589997
Rathbun (2006)
y2 + xy = x3 - 10765597468846463769989866234784015x
+ 429437215963429112259250987840325055982837272783225
Torsion points:
O, [68097051604636630, -3480228737042640103223315],
[68097051604636630, 3480228668945588498586685],
[57067358514616870, 960898086922221848221885],
[-72991692045129620, -28746342256925421850463315],
[154219902306234730, 49366990786347688591395685],
[57067358514616870, -960898143989580362838755],
[154219902306234730, -49366990940567590897630415],
[-72991692045129620, 28746342329917113895592935],
[36964138025185630, -9055497949558676131607315],
[36964138025185630, 9055497912594538106421685],
[61565163040626630, -30782581520313315]
Independent points of infinite order:
P1 = [94372790619160218130, 916790139697417651285082721685]
P2 = [10648645639246599670/9, -34619591821050285851318539505/27]
P3 = [4546031826492198756747368898798898334706344174817297519000203419829599630/70818683820343903784092432918799831168232410478868871161,
1011957335675187385707159185359301343009045695852945654195309501369414728345507611214483818890116562286982865/
595966401693780501925131493150107551091702167893929403777190749386213815374779440909]
Rathbun (2006)
y2 + xy + y = x3 - 61702104237947860196526986986138x
+ 204569139954311721919470430471356240484023032156
Torsion points:
O, [-36664925471796201/4, 36664925471796197/8],
[4630771503485437, 134696935813762974477989],
[4630771503485437, -134696940444534477963427],
[7377549708790480, -388466016091992670753213],
[2340043246746670, -270179870962407153178408],
[2340043246746670, 270179868622363906431737],
[7377549708790480, 388466008714442961962732],
[24268295411897665, 3605548596039884607633137],
[-3472796868702215, 613974740175437840622677],
[-3472796868702215, -613974736702640971920463],
[24268295411897665, -3605548620308180019530803]
Independent points of infinite order:
P1 = [14837027629273610958329984365/3459882725776, 883155905568210285846047924474241896445197/6435644821030518976]
P2 = [4269637765854485728596484028232461755/4632366379366468213636,
121490000222007875500659091163391347733182174233226786813/315285756588082970571565204267384]
P3 = [840746203605374249833509925004111262456129774510843874386746815/127606696913527282784725094294116459150838459044,
13215024800932961757818470966224071473012694600302724477953654733613453053875580054760026254211/45583765813990618407179007470042704633528503454274780571288043740291928]
Dujella (2008)
y2 + xy = x3 - 292332123376858729855216713444859791000x
+ 1923979295088130189073975409299432487933245589378532386432
Torsion points:
O, [-78971755725786958209/4, 78971755725786958209/8],
[9871564096219405104, -407413119820039176032979552],
[9871564096219405104, 407413109948475079813574448],
[10423672313866491204, 3060673722460618997353431048],
[9329560543014560604, 2949666254354597189664885948],
[9329560543014560604, -2949666263684157732679446552],
[10423672313866491204, -3060673732884291311219922252],
[19162439848787064354, 57953543882527460605198470948],
[2799414261660425934, -33579142427636263799630098572],
[19162439848787064354, -57953543901689900453985535302],
[2799414261660425934, 33579142424836849537969672638]
Independent points of infinite order:
P1 = [-1438470646479082146, -48389192938308576738358286802]
P2 = [1036559959859347576076718/94249, 181139348712386839661998776480173274/28934443]
P3 = [58289041757225251071834/121, 14064049905234837185009050342018038/1331]
Rathbun (2008)
y2 + xy = x3 - 368311005290957023970056723656617839660x
+ 2991562337028224568521291841920383470993353523990000259472
Torsion points:
O, [59685776674626585584,-440037229730719095662656610692],
[18103852358159279384,-47510444065389638604722392492],
[11320983430493874392,-16518765308696523104230952812],
[5673932603201888984,-32931054172385799244836477292],
[-8548063524205522216,-74265109026858198282241149292],
[-22402026950123580712,11201013475061790356],
[-8548063524205522216,74265109035406261806446671508],
[5673932603201888984,32931054166711866641634588308],
[11320983430493874392,16518765297375539673737078420],
[18103852358159279384,47510444047285786246563113108],
[59685776674626585584,440037229671033318988030025108]
Independent points of infinite order:
P1 = [1842132250373886199664/361, -242016517684164998225477178454948/6859]
P2 = [1727109742067019170965656437766104/97967256461281,
43121574886037672349315733581934292875199747782868/969664327659981994321]
P3 = [-5654980629927202782240300668518663803137619973470563361396380015348172676/252436462222937221627904940270941227852536946033127761,
88385759528923787425052701214259971773591004010805574311212479827154127495959789244636813493381383917985728/126831791722783852257171825056831531130787673575626583906410881414337315938097241]
Rathbun (2008)
y2 + xy = x3 - 9090762577164435886370784189944067660x
+ 1847477618017380107957106443783943446041451396851347600
Torsion points:
O, [-2796063365467823700,2325142008637115476142526960],
[15131950288560817320,-57698689263939708417255592860],
[-1126468607301583080,3264739615277469808419999540],
[4239241887531056520,-6284399758128496512240872460],
[54415792913299140,1163167096150244555453599140],
[11631278160428664639/4,-11631278160428664639/8],
[54415792913299140,-1163167096204660348366898280],
[4239241887531056520,6284399753889254624709815940],
[-1126468607301583080,-3264739614151001201118416460],
[15131950288560817320,57698689248807758128694775540],
[-2796063365467823700,-2325142005841052110674703260]
Independent points of infinite order:
P1 = [3233394754750284602539231412980851/1057380912551236,
55898280306505659542684414056703761587033672038523/34383271741508086198984]
P2 = [9320898499370061213308676792805266008556180/41166973418263232929,
-28456839737855855191746278891052550755755763666857504780680574820/264133452744245979619517949967]
P3 = [4101061374663135257281095912041049377305193059418157104938982253463649094577489215597534861505521606930/561329073026319373667761312445085827744400087077824340534934972874721857114000824169,
7586446753162858256817344591526103760333120624583806051019990217685744149950297048336744159395840097291217569431386910935945757069371272590265573528506880/
420558392927624415526322250131428099798565560176522077581533284789908024257362592858988219650503524917918714848496184448070197]
Rathbun (2008)
y2 + xy = x3 - 1058306588646713747729837253600796x
- 13170172426202006495584011810752117863858516970224
Torsion points:
O, [821667422062777136,-744214768962946672198993108],
[206428861336619768,-92546701963833513398819740],
[93833778603815096,-26715361014174850176264028],
[56303153242702520,-10282381202784202739255644],
[41580251764060856,-3835882098767147912427868],
[37538642190267064,-18769321095133532],
[41580251764060856,3835882057186896148367012],
[56303153242702520,10282381146481049496553124],
[93833778603815096,26715360920341071572448932],
[206428861336619768,92546701757404652062199972],
[821667422062777136,744214768141279250136215972]
Independent points of infinite order:
P1 = [-18680313608576410,-284172846931785713733664]
P2 = [58841592758060754488,451363632031397800846670161700]
P3 = [-55503893022197003547016/3108169,1009606773504356300135374170123724/5479701947]
Rathbun (2008)
y2 + xy = x3 - 4371082356409721600147888899873485x
+ 111227694692608628418999682284467162597490459882897
Torsion points:
O, [236712391063556964,-111086389963671466705907187],
[69650325919767174,-12027710096340209890447197],
[45221507272965642,-2457245128788936205642137],
[39873862421246994,-576372363903853864659057],
[38611472286494754,-132364714003168245978657],
[38375144063182338,-19187572031591169],
[38611472286494754,132364675391695959483903],
[39873862421246994,576372324029991443412063],
[45221507272965642,2457245083567428932676495],
[69650325919767174,12027710026689883970680023],
[236712391063556964,111086389726959075642350223]
Independent points of infinite order:
P1 = [6732240019578911907880309698/349802209,-552378577916643534931931569463285500150575/6542350714927]
P2 = [492357291398103046277993953609/10898555279616,87827471433844296220522431153029482340704333/35979356950375182336]
P3 = [136459941931643043236707533293646/3972432099636289,317676823805284769469548713851099021532608794631/250371403520455602058337]
Rathbun (2008)
y2 + xy + y = x3 - 505211981698889389232955545175666638x
+ 386585666729481477236523047724751075048363702079574656
Torsion points:
O, [4817703385491914085,-10477251590858835083893361123],
[1246948804321415880,-1302101991176955414452970713],
[537815793813490437,-520034286043922438566743011],
[57147019388979270,-598248224023485501329215508],
[-568485343007692635,-700050490769618295468863363],
[-3816552197658204201/4,3816552197658204197/8],
[-568485343007692635,700050491338103638476555997],
[57147019388979270,598248223966338481940236237],
[537815793813490437,520034285506106644753252573],
[1246948804321415880,1302101989930006610131554832],
[4817703385491914085,10477251586041131698401447037]
Independent points of infinite order:
P1 = [196437447720411062438805/10609,87002042180779598578627346987318299/1092727]
P2 = [31791567568065619689106845/62047129,-250283999712728109650651473478638449079/488745235133]
P3 = [21379097466829763017273454232764674936338262317280770485705214765/61511836689006481985859085436918625244818519721,
-7673260763873868950436647868224420152278026444143566481852827964017229759530720681724668536528543/15255907341171888793008182612121455946095393743626492115662709580440981]
Rathbun (2008)
y2 + xy = x3 - 4647108016146476298277842278575045x
+ 421469301005236093566733738544111617060167084070337
Torsion points:
O, [512083936134724124,-363765733690199277736848547],
[131298846925677014,-45550203561772553181543157],
[54982873080113114,-18225739309083261305731057],
[4375221579971714,-20030499913250473386089257],
[-58086329717976046,-22257992075327793686978137],
[-95247552553159822,47623776276579911],
[-58086329717976046,22257992133414123404954183],
[4375221579971714,20030499908875251806117543],
[54982873080113114,18225739254100388225617943],
[131298846925677014,45550203430473706255866143],
[512083936134724124,363765733178115341602124423]
Independent points of infinite order:
P1 = [4375736146837571563681639/62821476,-10393523243286419271593448523700282857/497923018776]
P2 = [11236494820328624159766536315228/147297375111769,40406973345348941657752490382194712275896019275/1787691237647372098397]
P3 = [-2649592192002096425676292854397414/103609691210775649,763122433469314877934518042086748532477911822076551/33350363286236196992675857]
Rathbun (2008)
y2 + xy + y = x3 - 914867461880639031040087262777378x
+ 36673403428876500284328254193985931160171307304756
Torsion points:
O, [226799390465034165,-107216047385966418996299663],
[58160364135270000,-13423831538216673275870453],
[24366953334857037,-5371099582503477499404047],
[1949174137883310,-5907416770642623321904208],
[-25743781969686555,-6569935935470405126708903],
[-168916770144180841/4,168916770144180837/8],
[-25743781969686555,6569935961214187096395457],
[1949174137883310,5907416768693449184020897],
[24366953334857037,5371099558136524164547009],
[58160364135270000,13423831480056309140600452],
[226799390465034165,107216047159167028531265497]
Independent points of infinite order:
P1 = [-31925917259037660,-5774118274689204200068628]
P2 = [25666303548967766925,130030337038093299679964401297]
P3 = [-6632980089664631155175090390754568726383783799426772393718/340281037264400410690211878080067907977921,
-1362283629585272741387888219829073481811328648189374867349640976432679280378758204451971/198498222427995040221298557128488943204977453165955020798581281]
Rathbun (2008)
y2 + xy = x3 - 536789595575465409343981144743134382750x
- 3308857398920275841720234966526320716565319402012239563068
Torsion points:
O, [-18100906571250061776,21837785358308446322341913118],
[140544719754628141164,-1642377089767260523038444713022],
[-12400770078809460708,37957446080641525019745967698],
[38498937896503879644,-181898915681490978175938660462],
[-7440923774649550116,16533870058145802376147720338],
[25789390162135049948,-12894695081067524974],
[-7440923774649550116,-16533870050704878601498170222],
[38498937896503879644,181898915642992040279434780818],
[-12400770078809460708,-37957446068240754940936506990],
[140544719754628141164,1642377089626715803283816571858],
[-18100906571250061776,-21837785340207539751091851342]
Independent points of infinite order:
P1 = [-7892254437769069476,20881390023246450262124663058]
P2 = [-130827060730220023043788284903276/8399858859001,-868763061070974073114159269328595930579599263882/24344899337958507251]
P3 = [-2335585900726377151833169622413980117874115442272438111478584607349429284/171002208062898159083678205771392024692121552398104769,
-2715651617995185321906555341608512946406954538435968711958541989397217149194289324678126957994476277033573166/70713539724742806137665764113752139286841029647962752653338560197819613774744353]
Fisher (2008)
y2 + xy = x3 - 12795536947987624172963879072416x
+ 17617116008605697030305540872825070114057601600
Torsion points:
O, [2249113636497728, 14685639115515683360696],
[2249113636497728, -14685641364629319858424],
[2100547820966924, 2779983957698838165716],
[2100547820966924, -2779986058246659132640],
[8271519842059775/4, -8271519842059775/8],
[2072316658862618, -517618475828011551364],
[3073322155252916, 85561592919866801226944],
[9471052936530038, -863707911153253233054274],
[9471052936530038, 863707901682200296524236],
[3073322155252916, -85561595993188956479860],
[2072316658862618, 517616403511352688746]
Independent points of infinite order:
P1 = [-4453056846193608952432871122/1082455048921, 28362496278490461291315941463489067096066/1126198139902946531]
P2 = [938545985288138469667171987362308192326508738149779326/458389142937324917430556350699089703025,
13533310438158189890242433405538195699147227624080203435530511813535089981849364/9814122714951241297042916489184193382047186853733017552375]
P3 = [269877995705673238873003021751549606031668935527114473678/138196240879121180104353616815044779863601,
450135755190396232660883587209910615741464920186108762064847260325739062109847473354/51374113956379768078631023086086826955667104640890515969344599]
Fisher (2008)
y2 + xy = x3 - 37727535210879763033559556206491980x
+ 1315555487469516989897295205531431859305835856072400
Torsion points:
O, [694564567192717119/4, -694564567192717119/8],
[873837390756691980, -797247062513725881808529280],
[-55980728162080488, 57027498898250960348354892],
[-55980728162080488, -57027498842270232186274404],
[26253129169195470, -18525225850305812849160990],
[26253129169195470, 18525225824052683679965520],
[-184096249618942350, 44964077211996597534642030],
[-184096249618942350, -44964077027900347915699680],
[248943177823754340, -85739286901697244479838060],
[248943177823754340, 85739286652754066656083720],
[873837390756691980, 797247061639888491051837300]
Independent points of infinite order:
P1 = [97099036670672946032209474453407/2705321585442436, 389968439654568331862801468799724565538080992497/140711096259071303591816]
P2 = [67844611464942472915108286969229425502342160521732200517793502894016701951371397148914110/40233709034830050110240081785017396052108758286405443989961163349088009,
17556300289795015484447344895397880947518051873150200167479266435069977188896942163031935063919903975738887682570923174272749402423440/8070215023275818790351355504660151128520269470169549872591828254611723258788077463370389883280422042802277]
P3 = [8822519597689784700362868142612206102510115357603789972666171428789885264957373169079926882708572924547550/42272419670786654875939615921741539097669738884150598747472054781852964874117825827087081,
437379352273104183966515796835237864163032727044421271929076179090038335552312606323705107230258199139359305955539351333376298830687709474262934875415417755030/8691318420518690729122742459045727151670868834537246626189631774816903215935666026113519703007168482265323925468241210118674664643979]
Fisher (2008)
y2 + xy = x3 - 1206695956028807525728221574787589130x
+ 400018520601948885677238421961394551765393619793558052
Torsion points:
O, [-1037890786222404496, -731028891648012538072186042],
[861656859755737268, -430828429877868634],
[1187501081743434164, -801018658705579393618707802],
[1187501081743434164, 801018657518078311875273638],
[3994017684315901124, 7700242307366331937138432358],
[3994017684315901124, -7700242311360349621454333482],
[324338578729954484, 206783540409180024416856998],
[-1037890786222404496, 731028892685903324294590538],
[324338578729954484, -206783540733518603146811482],
[-148621159337792908, 758996898210674742004390118],
[-148621159337792908, -758996898062053582666597210]
Independent points of infinite order:
P1 = [69578463598678295975319298784/65961135241, 9292037253956862845252346411669677738586562/16940732402810789]
P2 = [8364280171116977430331944219088716947602007043881801235939572/22673639868677134207951951628861296690387801,
7688918779340202845710962397392951058847505175028896345592875906371248006212737058328459470/107964720928665642437968940219337675128557378659678330173709396701]
P3 = [77864947915988525253881932484137859932991140097766525691019153611988919546313894161051043192733923133919085844/932203604340681773883690979265299102737219972855618212681777635602260311376906094245663521,
687029815843334012492863464037911053823628246882332237319568701397905616300607004799734297807384134292426902372437318810198524704938250671312233730787004875442154822/900049026868158817106312358691851468577410294555075226649006165786943510869586914000163433817417114688103786397992375095265130833067569]
Fisher (2008)
y2 + xy + y = x3 + 242613277468856567568770964713122x
+ 2296065019486513214147768546803320753737832836756
Torsion points:
O, [-30527004632460841/4, 30527004632460837/8],
[12797251624376037, -2738001026690549463188741],
[12797251624376037, 2738001013893297838812703],
[-4978175878501245, -982305005596385060735303],
[149644418051506455, -58220759762327613424829153],
[149644418051506455, 58220759612683195373322697],
[-4978175878501245, 982305010574560939236547],
[1936626497133930, -1665286667533349529618128],
[1936626497133930, 1665286665596723032484197],
[35985272513403780, 7591135132863915293751772],
[35985272513403780, -7591135168849187807155553]
Independent points of infinite order:
P1 = [312755838914426280618924/344569, 174933401968270285691213339592215972/202262003]
P2 = [107591796003760454885667784740226513380597609584952987383718/9413455627977684203324798143268674697491849,
73985436437316046108320344665514791713490387610986593242794864981377049770963217121144581/28881757668486578792625244991058560343252536533764932612254590757]
P3 = [14035967086823536168474076780864185899368910252839658642732039925470/21645609917436184972469641382271045381155077252009,
52600587522259662827167511169972512257903475044154024133852544616257866212971706600634299533865226056/100705859736471222412852725944565854082913402976868911689709904922272959723]
Halbeisen - Hungerbühler - Voznyy - Zargar (2021)
y2 + xy + y = x3 - x2 - 108602416269007156337692601013988599572x
+ 435619519256667335772068906986097244861364762892400124919
Torsion points:
O, [6017592241382147877, -3008796120691073939],
[6196009958049272877, 765526615963850790406176061],
[6196009958049272877, -765526622159860748455448939],
[6040855354388397877, -102580636022014118884823939],
[6040855354388397877, 102580629981158764496426061],
[7385976670936270377, 6034005029746178832674601061],
[19068403406870429127, -72787998670484099194616855189],
[7385976670936270377, -6034005037132155503610871439],
[6020031391042430277, -13603818125813460626261939],
[19068403406870429127, 72787998651415695787746426061],
[6020031391042430277, 13603812105782069583831661]
Independent points of infinite order:
P1 = [-2410801806210286291882779067389272445789862523/698035671800487622592194801,
-511589582396104013855213463201860132095896396019889252127571488759739/18442357034724907351722031136590706432201]
P2 = [27782113652483303841730771741634631292883413101210166914121/4613297459274613617958072161099792360000,
7188833721249957166089165179535454223836813817144302096682423561639654187467426013631/313340972768454032230396765563848928884603970631146984000000]
P3 = [2576151184143104562364507270677998676607850920856589686206090353/289088844631979513445722498179468043573003089,
65113013010479123558643434104215875094035815186354956977913634404639510208114957751233524501407/4915265712224983044648549266014311485799135455155234355929514603687]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 136758485462712161965680997660998722951250100x
+ 615572964076973829651047790525744953455537112061436953925691122832
Torsion points:
O, [6751753818754817487848, -3375876909377408743924],
[10734764531835170204744, -620100988435535137876853957878612],
[6751767231849199858664, -2088241064298660345405520372],
[10734764531835170204744, 620100988424800373345018787673868],
[6759063025183735804904, -1040628740781325842733668350452],
[6759063025183735804904, 1040628734022262817549932545548],
[6752080318104463766504, -46655396558841343465380657652],
[6752080318104463766504, 46655389806761025360916891148],
[6915382011822949603304, 23381785263972837197816682292748],
[6915382011822949603304, -23381785270888219209639631896052],
[6751767231849199858664, 2088234312531428496205661708]
Independent points of infinite order:
P1 = [6928748740798103585917961/1024, 68129937568623659682379973880305419/32768]
P2 = [140777862406874007613279015950711464/18345553815241, 10542069914448866849992789516815518405611151479948228/78577144080379609211]
P3 = [491883958490833139535448985018011519177994892854696/233631013647535689565720729,
10909059332373040590168077617594826059720648612328007234980283479978043777244/3571048428342470446730651071381584335933]
AttarBashi - Voznyy (2021)
y2 + xy + y = x3 - 7519252981341224622470545841330915534x
+ 7936151311157164734917847096649413205684161510782408996
Torsion points:
O, [6336340081135122135/4, -6336340081135122139/8],
[1677482413829700933, 207566116272697585311679543],
[1677482413829700933, -207566117950179999141380477],
[1599085611439867434, -34692483020463561803192768],
[1599085611439867434, 34692481421377950363325333],
[2165600310608316036, 1344894254140686987354080236],
[6272515791181728543, -14406950737331285983316616377],
[2165600310608316036, -1344894256306287297962396273],
[1585945573109966523, -5717242705045444996362167],
[6272515791181728543, 14406950731058770192134887833],
[1585945573109966523, 5717241119099871886395643]
Independent points of infinite order:
P1 = [5112031451849495544472016061909/3222028590001, 41551977453862604659294614755208007961496683/5783544541080385001]
P2 = [392339143687142372205331997910254859/18148600305661081, 243861695839062096704280302243388154166696382262502773/2444920286890264682857021]
P3 = [57486634474567384885722055381904901952856237155468491/3164906964870711335456904004036225,
13634466237529675290099188423378347627449429548518718915633768620687416475715381/178049772102394268421010623851552098007689725005375]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 107228048655855252978382765773252299824120x
+ 13506146313796641511551400346692686149883254675408293650190400
Torsion points:
O, [192957743065353990640, -96478871532676995320],
[126099511180489990640, 1410624349677464134834043004680],
[126099511180489990640, -1410624349803563646014532995320],
[210158338034953990640, -503231297058082572294276995320],
[210158338034953990640, 503231296847924234259323004680],
[452833821693475750640, 7603096074428240289263598204680],
[452833821693475750640, -7603096074881074110957073955320],
[182126291636056742240, -135003761804657046804978338920],
[-219731470374646009360, -5143779353627129485292676995320],
[182126291636056742240, 135003761622530755168921596680],
[-219731470374646009360, 5143779353846860955667323004680]
Independent points of infinite order:
P1 = [138949500563500610032, 1135585959306005961891070715656]
P2 = [9953659437263857359075953471005328983666831856/2193558280581762359499025,
990539816722177953127154523454792601403892596358606626932460509689544/3248805909666970967755431393090213625]
P3 = [236786669666871724309255141890673230877762232347609672640240/1280082793180034813648797597649258042161,
1198225505063644384609194572192116626581006102819153464484127530826757618266942348341320/45799115399330188097954346664800067660913145304433842714409]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 6591748957864447564450856465047169650x
+ 6514020220123681844736738727062161271938118115517446532
Torsion points:
O, [1482327416491580548, -741163708245790274],
[1470719178754372292, 24415315624861839239108798],
[1470719178754372292, -24415317095581017993481090],
[1483319322793348484, -2123659132332961949453122],
[1483319322793348484, 2123657649013639156104638],
[1618178134571877524, 290854605937539520837448318],
[1618178134571877524, -290854607555717655409325842],
[175884993197760644, -2315182842789212627868668482],
[1482224272884973064, -182784386295611047899142],
[1482224272884973064, 182782904071338162926078],
[175884993197760644, 2315182842613327634670907838]
Independent points of infinite order:
P1 = [17330161235554600219403061741435779624/11687258081871566401, 43204393031483470990348090658550496585501888900288958/39954799125084169263326709601]
P2 = [142052443940430357861895528438741858547709346468531784/52080356014481345084018624559991561,
35310776020894038283399233485467704511151526712903020162703165287016014697598558/11885321022767222356096059317109245108048266494177691]
P3 = [9899403921442103034843276701423236627039873270060638173381554100730078872804729993738328153711157450908369361531765907488515917105821287715600744/
6256603562226931755643648463347732475459930809724620148796052376542798184493525015734449090824953129255119272835435269268509081,
3334408061172533590960965115075594706448015289191264761684718040913775283398041824657828489218235616898296117541467477729496505922061906079628381020156593282909687801959064447413883766353605239323201607698083945835782/
15649769898254715911871246707802692068593190539742915001736781924642861711105902197720516493151711032124737180235898058530296246049828991962177112113825813166599919706588358698921391128247229]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 71199928138191294119578998748397377070x
+ 231242388479932542711508129150401140150629088302571431812
Torsion points:
O, [4871718166932524028, -2435859083466262014],
[4903111731080005564, 120274398525285723205265218],
[4903111731080005564, -120274403428397454285270782],
[4874236506042023164, -9756421396653172525705982],
[4874236506042023164, 9756416522416666483682818],
[5263069699442397964, 1516153837500728898033540418],
[5263069699442397964, -1516153842763798597475938382],
[10501432853674846204, -25330615966530331107428959742],
[10501432853674846204, 25330615956028898253754113538],
[4871893230132832024, 787685562949195328656678],
[4871893230132832024, -787690434842425461488702]
Independent points of infinite order:
P1 = [4865123588985302764, 25075970610403687983386818]
P2 = [36322736843040157893856/5329, 3078005048331897128301396029643406/389017]
P3 = [130652965701916849687115005494025216422338608696447982695633117973769483065550731985348968503025666716/
14144136758108255484648810149284557567400485076988113142728470366347502261119413849,
31993420185781308575013578741812522620631084552989430294798409853392046026750134217543695268587504778831545605665960971515805717001768332566769266203834/
1682149807620825133908958866542267009385301770601799199369467702560782952916028276794611810514576175180081198833787619846493]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 576474958964749469059294022819042482637100x
+ 168468529143571779114041971086165090298387775566071563833410000
Torsion points:
O, [1753445414032100526399/4, -1753445414032100526399/8],
[435702447076075524312, -96227666165568571792026648564],
[435702447076075524312, 96227665729866124715951124252],
[438570494655514037700, -7681766487598175257587233100],
[438570494655514037700, 7681766049027680602073195400],
[472165239059709830700, -1241618643370938063509886129600],
[472165239059709830700, 1241618642898772824450176298900],
[78883541939917690950, 11112380676900714062937919288650],
[78883541939917690950, -11112380676979597604877836979600],
[438341686693589427450, -607951869257264543155097850],
[438341686693589427450, 607951430915577849565670400]
Independent points of infinite order:
P1 = [3237237817798324708847347529409532276766988/7384832699396521180249, 79842210469144092197000247666742329715166114996915090322048/634615962146585956768967649537443]
P2 = [24427689590137207230060518873144154734261698200/3130884372393985285599481,
3800451141173889204233515804153137190722542358334302692947182544712100/5539882369551453951529853880609451379]
P3 = [26354558969383468162302301143025422978784019628779532876090/48405856297921352331723910843673253529,
1346940922977026390056370376797520128162053854097450027353496135386763958234301252857250/336780440595633015101643210220284805331355237459645865667]
AttarBashi - Voznyy (2021)
y2 + xy + y = x3 - x2 - 221055242947662733823007608080261831130543x
+ 40003624610870921619088966861375087499199719739023391948458807
Torsion points:
O, [271454054238743043891, -135727027119371521946],
[274036251033841573683, 73921513896962560475691544678],
[274036251033841573683, -73921514170998811509533118362],
[271688992454527557427, -6821215589934823016183828378],
[271688992454527557427, 6821215318245830561656270950],
[299834878815757803315, 824011191720726955681324527718],
[637547832851132981043, -12578260650704799331499486941082],
[299834878815757803315, -824011192020561834497082331034],
[271472267441693091123, -625769890284812973395738522],
[637547832851132981043, 12578260650067251498648353960038],
[271472267441693091123, 625769618812545531702647398]
Independent points of infinite order:
P1 = [22545178219521146976307875/108241, 61648865359069826782570040300297566454/35611289]
P2 = [620221545501004740541206720908077363/2630491665845761, 134282191094437994180904089989469715351194718162645402/134913495684738794965759]
P3 = [15668612913145540542673022005066319979640838259091552058418439193947/44184539389753240542257727726265353013837540921,
23140942544968555345316387305503200507902319471945850815178546751180148949976279155054000535853000850/9287642666034111685627279581302972016835459726152984276513483563264531]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 9045135584417178890689102424113498977106700x
+ 10527975287210294929598449696926655748632274539165707271266329232
Torsion points:
O, [-3474890531035534075752, 1737445265517767037876],
[1738501553166849136792, -7577509454880088156430666558540],
[1738501553166849136792, 7577509453141586603263817421748],
[1373228065217725847704, -26391539882115273796232618699852],
[1373228065217725847704, 26391539880742045731014892852148],
[2131295968739655575704, 30518208589352840744559815988148],
[-458789906202344040296, 120752732234808679466970963252148],
[2131295968739655575704, -30518208591484136713299471563852],
[5536565121286168463704, 360783019790800689171056032500148],
[-458789906202344040296, -120752732234349889560768619211852],
[5536565121286168463704, -360783019796337254292342200963852]
Independent points of infinite order:
P1 = [2026361354306165702152493089925848/1346057078809, 28066936676904995879760195661575266520605884898020/1561691384662965373]
P2 = [16570349936391060998257684893353307941047585211717720668/2656593063207220857068192026894489,
60740700366190343435583378825743090410460232512844395610196365609273407498792726804/136926513941398837851322621712946452465491787902013]
P3 = [7345181718859525521555808103963939338142092454470290733412530379663571489164940713349116192269144/
3364991085202189459455396320380759632539213056212919829023573874883654458161,
6718280445922273575168870450464413267303392938093940317156853400048885893092739098071340082902521048294739069535124248887738497686774607615843732/
195198230763032200981905802377682651453117831475043876734236966994774863046027392278300136352257458062075330970409]
AttarBashi - Voznyy (2021)
y2 + xy + y = x3 - 64593234737960731051261863124601622013472078x
+ 180048942933640763515855536831216626365878970592847201582978528548
Torsion points:
O, [23142323953229269741271/4, -23142323953229269741275/8],
[11771030627125482017349, 1025027119795653342178406333335075],
[11771030627125482017349, -1025027119807424372805531815352425],
[96909174339856125502299, 30067125499155245424888360326478025],
[7680844807080215970474, -370206247946354246615702380836800],
[7680844807080215970474, 370206247938673401808622164866325],
[24688283094457389086724, 3692308349557537205774121331710700],
[24688283094457389086724, -3692308349582225488868578720797425],
[96909174339856125502299, -30067125499252154599228216451980325],
[6178735011992661673599, -129725035374109775114980383571175],
[6178735011992661673599, 129725035367931040102987721897575]
Independent points of infinite order:
P1 = [266902039319806887599, 403519380049877224549854105271575]
P2 = [10933443327351663202391406/1369, 21103555011624322528657243265390194600/50653]
P3 = [451636621510786529666117311879669294659435313280180102879929742229211117971373437824655207011/
3222934222996507400152274355342856624559917845155725639832989382828689,
9582581601481524639850944393557771082269508670213480568222106334816859998343207486243817954965571872181560078997590126483906671876488315525/
182968851960582647293517719370910719274664230902898589938309300285020866032589682279928322941685012977863]
AttarBashi - Voznyy (2021)
y2 + xy = x3 + 67480978902898780681743972945281211384844x
+ 40006536200525099920202958021898188678202358391628270833317520
Torsion points:
O, [-190244449537726112732, -4503681444529336278907361913284],
[3149786507997518277868, -177488246149374008268974229588584],
[-1108810807962714100545/4, 1108810807962714100545/8],
[3149786507997518277868, 177488246146224221760976711310716],
[268695633668716542568, -8805537551158564696160392628084],
[268695633668716542568, 8805537550889869062491676085516],
[9410551658959612504, -6375139435551400999107817364660],
[9410551658959612504, 6375139435541990447448857752156],
[762543328874959392376, 23127073991903554415525112849484],
[762543328874959392376, -23127073992666097744400072241860],
[-190244449537726112732, 4503681444719580728445088026016]
Independent points of infinite order:
P1 = [-1800633578030491067810687641677982622961058157574680/6560029172903843732505559509361,
-15061757473796574704070757603110195140454987618316930473287602325279757841940/16801910077785007639914922278069557510591861641]
P2 = [8042543025538381237791824044888436485971956360776/5054395419804505468484265409,
23221592851035418054954585051220491146496685345302878052889541435122852332/359338559521932766166840865808932682620577]
P3 = [283196442825614512621601834723973983819047296801102268/913001941179111165098689573092801,
262848643424118431919477190529834963725199693122542585974762107265882336530722616/27587195423429917528077179033749328319215766297951]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 3580475213627851258501736213342341810x
+ 7967547480000919668516974521594904510435867601399933572
Torsion points:
O, [-2581930149489359612, 1290965074744679806],
[1470058828395277892, -2425065497676738844203820930],
[1470058828395277892, 2425065496206680015808543038],
[138374288542328324, -2733999137518797200342192002],
[138374288542328324, 2733999137380422911799863678],
[3453649709645265044, 6065964490402597933188397118],
[-1554615100283312296, 3126750844489802629004068778],
[3453649709645265044, -6065964493856247642833662162],
[-1554615100283312296, -3126750842935187528720756482],
[13400133667825096964, -48643239063380242134081004162],
[13400133667825096964, 48643239049980108466255907198]
Independent points of infinite order:
P1 = [610888363152126620261295236/93064609, 14678291638086383585417839694232851223394/897794283023]
P2 = [-48167440972953697890811784618211884664134103316336133720216647244/19999003865915668122757490805497261549226993849,
-4577720173393938699142985405314682567082652460477839259844793269443675904363868103539400079028966/2828215815427599248319292240079885062010173255048765808747936430780243]
P3 = [12704876276212452778085618674117644090472642015407803123568173225107520618177684/3470937014576614921897384113830705550022286811990453503366881,
42847196994125868310600049300932986232075290983100151993950859546599475343554978835586868241886107199933448466946556402/
6466512169416449877165064925369971287395935589874274322443217386343540103706312454958431279]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 289657588849899919843697062256150341x
+ 74314849107417746343194036230358648195157490236003521
Torsion points:
O, [-637379028549813646, 318689514274906823],
[-291417179195065684, 366029701290367957851996077],
[-291417179195065684, -366029700998950778656930393],
[326518522674076826, 120614425806744723145539407],
[326518522674076826, -120614426133263245819616233],
[122629492758611330, -201589650849116558786150569],
[122629492758611330, 201589650726487066027539239],
[585105276831241238, 324259764309909643713435167],
[2048172835010490386, -2841329898701633879475556153],
[585105276831241238, -324259764895014920544676405],
[2048172835010490386, 2841329896653461044465065767]
Independent points of infinite order:
P1 = [2193734956782176940430380564633306378848553030266/8298165710031526663796614972681,
3043981978901644888819634480830686778160024660663231832265532880508714163/23904141713625155164692474235527766233632745829]
P2 = [77889646338915910462476661094440849775736690172719913534792237346/113589321010435245060068101562355991652798411761,
17039879390769651448585578638196670552717115260605294826813632087719524617665708770313928880939873/38283025730268137157153277937372110770247658761170746939614083486296759]
P3 = [2411202132760745831745631558384195738089679654275384449699851783154/69926810102019546394111427670915390613650696601,
3743673070609307717516604302789645903721487255963246711967161243617305349229723147115269692746704763/18491220430990256043154189218812642774157730670352202023777988439379901]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 28334079636969549517161253711039163140x
+ 58051277161191659846604728917542849755283879594840323600
Torsion points:
O, [12292914869450496959/4, -12292914869450496959/8],
[3062065801192907912, -33853944931977482866525828],
[3062065801192907912, 33853941869911681673617916],
[3073971516656748920, -2275949627037275189616580],
[3073971516656748920, 2275946553065758532867660],
[3240986950842041240, 514013722002954387069943100],
[898865683253474660, 5771394319107688650341066480],
[898865683253474660, -5771394320006554333594541140],
[3240986950842041240, -514013725243941337911984340],
[3073171408304542700, -152116508686708135116760],
[3073171408304542700, 152113435515299830574060]
Independent points of infinite order:
P1 = [479674616042159070896794120434670517080916090/156082339419733782763614841,
2563401153118163074213416043913029651916614952659041774540490/1949982207572988822718012461869703577139]
P2 = [202539503207161631325004035164743102553585035347667895432812760/71488085658713771844098637199571482390147129,
434754961115021223482966117196202325291204646305050541422293104310368256219380583902591987780/604436248229033661789958221899312204050080658960663753552250628883]
P3 = [136331194731180724801980290023454612369373904440146846812013402862891968/4524628196946106928266848079902687653779487306015449,
49600148598141765402794306211582600454431139876435999589431465919067691624856671507496996092430136089752204/
304350729096887009812938139991364106359965758441619226548334711489616579476707]
AttarBashi - Voznyy (2021)
y2 + xy = x3 + 752739387948905055833055282840072008935x
- 35160249719461013974668850956156357016840327604093531672775
Torsion points:
O, [25270670113185344730, -12635335056592672365],
[76928773948471653730, -691385812921576859304224487365],
[76928773948471653730, 691385812844648085355752833635],
[701995858053440525980, 18612779056400504410230808427635],
[174856609778770292830, -2332953712139427246206973359465],
[43110312647925354730, -278228424204644895392694582365],
[43110312647925354730, 278228424161534582744769227635],
[174856609778770292830, 2332953711964570636428203066635],
[29214013348242846970, -108458466888668188743318785165],
[701995858053440525980, -18612779057102500268284248953615],
[29214013348242846970, 108458466859454175395075938195]
Independent points of infinite order:
P1 = [399777855950533112675304391422158680/4942993115054929, 258842927392928278921328685578604212522563097842747195/347524164833139506508967]
P2 = [3155234970089621005294110757061317477244775856459630/162339686108270328805993535881,
177234388690143806915103002987544919565097860259764646378761428997100368814835/65408931223377500913809448007389296637437221]
P3 = [294917566502034664105731723973715291892702970028083801942255/8925616593074133686615919693133517609476,
135406816676768723665371283560463907839362314074704972584861313827998658669422126461798265/843251924767927361470982684763757466138651119244145573449224]
AttarBashi - Voznyy (2021)
y2 + xy + y = x3 - 78056287100121146374722038519376379479098x
+ 8395270508371729029151029449471448424271358359726679128530256
Torsion points:
O, [172680121460919161820, -256028336952549306479446437173],
[-1290451271664209648361/4, 1290451271664209648357/8],
[334725198469585422915, 4446436368931047678672928802077],
[33643473236444864775, -2409827045180836125847845198323],
[334725198469585422915, -4446436369265772877142514224993],
[161309493773630706045, -38010645896944286766984834773],
[161309493773630706045, 38010645735634792993354128727],
[150199905894754552770, -244407795346189912184180530148],
[150199905894754552770, 244407795195990006289425977377],
[172680121460919161820, 256028336779869185018527275352],
[33643473236444864775, 2409827045147192652611400333547]
Independent points of infinite order:
P1 = [1473992406934354397752375444905/8163483904, 319821811519428684444827706688329018238563091/737587097694208]
P2 = [152944763082183604555186934250907236400375715428325867385580/991638052156215761010210617905318681449,
4964199968491862208228355603893298584347018721587428502130862694185198085171422775835511/31226964922936723895694409062665926633672352204962726666293]
P3 = [1107327123487782315085097118402788355825201631283017137669745899930561282515116666/6836614540062556683077564201750809861047069335328050796842001,
728358845683355998583971640447303620030330942189014701627142355532249195120009734281505648251057437138430492804652086764/
17875641717838450409738295254609723549131834514112290858036835900300177228247145160556763001]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 162937326694007704003409544055936413664860x
- 25273359543589414475086515394258977534079039443044671572788400
Torsion points:
O, [-239685885130088598630, -103081837460687559807455282160],
[1864061060298855077439/4, -1864061060298855077439/8],
[-226308043470511160730, 101127735024685881795958371840],
[-232964960077585881288, -204199053960618915716354990868],
[-232964960077585881288, 204199054193583875793940872156],
[-226308043470511160730, -101127734798377838325447211110],
[699006895470184829220, -14225840294279833302788242488060],
[699006895470184829220, 14225840293580826407318057658840],
[2562971942551384641420, 128034516716936869923376179712740],
[-239685885130088598630, 103081837700373444937543880790],
[2562971942551384641420, -128034516719499841865927564354160]
Independent points of infinite order:
P1 = [178646749809101556358640258344619713884843975/305115351294499407920164,
1507887249225500049225912761781655557561091003827610107620445800895/168537321798363471722714507010563288]
P2 = [497752419342940225454871238286729905414853491876049457508995005470/196566054278698154247648585559959026744856081,
346404787286412723800890564849773741653012594939237754892262478071254918038767916700880644919135410/2755895718336158979079176453057340950147353391082076449552919556729]
P3 = [76172782126289963570525787733152191888779132245403431990943173337940655117226577749083727067152889175666809445/
68619050567616155546284231245989493788168572903709026239509783308862915011839592899488656,
612675333578974275381365831697047672729354066251216749910226071378364325876662043261058228327609530369014907831483160437751668601745080611024320427297839537703839235/
17974923764072990190201261863706571956758300753589966155741256119126015390235672610137395939818882701492857172690996373215046506714304]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 352014429123220250070674880734439728427580x
+ 116508272936183260903207255224892137561741585599364737962000400
Torsion points:
O, [2659151572238184014420, 134102725129437804625192995021620],
[2659151572238184014420, -134102725132096956197431179036040],
[731556860077128817160, -15827222327575556870386686938380],
[-364409933123840932900, -14014069945406946961231183763980],
[-2869010435434636908481/4, 2869010435434636908481/8],
[374232382160657613560, -6097890884253979207523298622780],
[374232382160657613560, 6097890883879746825362641009220],
[105035974398273449960, -8982923223141027998150061814780],
[105035974398273449960, 8982923223035992023751788364820],
[731556860077128817160, 15827222326844000010309558121220],
[-364409933123840932900, 14014069945771356894355024696880]
Independent points of infinite order:
P1 = [2766237927266348746640, 142513877022190979043650384527340]
P2 = [-66674220528915078791611033488274966958547016032189640/174691759224409969531519046334841,
-32264044268803191795959537549766289052219228665165589853784039078693149834765580/2308918628049338412508487105206378225084258102861]
P3 = [-6488508145660952197522380099339828016182147626483126319009338560/18752945584215308668999452208914836946005089,
-1139485853341895602930186993924113773316781497044890915217526500598835135100895213122669484598660/81209014486871307600016289159705743208265766288139192341009233937]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 1893802992784290099731080049057616373621260x
+ 1003117266058024606287199405610823709839745280044070861528763600
Torsion points:
O, [809314622942702470860, -726584141143626217170470424960],
[-6356190630995260064961/4, 6356190630995260064961/8],
[447171596724320860350, -15674178769601831311063554904560],
[1201130448329815535490, -21477918126071595451029957941730],
[1201130448329815535490, 21477918124870465002700142406240],
[794524112306933762712, -56750289053351934817628917044],
[794524112306933762712, 56750288258827822510695154332],
[779824813581320559780, -717650199844073539162264139820],
[779824813581320559780, 717650199064248725580943580040],
[809314622942702470860, 726584140334311594227767954100],
[447171596724320860350, 15674178769154659714339234044210]
Independent points of infinite order:
P1 = [-32787872602268746459292363265/41190724, -11841018962295620119284931539757347953314035/264362066632]
P2 = [310276920928613898158170399357479906844875555200839629593665908/2199962692478484414328929065620669489,
5465428404008726059427962989173328768973653652822014716157120389099023075090520991615878284152/3263044330678601037558575047857541417610087248869741737]
P3 = [95141305913388901919874686715820999593193998453945460277550385441530148515955211630097025092305835248363118488707448640046493491552625481532968086497943777466259950792879396/
24446329056588593959963853600929279820791537407897638644852573452817883852957669758482340781127034980749173162166755148581194591113723889938553174944281,
27716109621063496549629281279316970610886776606915139534200934108273077970084813903739424669707625907218380711349950521169395650087999228613809524239586791704618041521082325100622555255882747121983506084658349707163073298496528997163099131958808732666939656632/
120870544864976274484023282353774039632464939773332326650542811543036765952089752104471190741890204860168691460020499961814752323376405152194399399250290163552852477699699161640794271917904758475009945223036840013379458275517571]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 42830408591126690133786955349037388191870200x
+ 107888819137999075142173514650183701943360125540460970576488583232
Torsion points:
O, [4149255329376302946304, -40117635351030050242656767372552],
[3778731145968189798124, -27813142758374392925758336232],
[8686834097200297297204, -625576618621655118388293154379852],
[8686834097200297297204, 625576618612968284291092857082648],
[15114051687896700248191/4, -15114051687896700248191/8],
[3811240791607943582704, -3494532669746391107657042359352],
[3811240791607943582704, 3494532665935150316049098776648],
[3781402026186100724704, -312626847228760737249118447352],
[3781402026186100724704, 312626843447358711063017722648],
[4149255329376302946304, 40117635346880794913280464426248],
[3778731145968189798124, 27813138979643246957568538108]
Independent points of infinite order:
P1 = [125288328191308316196933589456/13935289, 34879325033145151719696240277765128656070376/52020433837]
P2 = [58554215905338964760375944439290297751073889858047925134877625584072681238034828746923128448/10016288734855797634977641390986821775850052384022172408171050131574609,
239933067652622913873811931241594877821831572219122430348324871131693036423523342063872930141322494072986280864396813056183505665455384520/
1002444304919235630478088609450251773211939178678863986770101545428983718226668793779415516468556310269273]
P3 = [186796286045557099155072400482475518828158834782362223563272353173399987774980111121024088976224/49279514334061743569108563077954904263899015602450110159425870878743939481,
445183678903206559176480683959554099348601186444519470511640206852309060996360462014290398847439318542784036548491998074138331044093827316792/
345939081979572216607053277175980891191576791070069123595407216884950230956606932260672840583803967897015197629]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 3260906407825473602426070944987817036103365x
+ 2281831497107030020077208920114047648116308096637095179520396225
Torsion points:
O, [1297443845795362241430, -15331481023198886411467671123765],
[-310770848304068214510, 57142036707560272394488294607175],
[-310770848304068214510, -57142036707249501546184226392665],
[3432752829587668229580, 177591641390215382313070177663335],
[-2086721611923373526670, 1043360805961686763335],
[1044143260468722114330, 3916596847027974085064349757335],
[1044143260468722114330, -3916596848072117345533071871665],
[809801909650098483330, -13122288481036479008156645146665],
[809801909650098483330, 13122288480226677098506546663335],
[1297443845795362241430, 15331481021901442565672308882335],
[3432752829587668229580, -177591641393648135142657845892915]
Independent points of infinite order:
P1 = [2398486064542560171781251930/57121, 117357410355928728017171050406281844579865/13651919]
P2 = [314448190095941883187749295706357917478665719036045982280270/113994983692730620280355634931410949569,
145421266720529804540219225762771373157526729170506843071048986894927297504076317653419005/1217106582357484830629544122346867534931769048825143089503]
P3 = [-6940655917845470030727288579213826291105714505523735037514280/4804094434636881692781464955634611054409,
-20999972729853159296499567387182638997099165448034049209014563912431859718371608411567521795/332979351909438853378931380586278557300191906791406592335173]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 18455671996993115034020498443521081456902380x
+ 46836457553640733761464794022398648774581199871325719596949824400
Torsion points:
O, [5504295317714827488920, -334688053536373957649078701353580],
[20195741100130304374640, -2812704424343434234761645968725060],
[-20939093273312247833281/4, 20939093273312247833281/8],
[20195741100130304374640, 2812704424323238493661515664350420],
[-2727829021535899702720, -277276865071662745573370276164780],
[2749766936805294951512, -129920162896402149925633244994604],
[2749766936805294951512, 129920162893652382988827950043092],
[701764127002633611800, -185014942137764660443220861413420],
[701764127002633611800, 185014942137062896316218227801620],
[5504295317714827488920, 334688053530869662331363873864660],
[-2727829021535899702720, 277276865074390574594906175867500]
Independent points of infinite order:
P1 = [414182765648171953091265858382118/36228173569, 7952757269735825089002457306493944930599761654608/6895561872602753]
P2 = [4239297481374706492200537001031694556755803890773805091806808508560/366206367387890194539929777342182965806631289,
8245902254504704794579949518084200399953887985162423704777823259203454516882713704081442374587406020/7007915183512068812094724772335270591133678803236032340133131470413]
P3 = [-746943437228669992973187703524421466029784635621336894798013800/195996639513250590687602110184418978355321,
-21574526460431614774199494957267793600679402686628431934925462447716372745310176066154372062780/86770667378229115401529475452281344122379301178270801990258381]
AttarBashi - Voznyy (2021)
y2 + xy + y = x3 - x2 - 173732247593653127064473374388952924487816247x
+ 30231476826254200671604110108483776426569463402185407235758906851471
Torsion points:
O, [-33008933302177108344765, 16504466651088554172382],
[244495335992362235838531, 120843657040311915862212438208421854],
[-21855819177060543857709, -4856801308648900210089799655074466],
[60518883447877711434051, -15536085070926285574728302730295586],
[22624121491255524872259, 6154763495979772936069719823290334],
[22624121491255524872259, -6154763496002397057560975348162594],
[83219312913883643971, -5497000957277564144058522012147746],
[83219312913883643971, 5497000957277480924745608128503774],
[60518883447877711434051, 15536085070865766691280425018861534],
[244495335992362235838531, -120843657040556411198204800444260386],
[-21855819177060543857709, 4856801308670756029266860198932174]
Independent points of infinite order:
P1 = [29929644280551579281642412089535034717671417607951/64195227476555836862121561,
163698057899837106288678688732686247431645938535116760223194006627142672094/514344515394256388967521959336859222691]
P2 = [-16625799379521837811997556870927515080940611975741941/885043766324919565459653178009,
-4315674356043979472877794540916392563151094794483884113885065440368434727080422/832620541858785959368985170732149557399801027]
P3 = [757919835681211120463354514499092061151465398759946750489249226846600513613629379/
13317897824812596111839066064800579165199795705582407828049,
21987219412753795205878726172284896538443123585253106244300001441683135007767155544256395407946101204888126617093618306718/
1536927983244060909031419325918025006519697152388158895072197942425156318964820275805657]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 759567427329236195681587390983412972582120x
+ 199966865015055575508156297289641141498027828715533647224488512
Torsion points:
O, [257745070857462920144, 4616791051190790038324806198808],
[-823379856018855454816, 16345194956897820296619279228488],
[-823379856018855454816, -16345194956074440440600423773672],
[683321127763423179728, -341660563881711589864],
[3166258148471629167824, -171864254385312489891556224914152],
[-117438426418975145008, 16957287018602326026298139170328],
[-117438426418975145008, -16957287018484887599879164025320],
[941570071762614858704, -17875508656403996927168722786792],
[941570071762614858704, 17875508655462426855406107928088],
[3166258148471629167824, 171864254382146231743084595746328],
[257745070857462920144, -4616791051448535109182269118952]
Independent points of infinite order:
P1 = [-42568251310361700401027333668486/73923628321, -424661541707963281038799424563258929839467706318/20099021380568369]
P2 = [10669592612125041104553791251989116316927907149151331158641991652274475336144/4294837913088642395646792646194154633181313479019379041,
1039702708324486692923149170435103568829348891938224832677972827344939432225634928669179514589990294320317666614168/
8900618104918031575586933785631501128242688043872344799581346357708298537660470161]
P3 = [1495700933074193725043891435658808418687594310035822373378889800874792518755319156944/107204920877415579506555103323798534784931167333383351275012201,
1825720091354298906093315336964211624232233926405631641943642320731935949762776191053485328044923690793677521443285836048345208/
1109997705220795772524439470324136613508692301344439139255718437480811177276857560545015333301]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 + 44169739223759808566850193913969222x
+ 1354123595767371345495791491912609176897279912624848
Torsion points:
O, [-120173352783172329/4, 120173352783172325/8],
[186468891790413949, -126783477113445751032800725],
[186468891790413949, 126783476926976859242386775],
[59664586655867074, -64821991497073951460160100],
[59664586655867074, 64821991437409364804293025],
[492514126054063324, 377594460273924772157917400],
[-7365739865601401, 32068382640657200990986475],
[492514126054063324, -377594460766438898211980725],
[2037086745468757699, -2923127817208030832021488225],
[2037086745468757699, 2923127815170944086552730525],
[-7365739865601401, -32068382633291461125385075]
Independent points of infinite order:
P1 = [15228133648835824, 45058602190084662072652400]
P2 = [14503504519738445224, 55240184462536885950710532800]
P3 = [4616308785130068853566520738611882124480698970135409567370389263532213016715618101748710201787355051506975909705617765518566412824087935828652671981109702273471672292792505867372606930977951209681193331683279053084667239544510922759621534313047971518149294191855260351138195339343582873021711736774321508034101116288541353747569674710008053855360687164955581908960064872884204364371009446440503159450477605857967998373773040593825243328539917856841078567596477317648518615778643678105989120956353650435532679826450951051072738793531166175945009496697328977359372986668266286072661940960475176777095164016865838219974883774069829724177055529768121956534626380675048310098194743774369786541458390243244606417291153205399063769826245357937144262357809530768829213811856713963828614/
558516518069252343676646828935056016960775574062702143806562939884660083160020870058390518922059831194505867937170757027014128616263827756829151527954948595476349770098741602901489968203105349643258885232069400821352237440686358706928364802216131857641591733770598505676661838264951214627100008045591122998392304405682822467346306665938235035251647946262964013670481753321242789615982707060157355418693208682851131309875488270099045887114401388710730123140427808419783144598795350006374860364525614633783533191049650219513639967672556617038398624409575627960622901404719722630060913144900036704053398199810895399760203811986765008414539119012108108747791582288096277210239534713119056129719348607403726241478253085082795681814444929466997066791464818047517961,
313749577607778532870876859518012255193344818830819537757656154050538365411877222238440757068134575500119825127708850717386764701060957643495100562990716033573943282281414393889993630638018154551172310770690154645924260856463119933751232532760824594863605959523061353821060163173730574419532550779683566398257965555027892869265676578643019901030322465190571421260771374876347023308882840880505338244917753365078366475609532401201601364517315102613513344594618829547614286848328700584344845924238767479954323747234834685288482683214238146874049207770576761779872238343572299591744234696061124672552093007372918430479047192162116829820957103451675259337872589703783015394940628989001896354701415073102810357477401051870329373757961481331561321250658730651298683777206726121812520636455734405911057035672471489691992914843480412414784127376903066521470454956337642382763688166583444184818997387197999952128356410964813679361291300438811090066512097260176736451225996058760317437164280541789950036544019025062242336769276153427441032045653223351631057117347934544352358456738172254248574674041512513855196494381995955387570428808713484062136155746575102026303735400864025/
13199395218802244258549158117699810331128574933642164209885196912011355405004838898847167097020146935113205989417380613388793686131558167311265943793339122966131172654503873152241531507996374308152897908229187681908875988732762724087575447582611559938367101584928906004857353155057095937690080414384934051849242087533737161789862791261380893264458795085983058915272303322628117134750641333815839284100764328367910572468442042717674510208846892976149129087054294046569295108028812451943194877262876827611505185999887891194419344207154031425552630115820625672831058132417526547107888841454375482961989393565107588324586090046132873583012910496684787779134176174808173798816015767819216440651838842936281582083413569471443922696764383010308931256286106498257412976210108711366050828647983525556907608237283364092687715793998520290455331051425829518087688248810113811405731688423096518297119749744269550621783250088192797106467418389274838677496548147457205077459570068221020237038197547064496854898257882193251413950151620586703338855729623223053171650703718296316998877382162558573653749921785231362297580383218071523338095776969843483101541]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 3305075082868580716146838734865237087950x
- 73064779278405376122666988564936362022669550873927543797500
Torsion points:
O, [365061497391652125900, -6882738384970328719848230467950],
[-32464594386374871600, 4133650236205374800003842050],
[66376487208117315900, -33188243604058657950],
[-33910143811022242500, 4194104813110251236350020450],
[-33910143811022242500, -4194104779200107425327777950],
[-33184745605661684100, 8327508168475553361145342050],
[-33184745605661684100, -8327508135290807755483657950],
[99563419064217315900, -764741992354516573430158657950],
[99563419064217315900, 764741992254953154365941342050],
[365061497391652125900, 6882738384605267222456578342050],
[-32464594386374871600, -4133650203740780413628970450]
Independent points of infinite order:
P1 = [-33898961692645628100, -4381202673925831203591457950]
P2 = [-1244768220023508987921282339576607072740/38422263858727389001,
-628761650281763009779644916020673563128636878327784309910/238163072914082166134961458501]
P3 = [53920196072187033417273705356774442958626760912546816136369999300024753661831375671541948284240550579698396233665357/
139845143335896208661449711627092672217282861358228402282860000641014072442768115702670733022096,
391256798463075236945142720702057013521613309307407448865128431431751740045144180814729375893505961361040745436377873196453023846264634565145795413173487151288513558663093187/
52296314366152408066975343284407892511556424305054394515690765596499792672004373595688207615517614606191289972587796669768275118409858299009856]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 191288810754168955458214009933523766860x
+ 1018315757937853904318349863652893147118383146612552851600
Torsion points:
O, [-15970339622945640680, 7985169811472820340],
[7804714638944448280, -879893471573817989307160460],
[8166994657817084320, 893301122664682700321220340],
[7804714638944448280, 879893463769103350362712180],
[7985169811472855320, 6332239660497955764340],
[7985169811472855320, -6340224830309428619660],
[7984827399136919320, -1675919454862106507339660],
[7984827399136919320, 1675911470034707370420340],
[7985512228703192920, 1675959380711163871476340],
[7985512228703192920, -1675967366223392574669260],
[8166994657817084320, -893301130831677358138304660]
Independent points of infinite order:
P1 = [11537209624074168759019603/1444804, 1202200938452572527488794570284863/1736654408]
P2 = [-146763863257903059446790360379943730862384780557157038312/10450039075037995701011475060954836689,
-1032785535561651516292106529201480933580268202601701889695587810571048959039495599788/33781339913084816139032420647965416207575679010432618137]
P3 = [296796953618272401494895407455323310967178336562559224872137428732335670/37169635014684397272378163263666916619043084124956721,
8392418584440660955488505336568188548252518122825813713430941027384709972567247049078665568096703756790/7166093079703434726872747293874988494643196044706502331677375619712708127270231]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 2409838324537918058964990901856106931380x
+ 73979632782856304678166303145739286000302244099282995168400
Torsion points:
O, [65184889432821571560, -440306409057183884414847508980],
[-60304312958999970840, 30152156479499985420],
[241081824274916729160, 3674887013328449992669660785420],
[-32101316504534762520, -343887168657607271619219758580],
[31891089094644317160, -171935532092389356380700974580],
[31891089094644317160, 171935532060498267286056657420],
[7430535919018589160, -237662583770742557672067374580],
[7430535919018589160, 237662583763312021753048785420],
[65184889432821571560, 440306408991998994982025937420],
[-32101316504534762520, 343887168689708588123754521100],
[241081824274916729160, -3674887013569531816944577514580]
Independent points of infinite order:
P1 = [3327435925447453312458315/484, 6069508575620750007770497976732544285/10648]
P2 = [6954384545882985581576615057747597815389433989024003960542662239390/336144890002584013386366182352513711069956872849,
35392004017372839479541308833580096873594801566183230492838856556999557840083039792266237605607238710/194890096385872358381878954268311414828986158416455809305434736367084743]
P3 = [30273516438089229548014236302011335969278828129862768918761428968908801640/192475875841768345245316550231637869609790722310154129,
159906334994788210322454250063909326543466715578418432313721587620720069394458248664077580738899772066286955860/
84443156078874228509993936187971977778000772683457458408821207291198752497837383]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - 8951416433486958038760577466434122941198x
+ 325975818774023018048480321080234831775781459009061472792528
Torsion points:
O, [-29346827972037158391, 750597723873131743048118947945],
[-29346827972037158391, -750597723843784915076081789555],
[54504550508912226369, 1437526225029560571266635405],
[218661794998764388311/4, -218661794998764388315/8],
[50988843314190335109, 46015347743344510855027153945],
[50988843314190335109, -46015347794333354169217489055],
[55279299238171459734, -8385991110631671210919010180],
[55279299238171459734, 8385991055352371972747550445],
[76686165165209883384, 300831448281900626209333894720],
[54504550508912226369, -1437526279534111080178861775],
[76686165165209883384, -300831448358586791374543778105]
Independent points of infinite order:
P1 = [433405281719929096772526/6889, 62182644260476837894569745235490215/571787]
P2 = [8067238099981817803842206245760611599/141978536918555236,
1513615136848759061988417672192868436761277230301396005/53497568650455158835562984]
P3 = [1544114624256946541934335238513897982597033384339613783162298236208399644370010747039429707951436425849473179295387093340411223236791154444720413949797479344/
8380322953939032327332032232325771435854513371704148194357511537069060489199401237478068007967273264625803874300136612017509247540469641,
1703746521999245276351336638612584944678159533187797289217317140670572765284803789097170782938016464701802830771329024892496161979444507877447090064271077512097355474837506982029844590874017480605097655855707133740592924011117916962320/
767169154985981753339898220694516868067392927102113485978729686642288605306787810202840663551796054928791442837403634102333921131959881807606413038764833060337240533269261566452241549971970965658599822811]
AttarBashi - Voznyy (2022)
y2 + xy = x3 + 791035680532773308578529101046077460x
+ 4081296905813872942869296517097801873441382978577779600
Torsion points:
O, [3376384619650365080, -6726279169979601392082725740],
[13865484109809295760, -51775588677360036151994258020],
[13865484109809295760, 51775588663494552042184962260],
[-1433732321186129320, 716866160593064660],
[-978950808789329320, -1539071011870830043899735340],
[1204032032764782680, -2603690876563788050543127340],
[1204032032764782680, 2603690875359756017778344660],
[12760741779630680, -2022719255312599947211095340],
[12760741779630680, 2022719255299839205431464660],
[3376384619650365080, 6726279166603216772432360660],
[-978950808789329320, 1539071012849780852689064660]
Independent points of infinite order:
P1 = [-235924016950636157903720/168921, -34860697052466174588397305014465540/69426531]
P2 = [-326660846267878062078631616347607575583323240/457238295466455549319826809,
-17356983771472029316743164439367733546633252053519498395219241064900/9777186414046567851902828144748401843123]
P3 = [19654150498445027747503773715485352197522091323577130092860096527426713895387480/2778402042280519048998165699394246909665324001785480356795041,
88315727190232908750811907650871640710337165626874882523056774298768242564449503073627922155521960133292760237343310740/
4631190378567086919237097484811277309783993734956985632592271010842009787797295051839007089]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 75933950698035326808283662886273057531060x
+ 8063337734071294771380882826024135390570596875508726889235600
Torsion points:
O, [-318232373299845088280, 159116186649922544140],
[410411949560389286720, -6784400633826636750734061830860],
[-5485025381741741080, 2911987699364805872636942524940],
[159137063876562911720, 97545224133950200252034544140],
[159137063876562911720, -97545224293087264128597455860],
[410411949560389286720, 6784400633416224801173672544140],
[138634312013754911720, 448068145825605339865922544140],
[138634312013754911720, -448068145964239651879677455860],
[180559915294582151720, -489186327571744880608599095860],
[-5485025381741741080, -2911987699359320847255200783860],
[180559915294582151720, 489186327391184965314016944140]
Independent points of infinite order:
P1 = [1847264005601394205480/9, 28633433994521941251547908691780/27]
P2 = [238600001781001780465290920/72361, 3673101794971294848821446559958989531260/19465109]
P3 = [78929020091174432333188095577737220498862745147974009781917141908943819287656005242526936805117964736804862791156009480/
356913516791058837910851917965711174346521748945588593979936855698791741798657973413031763910443209,
9738532939509687838018375408170943042282989036300742673385852539312708226275244282639357608201434965014812037113067851617841971587621764122706912074232213923002459004407770082780/
6742865445360977237535507299998242898510653697674556186426805544968718887211495489071436943597959760935546450133814523156206169185797195057355180677]
AttarBashi - Voznyy (2022)
y2 + xy = x3 + 196977492098299448721468406254002170904x
- 1173996958326314820364756899317997085401642539223370239424
Torsion points:
O, [5232683861940531664, -2616341930970265832],
[209401097216304771536, 3036785179024182627613541320472],
[6599792655654295856, 20334270390431314771485622712],
[21939581637869433296, 117081681105264113758190782232],
[21939581637869433296, -117081681127203695396060215528],
[11238349757677203920, -49589457001297230801445927144],
[11238349757677203920, 49589456990058881043768723224],
[51708867875686831568, -383759064963013650256982596840],
[51708867875686831568, 383759064911304782381295765272],
[6599792655654295856, -20334270397031107427139918568],
[209401097216304771536, -3036785179233583724829846092008]
Independent points of infinite order:
P1 = [3049329177464418255356540624/193794241, 205833567309530567264401859537351787993368/2697809628961]
P2 = [186477403566978243391246357362462481280/304946593754771809, 2547138499984926576621685308767006554960870204728764699288/168397515604442180670121873]
P3 = [294689024088036688195635074656971261245588845175243169370492942315783979408940406149388957090783545156379301604630760988696965007003729967538636212940777056014989326227404555987480658114411731345177261100064968160462912413826265712094927290926857910025584338190171622528734866219932194693722010415027777990177919563339760821917633828493465250628847233546819736747896213656815567975706204706411043581136/
1051881458231353090897371467070900854140778828166990829529835751356645138475748087561252014554416035586651575401452805368949507955350678153581470621353583616116395234501383489203813431412923411494221622443292781272342417983962333580340319086387311411542983086469949791007715142544366170271740689526041697173475674093630188215400230953380344707664254971513752257956434559468721511281,
160169075156099024540139487077146033238541673058827908865787982229521067284266605911524001015341667598898536879550945537617338342050673961120978368845433008797654340489857965790255246242150625752535029656683467456716634073916343539192489051512259375016842360507311850831147060261060793894509263579347347201439277164231518476487233611011099916492736602715270768311546622056945794199746510691085670428859781500881541887303169058122110379432968371598246890895199707827808697807360262355104610167315345383655967092577810784571677432356735313990746587107534494921451046470786099408065164454278326352993262552/
34115378942616725547679980669706784603365940175799105385175545511256107649094373807279912196310538944364029805490908761113050086394018582251095228384887816284393632905089087682656307047322733469382837971321985230557837002018041551606068924584102875825652086694891069527186357443957924453748115109856113772904313604420268313022837798327792290041355870205683653160617764834159110645200383164679473211392126878926356919662563041297135972600041669555372190183244508954460566885215732042516683363296568493152212022257267033532022718955393326778352017132194111024183058855069321]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - x2 - 8067029973446017017222741904563250056482x
+ 165888878206932391845653427548694227599828035543439532450081
Torsion points:
O, [76869909331615557825, -38434954665807778913],
[-85451866918418268249, -480895285188479057957440811441],
[17358985217363451681, -176307353756540528964283312481],
[-21414977138819828391, -573431081698863670813167528209],
[-21414977138819828391, 573431081720278647951987356599],
[108954981466745956561, -761820742753816152155579021201],
[108954981466745956561, 761820742644861170688833064639],
[377941973867496440421, 7148587443989322347613441013159],
[377941973867496440421, -7148587444367264321480937453581],
[-85451866918418268249, 480895285273930924875859079689],
[17358985217363451681, 176307353739181543746919860799]
Independent points of infinite order:
P1 = [-11554497841985209622009916519/169078009, -1387035106882693933291609320513926833899827/2198521351027]
P2 = [-1723829537032041338277879/436921, -128398055085157420117365299917783410941/288804781]
P3 = [-1161512183523890534415384934596205434100867503475374851008637498141409702230027401353667551620673945320448539480725348944006326829278699451755123807193743595693713534378849589532199163466926367758612421008013231082088445038898427592787058277483914422057998351477655152547956930518830116373407375792256291162479347424280479515761919/
83035365861174936774435669315291619479753029449327326288937338643927474806339305341874674030235961836249755738729699885135407601856069035787032960419335127626767579128907362069554526159450511430833766881724855349189107308623584168602319348809481209974567582082705443346127789568228839005775530638215028597886129,
-12570283493350993908251055259621030447951599644218727210799639238724051182805056003948535661060114310090478256601349931222713855619673889637906420230811388468566356192976071201406719767716008717526319259455768018327837792484169164320682547422826335996774741556707648407668964038068518031365269266333573410757643676870952570206250513558302226359881675828549360662824540954558884785792857183888781263150362274866883664834951322132245624176358933415716711708533053801387185299060936827918545351883513/
23927352919460733494273683093650378550209061517712824984449693924270225063134201113544966017088738076383912413131183577133899720976334967688866653946776233401874233845572521911938565044168005343167034590949774160153872135976504463577162398464819086181395905402645850012491818359626283943946633993977527385716006856227422886096294596170379960491533328582252078377859364552790219450161206640511096556408412316574001478196322274484218546515349145103088848919544365814633]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 243040347996821732791086146524372751047490900x
+ 1458363147044690029034524018980282626554973377074799384207864366032
Torsion points:
O, [36002988634042801702591/4, -36002988634042801702591/8],
[7273532302976135398834, 274594714989523425523738325735638],
[9000747021009792667054, 21855560901602969904575848],
[7273532302976135398834, -274594714996796957826714461134472],
[9000259825348961835304, 80078883750184523425895449348],
[9000259825348961835304, -80078892750444348774857284652],
[9000755206935312250804, -1323273147673327833371641652],
[9000755206935312250804, 1323264146918120898059390848],
[9030255245121984989404, 4851524080959881915198543323948],
[9000747021009792667054, -21864561648623979697242902],
[9030255245121984989404, -4851524089990137160320528313352]
Independent points of infinite order:
P1 = [-234095939050679836218626/81, -1065594580274747368556898448788606808/729]
P2 = [1737844877204973441211883826804598028514015721804/175698518459170661126410225,
346289838786507668174046202652233377498134740368222163097661880867678412/2328907015422232733213629673660128759625]
P3 = [8044390238798377963004116641763372272120334340819486942350613670646322851970864396479215883261146561918182300201104136206668431126289370745511934389534552874023317422817700951797412477887971458482698026514494462602854181003280117379347074939555080767482042355533501588447583812639820632082541567477825707911936038357383012261774298093616100396089359270212002618250975340974516062046179099192175443473524097089874278895993810990264058985088218058075652401943851055119192169851073581609884956420209844384359812734938484600063659227341280761707190638487345659593547758802987440960553866981043866561963622717080106821982087620588484877236/
894864641165345249956439567958298820352754476580743856413719085801800189869402372701532190986649618325576645505878832920364581738858848109840419909950193940858550288163064638226002922090998947952573161851614312426956652205224643329342447345092924684493146235175570380642563641681913183729923868503226168926864943378838867350964316055275072194453828307541083975300824400954086423773244184267592385388996017776937466572447757985525096397012879652547711441670417673982175137716790356489940098918186300946643545807666762606493485041457630564027656899138584680690963982848223496718331472217736912217277926711253097009,
1563478448139013116278638491470061346687023522377900177091720578701991091057050474481321456058909029053785834545054883871688945119976916653213101136268714465875409857196241538557928400230475225098776397640437182683167219911234966368627644729480163171492580830721968540413628247172312705735258213804667216291768388214645942738566714559259149257462732038539831046702610757943265258149430221722397822978687789483399997146407105073473727789816973963322730261559719897699601218149605182818387081698422906686155869234149467325535072209986398550577570048835566866547217359096677349195483533289919650884830826735497245511281884309724438321442838686554485133821948762870110597182371571828897905783866963933460992884000145431585291221960639344158101544648444592633261403962528308134416909306686513733429895602310854026056891388508053067493402317632345108366459555820153822703853005370059533181506267887875555071993819308483590508466777289063774649713430733396/
846517658859246656779718493714477919472061410886028491257982323166311751056956787095084358146572299826206428099373423010989723089101807676140470722090977228623710012790370922306749925523554087738760004846497810872081380608685682757355588122990496252727419106586892066428268667175943528853585496227433345315068387079291506183981839714420907597597485876398531834404005418939682668199702608049197062866732785507628621534260467583733575249814289858651627021165367499174806986348212715869937219660578816771302366500975011064368933156287667947434762211682549563277168730609131318254373722181636765461150712411157661831559237825742995152479134878699550186651808780453979235700699934161394381284007601207328379054502688681051676514220898360463345910224196493321539282403423425777541750653077022537880207681653842669830732857305807625861625368167111295785672747081183072232619982648116482756156993009812905451810236682440061527]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - x2 - 52162774702261334811558801584582954099965907x
+ 144990966792855664389648136792204207403747894003593101317734110131
Torsion points:
O, [8288382743133244908591, -531070000656151014772692984648146],
[16822627694722216196139/4, -16822627694722216196143/8],
[4097883102249095219781, 6950807894717607193472433031294],
[-4144012457000228234559, 538506912866210670890010238857904],
[-4144012457000228234559, -538506912862066658433010010623346],
[3257039099240590205691, 98216240868352722059501071458154],
[3257039099240590205691, -98216240871609761158741661663846],
[4426067457387625949191, -28670409786237037397286670590846],
[4426067457387625949191, 28670409781810969939899044641654],
[8288382743133244908591, 531070000647862632029559739739554],
[4097883102249095219781, -6950807898815490295721528251076]
Independent points of infinite order:
P1 = [1006535296183863945982506609711393288741/220658391160924201,
4592391933765707714574135327496445769164244223970406846796/103652712352608509696998699]
P2 = [731882098278521717315324703934777466357236238391169/46121678104044539309237818609,
18029096968019964158607490465748311715968255684844037022765701610417495880992/9905072315405166307572253410917520167540023]
P3 = [12427335800709210773007012052316047088700768028394025527341393927846671144799393686403461093924446959421561821622908185593371371304966664152972742900234293944284174828802382484132142392967329504350381868660029/
2863836477536708669400609533166115570864293943054902007937630340218462240419666149941445804325258948926728328346481954702780991895969404524379735342060219308162411643464234367715573951225,
90465233051037481047302955582477947866462932459010488790621161632061819255621293150498587689776678034845138662519948695410819831178062674325287682138970835856530733684322326551115491223920245325496775769575484580207265661429967372390136495069877017557577714932916161973333496509019027187527175762862625735150188/
4846434245575716511270119291629359573762246881599733645995835246844857682196057510256135085349319080768349076295217086564050953731147329289640807690014060011745523437615697490998197249907208361695661124408773042503482235914023807769052031918232045703522908607648028956390480074125]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - x2 - 1987212454379639639823189044562921429062072x
+ 1078179396837166636890227806567103839079340160358732935829487419
Torsion points:
O, [803537789533698779127, 449146285471405921900819663561],
[1515116614043644821777, -39311444832834027872974993592339],
[818769188007170072877, -409384594003585036439],
[-752753962136441275443, -46341364338564077755861637603639],
[803537789533698779127, -449146286274943711434518442689],
[664054950426648089877, -7168595486332613192906142751439],
[664054950426648089877, 7168595485668558242479494661561],
[853143545425802082877, -1940562433452423518658183346439],
[853143545425802082877, 1940562432599279973232381263561],
[1515116614043644821777, 39311444831318911258931348770561],
[-752753962136441275443, 46341364339316831717998078879081]
Independent points of infinite order:
P1 = [656621735852054031627, 7512412959298929793500942898561]
P2 = [345034384869192602871018984710390503447312274638524657633/1849225376579618036161358900764972129,
67189558895314976656771723352509225043891026423073454858391751370612022728071192986387/2514691806921164827579629544214607871808392125297552367]
P3 = [24404740991442559274355203457612353277922921627147483814800089378419484424962013/28901393483005663047517889948952473709156563575010175403729,
7363671145533757828913434464128568484420092658488285023612243311494375207549848538720100111413457946687380977284190303/4913355342449780729989360655718548822794642617619197996734099542335685542106956053966183]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 2253282003811810446601779835812472349288640x
+ 2588514151667542737721176948139252824897955168076956256048025600
Torsion points:
O, [8434046829072285345840, 763887761357766166475111773239360],
[-1070023438143562981680, 61436594988686511564902959380720],
[2232517443271996099200, -93194362322321482029338399547840],
[-7605009383421866839041/4, 7605009383421866839041/8],
[-1070023438143562981680, -61436594987616488126759396399040],
[1029788330090695446912, 36880402605120529865121712932672],
[1029788330090695446912, -36880402606150318195212408379584],
[176995810741633964160, -46853361841549038531237967177920],
[176995810741633964160, 46853361841372042720496333213760],
[2232517443271996099200, 93194362320088964586066403448640],
[8434046829072285345840, -763887761366200213304184058585200]
Independent points of infinite order:
P1 = [5974441668212683759290107402984265513612345540/1278095195895337876058209,
443469321317408640445872273584965917937562252117329114177018235032980/1444923331026156840776038050670051823]
P2 = [-790116488071296264314033612090292605841491072640/636735776440969745133637849,
-946990099811502955998248617417370613278442785717285422716674345779560000/16067151122968420925833247792986321601507]
P3 = [3154034301784670712970550952439770781990907637026812215695173069579791069257480846558970943808297180374351271871902168544146734927909774651676711414954645922015669877413020646827815120493138573002538127707025970122174963614770873545317625158190909038576310344905565772326467643057704087377965105053560163812450379190921196974019401263058555219520176988861096929931077625457115884340628393341414022750579676465077179989598379588722863696013528874614324515453288610754947465916312152850470234610798341195643839661154073631684169399508941083800639797899975307784457940657012126816978695631863752038537087200/
11267458245061642605107291771427640520518823112603803821295101574391441951791531982685389526957833294044980888955850453258608062211374635015570570701996235913639884236232942434248541874862949420749121017599264378523875464883648564210817556960541481113240165181028657507267111302015156112590202005514362456387084763598100249646722103249264828270118146912942451682872996487109619953957006802945997074660556038796495053717797457704979529429359465061520068160715845073482124129251565508669448198531845011741321120497235194268062971601829882340789412289049535222144470901525498141737239121,
1682823795670920340801442421872138442271928244668793298610559845362197408615624691510730055556850590058860062644255569658526933471018179127797243610901322092474129665420134495385157838801430428646167109167314148122272935021465646689791701602791232205498091677953042356625530771985566893927531743421019244150060466295793256221768844649287529575625522828831338403792754588638094641749185777586701596523715538703880668287422242659201091782070013801413888727273508002026438413627669416221190856348243138179117723223025349808540812248046490238988886327322071916116154563859742346819127357574058760426634817412909243968145943494385286587127375392743478431063817759563938045135542180913826778854894354732866749119974128118715464576300122863004783135952068926896185174424999718569936497734032246235803496012759000968955812911680873448637087306431699652480601898536597380626775410781170134776221044573361856278324960/
37821516289227060536450794511050657730069110773337538787915115947450670786480913837545355454754485089743150429594789649350035629582930823230855736405005589686748392462504128321286755423812754340020732017066029750119794810813004930057014819531477401418738360027362006800555946610702563936240284288380318279259576434869487795148139679782248325205507756404509229149256936300657473281590444749368588802658700629421488672904201979362809391145141356700830706513174909830621130292954236749313700572024737878556340487278574637502465756547419061992213504716140897869388580914555596742471082505540965377484357745726780637769934582846370730298755823504814349228607494965340899634986127364115051944871936373308263243953179108593717309646480758337125241101910313747083019534166558729130696622128622159289656020126481998031484862423183813548046012507709594786947875934986062887790188101081]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 49120645851475638731970373386979220272767980x
+ 173347811148756476154362314221308788638983020154010754956574784400
Torsion points:
O, [7997548720698599526760, -540400362077605799463610980859580],
[-33433005906371467186881/4, 33433005906371467186881/8],
[-3998221219233637748420, -553017507142456955462171412773180],
[28444350320857070498740, -4667968317000828936064168723826360],
[28444350320857070498740, 4667968316972384585743311653327620],
[4309047264118385398360, -204192396813263178655980154451180],
[4309047264118385398360, 204192396808954131391861769052820],
[1452363439881672709960, -324145550146632844867665825611180],
[1452363439881672709960, 324145550145180481427784152901220],
[7997548720698599526760, 540400362069608250742912381332820],
[-3998221219233637748420, 553017507146455176681405050521600]
Independent points of infinite order:
P1 = [3536797787296511717376055/3364, 68391180870458985656379359368896580045/195112]
P2 = [-114508424573408487500916706856317996232/96624923005177009,
-14401207806097345131235273790744243329990507296414327379084/30035422214130980935578473]
P3 = [15634627426727889090709612672443752705990476771335668232876180381747082045137708752508472290040757694727643452589241559355419203269264242333700751129281982980471362447548516041292277397107817123070094344723418831599913597419137585019928980093127651582898734208195451344051207402992823430934029849203297783770759181752604440277727467659135668641409539890571946086138500/
1525274316602334822962993338644885196182237562934351862024902461223166938670757482357272389295697906400371485076736235127629484995559813757501963347654763396045446717820306832898553503402593989067106871157756974527389631601214873731703092066936964484841600306772514380191907969729537808590925243768269964851946132612826696286675724364944604686529,
51480027871731466520475990490991141178859540466697156785488904851802611903295999389989423909197276530383662578371849267798654360187414797471878836865150956029522511104452981800749416690248202131517646845250642650088210807792551839471881518117326661668404693693772167076007543198131543663058204851442736494548504770359428060174762550799039834721088609100960805642326855441477431888778435970243123111198047095471498805297281412791495871181901024124526599470747993198357847400774422460787096392892305985471546154741907473736258444058000647349522323555960/
59569223110029471662540391313804044942213444788964894266255033264001686913333794917015302646784987124510962755359615512617920633990062615642512231157939697957655714262891568644759509103570557506004519178291187941013317865210988759335191118561076168202638504355691783039977669933953264261415851055787124342959075590417841233160803819255939491352773494311302556072443757980655061043351901852984671271223259533152323875991863997046004686098871976405281277462590534127055643549408122402204603736216401321088502940606960417]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 17433020706476750943736904904595770755471826x
+ 27607520846462699739664406817051020897849957753429911056823569156
Torsion points:
O, [8970999012639371048148, -770189167370170468242487857956850],
[2066285283382953257796, 20199103675489219332519740530782],
[-3490590491874780237864, 214310353853355171210737904421962],
[-3490590491874780237864, -214310353849864580718863124184098],
[2644530541196413376324, -1322265270598206688162],
[761021941936767274116, 121578611514162348907598514127902],
[761021941936767274116, -121578611514923370849535281402018],
[3205286460474058504260, -68266859547861089200599713298594],
[3205286460474058504260, 68266859544655802740125654794334],
[8970999012639371048148, 770189167361199469229848486908702],
[2066285283382953257796, -20199103677555504615902693788578]
Independent points of infinite order:
P1 = [20860545034598570423137364/961, 93628924835524823035738129098777614258/29791]
P2 = [45499969691567310816011778422337719339970048336078464411728404/5326833211932557289084428401638847625521,
275430264128649948389479407160562956523050109782660360368372969904440505531891696710355445298/388779760826248975302789742528241626860038795543297212905431]
P3 = [363935824528021055850529877163700351849693912298838034216951493142583411411292234304355385680940555880539797300607663710849839103275912826044189873488202453014695623134348147839428900780857371307892872336875056947410874961924728294196/
94610708305061783930183105112320972092069329843349747308955132534329466600402752490212449307370294155521509777175834497802814877361441935717824137999690788949779570486248931584280366492887732555929039287608175129,
121624158692737445377294097112406504962483684942991901825630945192172569615315197380179725784890995272425725540116280790963840440997029631174839593901543605847943779244396456892241722525865445021992871950161607241233411046419417190370677571153995306627306214717346762200030962503098842488620873017268208248708664717717428171255137815330363463543928406/
920259778296285702256160771795799954576677363693418941141111995943840740934411466297879010389575702306404133743889506492805053211611825508752963264372791746840835537459712464118976396659544527733116028453642598276034295486053577194309318542051650397715714618272270088791629653619561570179532062719431200833207130037117]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 4406855319429603267673776689969923155397009165360x
+ 3560748519184563895670977523140270032129936776022200842483734803704121600
Torsion points:
O, [1253058599187054357506720, -78726485133579384492248348732072560],
[2071194031643725176051320, 1821646743252532904794221410969261840],
[1212003850085858205876320, -606001925042929102938160],
[1212009295258914776367200, -11544804047506325263664131366960],
[1212009295258914776367200, 11544802835497030004749354999760],
[1214166820087288832628320, 4126875053750200568582047303589840],
[1214166820087288832628320, -4126875054964367388669336136218160],
[1212117806189098707636320, -218521941769528761381087902298160],
[1212117806189098707636320, 218521940557410955191989194661840],
[1253058599187054357506720, 78726485132326325893061294374565840],
[2071194031643725176051320, -1821646743254604098825865136145313160]
Independent points of infinite order:
P1 = [-223879416206593763950280065780/96721, -35074060818706061072252850754574302899577460/30080231]
P2 = [144980967322250731539395369909736320/389377248001, 341158496419883387071926937037921047966568309509541840/242971792129872001]
P3 = [-191857259898361449902895357432172710099786309430305864593053919683007333540191080780442069755313231483440446247042096633212499220/
114075377580655359766122326656171471835310642513803394596779151940644910443120922324668440816417599774529,
-3037474280273287064510309386724131264635789468501852944937028558611533291337629485057824281885990398520799669481050993065849143219414233759662281428012608428418930890516288614984873678524335220/
1218394338755526045743513021142737377253446627527428139537298385854478672965079995827185216772070164553063190246654186444212549351708129091135591185046715167]
AttarBashi - Dujella - Petricevic - Voznyy (2022)
y2 + xy = x3 - 14741118961739511705641192699834935540932667740x
+ 967522895853302720135584307260582494591336007031122183018840265763600
Torsion points:
O, [-73072470055388929458660, -40675743883066264874426832420061740],
[529007856549736407299220, -375781638725364827045380157127367080],
[529007856549736407299220, 375781638724835819188830420720067860],
[-584616163214482868488641/4, 584616163214482868488641/8],
[75976308243824343705912, -16914866093780220454334475548840028],
[75976308243824343705912, 16914866093704244146090651205134116],
[22509874744352768222760, -25438313294800579980103380168987420],
[22509874744352768222760, 25438313294778070105359027400764660],
[146391592372465149309000, 44122463572397809560932479715027940],
[-73072470055388929458660, 40675743883139337344482221349520400],
[146391592372465149309000, -44122463572544201153304944864336940]
Independent points of infinite order:
P1 = [1778041495765241879805549660/1681, 74509651938653481903770558120606232086580/68921]
P2 = [377218517252391658791519105900/4414201, 168950371390795482576255345991940632056165060/9274236301]
P3 = [138189836830890370814076746385559683323760625705292436844928008994979451558774747083466199839441153755939922068912843755882765394611877567024655590598947618587732021803307424209396429524213191666732750084/
1766523221300908200357270022577862579680667660356637188828920256189178594508263579363058587806463595088096510957252535563017485065617978936603372051857185563812762012781927069321225,
40194782012232637535973855270642856655893499898724460809045559398338324580078657295816576477102139762774264192039217066991963926223523845646999732508443796067609735171987725728414271147809527066414361464348404461590801760848854715905982243453634093618190036172815368490973509094246788196281826385744662568/
2347896919637046072795344098100374317885626245258975796862925922476547190344475602216135595643276588674974526743751693084591241766391530527408432383162219795573577270846579770917127349132117541828571868601762925011472834065711082047271923600095892233231703548317620657125]
AttarBashi - Voznyy (2022)
y2 + xy = x3 + 256117005123186717825112319371191588673479904800x
+ 275979805316101865244959315947405587519566450838840396998120034789983232
Torsion points:
O, [-522046645566462184946752, 261023322783231092473376],
[514155605716931279584704, -737281433229129125925235912140176352],
[514155605716931279584704, 737281433228614970319518980860591648],
[1460167136556841765538304, -1939886173600195021933552832482846752],
[19628079555584342791104, -530107962788447532779866226637853152],
[19628079555584342791104, 530107962788427904700310642295062048],
[-358279554773945989594176, -371790312165835288501416907669389792],
[6034307872113223978362984, -14884486748854649515413729993240681672],
[6034307872113223978362984, 14884486748848615207541616769262318688],
[1460167136556841765538304, 1939886173598734854796995990717308448],
[-358279554773945989594176, 371790312166193568056190853658983968]
Independent points of infinite order:
P1 = [-61822719994965177256674020600156498496/144643797972025, -517311373683743461701448898725823664291959341096380908448/1739601306230960409875]
P2 = [32348165410671785229090478580312606774099243631567536863808/576540464639856416084337087731900929,
235959547250642068580276290085946044339260884667472512060287523173838501104961044985247840/437768683780866590660615875037336159798389226343795967]
P3 = [1212541715423276089279896237098597143867126819034306849483893442073373879858217665115086252035010143674518734571793061413230851222347144341490033467301093856478154177684063177633656553638526486976/
1029821137067142512339060006398079431796577478818065036993276068375121285217445822488351103793471837589026251829500877984355351615585932103885436348847232943452191703013369,
49127515075500680977734512515826326249910870002038210549671060671883348496158721667518317839676985013968267313820390265002089458601476767344499412362476269218815765279294373068672469379738523255516094625745283159236261481181181833945002143481070999464398801758816567446779312394726213239280544/
33047811301098200547396164697601566035198004698187246725184544759607351824387773508624746397132702167057028005728949901564389272700231616302105110075520843597043473772228508018246087982161635340320594385449617482473840980836256461854324546585371990059216653]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 5788818139125574019335163180113680446093110760x
+ 169524695292484859576269169711693496066477051086381253164135314231872
Torsion points:
O, [43928042416620885812688, -21964021208310442906344],
[44375918006218177579984, -163139799946885229539899280437992],
[44375918006218177579984, 163139799902509311533681102858008],
[48741985897564623418384, -1779465204296905483333661498551592],
[104846924179839454684624, -26742369258872934579618706177938152],
[43931335197741471563944, -1445475809873902267067642371112],
[43969711485763716101584, -15402893497492917562084314473192],
[43969711485763716101584, 15402893453523206076320598371608],
[104846924179839454684624, 26742369258768087655438866723253528],
[48741985897564623418384, 1779465204248163497436096875133208],
[43931335197741471563944, 1445475765942567069326170807168]
Independent points of infinite order:
P1 = [2704435968186797545263019059025445008/85696288758441, 3390782058791544179028200866664147158064286232652432824/793310169487014019989]
P2 = [585089996938114115506958862615335522946002069884749136/13319743982301654916605268357729,
502111797906539363828838337139763979127655699736191408607051140872208154264/48612036583501778950581754744476533160001884433]
P3 = [3948351011824700488504924627576029310866342400533660525060142196630428780132874007680373083951985971613674125398153432222657823074501242369433709435970978205166259044766425718340998718106227637694821788447281917171024284130937943612701756247557799363774595000852612226131859898441471358797479279581149085594569546004384/
89713919449631307164659748482697172809418661439814160821075894215900843239856981090915842527940453589823853919583741426515655424389105044614410213271474370120796744528975913538751366633991527953203997321895504674196388670632598585454696322617439807587751662847902503701718158466133825216699837601,
25665924897433189423599463876862677920289378085836739602486682615296999597050608720002273374767678132031056131731584979873791960720698351286631090603557111008705141791221772263289928387774563463092007603362455717591696712533118768929404570473124172397395805491619962834517766729153955710340562412540181035840707385899601345556307059446792873985611586044912551712238755059956920215378703063813635435120437155204101458827772683491577553450618407301992639955598022072196744623208/
849747207453230705422858814116636072721158176081011332512156274960877991220586331061198763632407305338179882422893490728561519721763491662379296673850994359247310031675517269793570281039402424590534972194440188813325044837974002380149570789216177750982289100866680111381612645132721263383313496458998596920730781945912461415114048120239354344546404834153391599200146230501903238733849832773818732922529839836344220414669618906945869210090635151]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 78045321400727555345570108079456705602093720x
+ 265380142832192019977975963296507783569105668978137971681026574912
Torsion points:
O, [5100598722888742670128, -2550299361444371335064],
[5679623176001023849264, -72980061019403048859880750836632],
[5045821035138501938992, -6751722960863312501176886757272],
[5045821035138501938992, 6751722955817491466038384818280],
[5105780878943006953264, -653157331236939468169910388632],
[5105780878943006953264, 653157326131158589226903435368],
[5679623176001023849264, 72980061013723425683879726987368],
[193491532846149865264, -500286196179067452791691384948632],
[5099987243465315437264, -62341154463054895733580984632],
[5099987243465315437264, 62341149363067652268265547368],
[193491532846149865264, 500286196178873961258845235083368]
Independent points of infinite order:
P1 = [48311911272366522913371316305266740967887048197497470956948846199254256/10008800239426252683328281879563585070849888575929,
1061869684132479974548190033699565760557720792367456977075292557445143825183636774809618779700769257161144/31664528984903947425772867065848142343987162338839175884866848341857635283]
P2 = [103856380248234455731458311085637670765703472660096290446933600042924540374594057182288304/1720397016193505972866091373658939099875698836057936795460386781281,
33129611697256178727477766143200475194138844912257674288247678113386502816980608233543594291866064340488224216556546712994458469766888/2256539920212352333476821559846006499703574490560711783467378849487110100813102887681966531840674321]
P3 = [1096252585802362671860786688947417262592111688377535635623156222190149552240990769482928/207466495354742316575825402906890240871966528405668042956583756489,
2157782562702784120840611389856474997218358524220021328704503519401540587583726261427112094450696377787042788898188552660445132296/94497856169384293101421153053206783781340186895013951214511166368542805309965627070299400540623237]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - x2 + 24877400682900192183904403735809356254630062x
+ 147130337457583497299094108273771234359789356460909853185104449617
Torsion points:
O, [-3766441748455241098719, 1883220874227620549359],
[4445479525912890176313, -587856411464835723646469833886657],
[4445479525912890176313, 587856411460390244120556943710343],
[12652697226232089263685, -1577173518625992583623319633065149],
[340695119098076517937, -394519317659760000280563876914753],
[340695119098076517937, 394519317659419305161465800396815],
[12652697226232089263685, 1577173518613339886397087543801463],
[52490071198177096349313, -12086107256541917929387941743792657],
[-2567724524719872902937, -257531513728374601917468328994657],
[52490071198177096349313, 12086107256489427858189764647443343],
[-2567724524719872902937, 257531513730942326442188201897593]
Independent points of infinite order:
P1 = [5997791405509834879423314570487627267525024476667934882314487029553051258782003506368953/230366341292544755642670760221624780858465849261051573292318886281,
474845876825865646503249825536390678437456141611206931728245881668703726975022337519486178386045159784043158760330045962156796719147/110567766615738609339048417208434402889623757852246684257846888568551288135584908862970151575899429]
P2 = [2826969158411765740428574895816907557550195537558280861752963178244396701596189232508724735560052228369825/9775248450742553315808334675903184975415202996153363231493403206482750697616462721,
150330640466128059034289422928820966096119004184456067998731923948920546423238377956097384602483713446180482886881424361105477669429368276919550266366655976367/966477407938944160546717362393652028474905997141058901189187999800242927894261322250801023945002541369099023618649736680769]
P3 = [9122790742396672522527979624893868701106746155977600869399015327282397600761397291371943971712267802083547445456711585288255522964468595419669965689534397038742453687840172777060497/391699793270099359699912989000143587584351301530490055539365224777603316034154312290307729270410393589000492823985618959353066903426136866452155946282564858321,
28335669882811239696610402970392495400795468723759008723679991309694073034241924587609955549540564595430232684702651265167077865998841088548154246678932397874376224981443836366910754665198935285789775834728267682858620070939199003698771674033365713429182050566581224726487/
7752290052496272883581730410548498516750784674778290249113162124740830867012659678519338912135482270436780894124657771826945372372483395782774414597527986677544350417052645510698589981265493468797551250504623881087089342733015250151257881]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 1982226298251304070279743993755101470518151575x
- 19293575444807996492238113414853368773764461994084770598936787813143
Torsion points:
O, [48763532656426162534998, -24381766328213081267499],
[-23009861112795300390546, -3759590413245392481626573845294227],
[-23009861112795300390546, 3759590413268402342739369145684773],
[72631139826625408446054, -14828514693189401028944288863502427],
[72631139826625408446054, 14828514693116769889117663455056373],
[264596649751788280095354, 134093230431181609810819005283082973],
[264596649751788280095354, -134093230431446206460570793563178327],
[-36226898957540374757706, 2229928556215700403588856670726613],
[-36226898957540374757706, -2229928556179473504631316295968907],
[-11848232166111599976036, -1590295550359281946661849969006817],
[-11848232166111599976036, 1590295550371130178827961568982853]
Independent points of infinite order:
P1 = [1070119993861117480797868843958811201463615498552285834294872717648319172506834726459398144700680603214382389541202494868006/100863508041312251474500403048190548958884587013488490062851574165672159080433947689933200504383289,
35006193583678430037158604203802522010594202974865316375895609165189880433667888129101204029198673135980378207005839645844554979935992500924258847438132419541317688371509521058437649201/1012980542237621881303922510371951543981593735229080536558547834211415151267433779660402691974569425995612602551371317687792153711858482826092009837]
P2 = [-929313467809153949508853288042711211100624039191269302892581330372478075238943610275897071348584231265068036664437842170826935415460417141538939828554947543389648634/38165291570373555332197297623094058732878812949636588120335435522853334312845322414883387480632939947185120239761639686361579751797828765637689,
-28426540529671891331610104588615427455429252812435013950229499144962710925721234415735323093316044017127661330602035626956389472164236139318702622313681456206406707758689511629606605124364209851067280086971528234875256214770290971271630788157628369/
7455948110563023875753045094880946243814245886690392092705901053526223438144177105675500137586485913044315776842773863287044569173921176602098720937717782200251872517685008085190945572326385595392541334643383386387]
P3 = [11473396028650056603297538321212685380975456803862917595799222860803846542911556681890321735940977881025146982697275355506936012452132830536117854514753028088296467972511816403961969186291104430001466288977471136877732701816506216337394376713042959735481864751760076728551148358/
235238096460387790684474333005136572979016976247158417241992015504642242616580727942335351053684057278334446745112169223780195519291133294227411409454828328684172281856427981803832132792939536474562174068243184612325799432791041039216427087555923751779089,
819535873270369565439429708249255883203597371009577292558792799275068053885609665793004002085665613176427279466509201024655891283277233917330568963737778016548649703710448197646141687199171953603118211912689693636540964064637198874894734779822631397493268019055619313320349500317159585915895072910279460955280348872076537667366421367576530882772668448377177384373404842481665603322028319414841280997307807192456445/
3607958094403142351299602233530435677614716158310780178847343081631538198730036485400251110943639193205071763636451835190458593363169652845211784244553802458867126659009167101338957612362703608087266591591770049400120712196722727102366909625890903639411104042066172981236062989749481377822805496422947335941589517364812705950323106320643684317161444712513127084152142718383700984313]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 1921415482008916032062216184284031548166205x
+ 1025325709790380185016255099147502663264614595275495720079556977
Torsion points:
O, [-1600623176871718961182, 800311588435859480591],
[800328338883613056842, 439452154305896364514173224543],
[800328338883613056842, -439452155106224703397786281385],
[858475888977052209734, -2918413579685476934339441396077],
[743555738514170483954, -2782028457003733958561212055137],
[743555738514170483954, 2782028456260178220047041571183],
[858475888977052209734, 2918413578827001045362389186343],
[1675949834730737769164, -50125350870526573587830200189627],
[158705292414725715074, 26914387839209495909479096237583],
[158705292414725715074, -26914387839368201201893821952657],
[1675949834730737769164, 50125350868850623753099462420463]
Independent points of infinite order:
P1 = [260192982952017408355490811365762/430004128009, 2587976296214525518339960373750531442766537416773/281973916929517723]
P2 = [132138269306090578268155161388765829419958873148524085845207952171270551279267/6953406160761097193123507814847497355648646084445195844,
47908999471520399043009159957757230926383762186259479653864097783526292402771801737331045117697058400378720300429377/18335653661112570319934656956883629187856110795081841065124959021525758123588655672]
P3 = [12070270324010921884460120465204201587340263061150833649731649047551886767564907854641452229466158331149/13956364234344812911201825765737249915808212291861641196019622809991432008832574736,
5334973808534818212636661903350722419198762131909218903325553953975132903416111590090967862180188419598810931635724509769899816565515544298491833153469707/1648763796931088790571832170083690932951172575769875404656108372172722725308206532027174136451548917089297660114550533649984]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 2384124108113174080248981682513137317311534475x
+ 44925260742461494300311511310637222202510201736296436257947683849457
Torsion points:
O, [-56397725242246151094402, 28198862621123075547201],
[33192667339581968568514, -1536212428561325032737151485647147],
[28207157178253033511542, -344593455801188829499881439163015],
[28207157178253033511542, 344593455772981672321628405651473],
[-4270958025438605982626, -7418210554986513174360608554865567],
[80921094081705703639084, -19541973717126569327563795362005597],
[80921094081705703639084, 19541973717045648233482089658366513],
[23499079795734753418894, -1369995837324965651710546735506287],
[23499079795734753418894, 1369995837301466571914811982087393],
[33192667339581968568514, 1536212428528132365397569517078633],
[-4270958025438605982626, 7418210554990784132386047160848193]
Independent points of infinite order:
P1 = [-53113654366335506784633666896479973474817599279/944869945556863098347584, -1054783400744577745923705441000393618508647229931992215586438990855811/918455359471646658368778498430632448]
P2 = [26144536355112309880167631259252443936064989292110628586675106/936740509148883612358153446284685721969,
10150629695998874893847715852324724852238542476741485493202288932366959130657140967337412401/28670083144166694912603835717501671363933209389654963132297]
P3 = [178609543560373014403879514690880452647342937443726093123299191081881710507060888707525768745436737196040837230537222141150095888528034116427633133759606538470948468369513300136674877429316245192464289306063849552644521/
7899397198525940980515188148288245191062679506230855484955444585089275948473957475586539357957754865940045585937126915434881390510501336510997618113687444765311600708590141682251219051553266419264,
1127340755568849544691137010177291114904714883708703154789089140978114929175978204256686966505800541870910418624236630432327598895338999811705510796470690948628710483758112513052540935416622684621922235610351748479395387042015576319488473010883400735650947276820175954408149766395299588806478098889627486066318556570822215668271/
702086993250589150926881405801861637192280099728618608058739603628959287537550983310633656175841863857555977164180706340253252367638255817403615583730604228039581123903171678533496403987973385546433169644550850649405485330979665308638098716516460469743428945307306286516912417033925091070310912]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - x2 + 6243360541011080452572024099032852332137359917x
+ 13325280754594062233148680383185541801288022154899202996691932592083827
Torsion points:
O, [-228304442286445265261829, 114152221143222632630914],
[174947483492199381986043, -140613272714368650740825251822351742],
[174947483492199381986043, 140613272714193703257333052440365698],
[483195876778896512495355, -359385276717584895721924061071686014],
[243755496234556484347, -115441771566985635873232003787601278],
[243755496234556484347, 115441771566985392117735769231116930],
[483195876778896512495355, 359385276717101699845145164559190658],
[-154431882467034353734917, -93155939185924194477169848503711102],
[1972947498105326900323803, -2775857400820628940499959106011924062],
[1972947498105326900323803, 2775857400818655993001853779111600258],
[-154431882467034353734917, 93155939186078626359636882857446018]
Independent points of infinite order:
P1 = [-6674498415134747804268346448899317/47855500081, -1033259486772384169273386181425596761562387876943058/10468821342219479]
P2 = [36379240244296564262199272546006339405026099382477590725344365457920467/128516459618044676636444412553522060679667219721,
8954451902112695580495943882703043263245526702761905424086378602695525194356365390186998981490396406562998/46072112882175465191668305416586160663024329414752714183931720113509019]
P3 = [1440919804271386164074554115644365536036184152854923212217385535506271070035128169079944239590535182905137658337510721537430273531178590243670258596700781551862239292624955230648555037572260265892378280493755477960282459541867/
3589794203830650061912870948744621376070653882019620979868891310814216115580890504075769182908125282736506687957617605525922873357002023595709985089533402784589402965890196965160037026818173428991880964,
61025173148713202372005002678651042260360243954012774566973116033087570088312820636149979503618453145218404191752280380981880932060411794604980707594473380006866324210878557436308389806238704269220617361521582662167454171690891450196074025892352431547205544461542134995608884982274167600376369547797780130495751136600195300626078235062671/
215082129641893794512310377027314051410234273148009786718144972995262918285592412632751811423154109410081995503712830273097323882602919222757015137489525927845662281700036094537019980262264791337866214037288282920982545959206029437577760715791046301950628600313346750714766354020016619642760896945816312]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 695897593102986130130636574541912449195737040100x
+ 223442671503392883216458145117085002875208400708254711787127046088010000
Torsion points:
O, [1926513472945134705278399/4, -1926513472945134705278399/8],
[481877701045337161994312, -299758162041579922408835973171748],
[481877701045337161994312, 299758161559702221363498811177436],
[488755013429291911819400, -8587594071128970737304384381120100],
[699331954037171637899600, -280710094661688673286259790276499500],
[481628653793590607220800, -368201886942120554877615720100],
[699331954037171637899600, 280710094660989341332222618638599900],
[481637091393952798421000, -10511388846531312205322378980900],
[481637091393952798421000, 10511388364894220811369580559900],
[488755013429291911819400, 8587594070640215723875092469300700],
[481628653793590607220800, 368201405313466761287008499300]
Independent points of infinite order:
P1 = [1517461032262334684266158934603850/3150689161, 11206423225477376605102795946640256982784650/176851333296091]
P2 = [43855994509152788600312637284279886634685638880/78574630493177498890681,
2078730931861891503306309170807418118262311883141891542237128604494380/22025385634586399367422789698038829]
P3 = [460463210053359149336744872390665869452143723809244923098130217199999336180944615997717133114569379014993508072681050/
956054999445058034416763185644265054541335014983160944643692654993404806446673928470098604489,
204958108932963237630749846155930146926974653293800617250885779258358985209715137018384839254998352629481756037766703141781799860110206305085640203317366496632119730200/
29561353531158666771011945645856172777181134654798320119709594444765360774028106567822893177812634732501402192638175571682651507449909600763]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 240922288728631925704167509609038572556986835060x
+ 45254225108501490237660943230699716765488982744815985104269757138877072
Torsion points:
O, [300754815535066415702888, -150377407767533207851444],
[909510428837030664218024, -760584185701952828956535335139152372],
[126289665794599464876392, -129778402385951511081083810849440180],
[126289665794599464876392, 129778402385825221415289211384563788],
[350755321171250488554344, -62471036049737369124231173799223732],
[350755321171250488554344, 62471036049386613803059923310669388],
[909510428837030664218024, 760584185701043318527698304474934348],
[-387131385525882374167936, -283730768630870166121736174527142452],
[256506088889557431264104, -18251165967278839906182685189902772],
[256506088889557431264104, 18251165967022333817293127758638668],
[-387131385525882374167936, 283730768631257297507262056901310388]
Independent points of infinite order:
P1 = [174708589419649845441074336336/24649, 72854309829777445455904096451506792634466164/3869893]
P2 = [331012416376622032766057067694504/17464041, 6020356352014996633951237541705440823526497259332/72982227339]
P3 = [391857483160287192548226842884596063197230671429397850283060044847157608564040839918628578722896167094342003415252955803382677119912337534710622992132995291065343746454356694072578816130278491848831979189723685716491642510270399606302790940081588824451894162543767145312232/
1101811008493452391364734372398015407201390440466831759920519967598373888470444292046641440003149297776861367030437675872404556262267727947922937241373908052170384567839245323251198702790532805740657233612809215789790034295267955364759813673161825489,
2468362477786380607170813734605081501818669390789744824007690041456097103952964883323262046165658573653952792048556398665846198918864984999334331153032823891260357471741083097504365182434406778148160241741223458943855169484878032460177485031473371527889153833996460879480101989659985123504908733547021106290340594557386556004425934148932669295526292358233235406509902880294298898884744935886140222959327662228/
36573006301802830570371023308650207786727705074381497474984502081801192753177978970871782871656860287223938982165357196094132638129185446912968652169625270118119862634167710952122667162095252576094057174149575738923604232724054315845719445573184359820534359177486072698141184883894504678210616829039449732473946140631335093872020440495985696198303369313840313958615209436263]
AttarBashi - Rathbun - Voznyy (2022)
y2 + xy = x3 - 5381248262567820814094243318417065585563356x
+ 7547887335280632600150185408937631611708820679540826529170677520
Torsion points:
O, [-11343883577642158596545/4, 11343883577642158596545/8],
[1493803288992484877368, 53317030496505881452440182488996],
[1493803288992484877368, -53317030497999684741432667366364],
[3016709705770405256776, -136995996739455950633376072537260],
[-1491352643718507851012, -110707994128947880144876017440684],
[11106234984183535706548, 1147919601537840349271267874317716],
[-1491352643718507851012, 110707994130439232788594525291696],
[367167250302796721704, -74977114386158621549163818031260],
[367167250302796721704, 74977114385791454298861021309556],
[3016709705770405256776, 136995996736439240927605667280484],
[11106234984183535706548, -1147919601548946584255451410024264]
Independent points of infinite order:
P1 = [1543434914326047224980311794781294424/316922348149969, 1755791968850662957120512985954850847032121749222226628/5641950838460719078297]
P2 = [15242033014216583127806569859523267633419224515653748319504758473042390883105295739999755791007874418591280522335494074946102977547017963429094378966951516609801905764332990047441506000140072582025948605686926695432665449916/
3846484983201145772453646521990925861359206547897012430477979770654009773645289744732743789718171811349813971196796688793364155969591994550803303155759756249002877939496537843570123956997806853078329329,
52507490629474275077849174045140473023842514399978663301117669084567684430596927396247349021081927657167287243406119946820319477156377869237917088457023772153654341281635104440489225676859977600211735230028052386046246608074858148227596957576467584456517370246894501726743330289821888912199311256905097677805269517997194137105455324148/
238559140783329601018105204356934501063078687790698925926288773848995136470395154222344980571309387942198297433048990114718029835011291975830083640778497141974687477989373196628755594099726083698407490101104892127704550495680633391481580430962368935065145028645954687393771195657655732393021542863164233]
P3 = [-4937847826311178762710462679724502895089824801424811078736452658787512061604808816545862195255207317794671659346768133182229729466086346676231670954506595173695919227987620300415844864906759802967086089173070039407654639843623199361002242550957596127859361488500761100925264479759592043686591774412097459518288031120498865368588146977776084982814900583837842705040337955402067761977478467127125683212479462887406196845/
2182872598029177833875499224739264564520461925243884969656315001142813574030089822148852421194338574912927942889893703334617177637722489827038405366216501407027520295841730377547995406154330286582469465670932320103930673449272595528179753783407319219987500312473884736787108590406486720671778551250905823538664882884511566462728435972878096437398500886115748718544299358919833002108655053005170884,
-291073660662225557607939921670154543068229298053262603993482985077380970315238322028406398904339058271898075273596622746016051544505504518957854307614595636538577023640272031808377727954418694533380243500007168246580988229629712056636137821717298163387954467689498788249737630005188893228593832875193960091963481540957878062499986488080536481319209460220927470074226419583824946185548564383310390188503080538423161590071363803224878600794282340078810505636007625115194940669828192784653482433268020194976902416221377212214079680892070575465974936228351010653435777710956550698850972531806241779717564791865097749066935118068725/
3225095532728429734935106792310981665788229538353929461125384289435803448956002790085018812976036549927903442995504806061597229580445359936847096512020428249813309974847743501540932217618054127889901781997409192283907728674830585418302024787775738364631697746435069543245315924433714314179106588217001794338742204408637813911706943335449649247322216781651210351620141449263621432486894599252270571934379036158116607805965129285196105854512802242125908697095622441453821009770337269417295550960701951858057097911417209807757199278060179956780081974310821080088246924209570623604197834022528363848]
AttarBashi - Voznyy (2022)
y2 + xy + y = x3 - x2 - 30459406645533579249308391742202557092048677x
+ 65371842716385090609911203340722087244870278349232942285238392029
Torsion points:
O, [-6380095849159391755713, 3190047924579695877856],
[3193694543775327244287, -25854974847109751178582588122144],
[3193694543775327244287, 25854974843916056634807260877856],
[2376149217376708244287, -80073017636015924708842404122144],
[2376149217376708244287, 80073017633639775491465695877856],
[4087571717402684254287, 95723420629034667667466208477856],
[4087571717402684254287, -95723420633122239384868892732144],
[-1171754983148493318213, 315363240140672671860175984940356],
[11218111496676280794687, 1065565375228839291730682071941856],
[-1171754983148493318213, -315363240139500916877027491622144],
[11218111496676280794687, -1065565375240057403227358352736544]
Independent points of infinite order:
P1 = [4850913146890701728974282008751/1591611025, 1850088138756591177310096969027461396977661216/63497321842375]
P2 = [159208137196539586474928328315406982163141566911461141536315997247898986266980586936433238591352831670857/
626304403027278157543397797076118783902859524703121804753551407770776120416408796361,
119003729278841492447109977406401658506717173621478301566176884363553657243260349918691991212128787118470513184515104151843989880281358019261934599007884899054/
495653522904960881055985636260275555224005054315484075744298203963125917903189757940677552573839193124867136392555887524692859]
P3 = [-1071133005079626221787598623376548791127297222015612725690344502175304980032428237187217710246255141767242646461521694800345623096643595064229753129381269560154457/
2900050611841386176410985863126645538679413202430161685895745087505058905321647814612355374863155769718549495893614910188143652966463555800089,
-43215775883303865125468683834808755626256896065976494024630778251031871855452863323076863106222141005947257710429056034799884453632920351904734471875718047358085165176774052244326132045253765055038571233381204523034519432963763611282296534559072/
156173867721344026800749449969775992327928489491462639006781215294158313342068075137777697226207467460778145566074896472025708150651300221809327814372070084152873277045562426861959010193846293670978443695551538563]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 1305052802901496677989790686922835904905903650x
+ 18139652570419009187531199103616249940941047173851530819344966322500
Torsion points:
O, [21184359920309036067300, -10592179960154518033650],
[14759524296101135067300, 1446707052989366535331446706966350],
[14759524296101135067300, -1446707053004126059627547842033650],
[-23147899911846471745200, -5995469498188461165268324205533650],
[22787562321109136067300, -483369695225752174141144618033650],
[22787562321109136067300, 483369695202964611820035481966350],
[46931896711353214077300, 7762949335005204107901609700966350],
[46931896711353214077300, -7762949335052136004612962915043650],
[20253243100314437129700, -125923706915080963046135735416050],
[20253243100314437129700, 125923706894827719945821298286350],
[-23147899911846471745200, 5995469498211609065180170677278850]
Independent points of infinite order:
P1 = [93310146488644450219688144130932718831300/3234005387759415481, 12343710072783606409345510390029681335988569087751079973056650/5815822035797258557414167379]
P2 = [119660189105820584954728083246945487231530623453719250013661050/6408883236463982687544523942418337292321,
272380564041998134087756939897437360711207873816217298966425936397813579008058536529190566850/513066358189636725872943031500439391665825921292655921768881]
P3 = [11538992048708625803245924784197731439162771507994339163160618006378517343479686871484031102019751031213374894936591716513480915878852555113534072183431942956446660/
512240529977558563256722818700493801737087348256439671600615621814146745389674617795323147087685223960650461400401665682168142085423289411641,
4812342128522797715514103766015078022307758774938210837643965894870950964860866130681422291292876178646346775024366188519141985008233848603011433221953957853667151101515308954292427408926841727085062270538316585090762731857043131247170267468810/
11593402319854185012057033574637951391620221609114529063142589211926452964202321251311493079049687499703957468379207910536357339034904009169807867500771282913020544668643104754966710587148235350574308468549297939]
AttarBashi - Voznyy (2022)
y2 + xy = x3 - 3948000654929348349164472343150678966931036490x
+ 95474457457793841652851408729175399428715843175654476717046671424292
Torsion points:
O, [36508878376263850509108, -18254439188131925254554],
[29388910261930039825524, -2197830467478898748430771282948762],
[29388910261930039825524, 2197830467449509838168841243123238],
[35789871977060457781044, 140716133653990941234566186666598],
[68296730574863543357124, -12016869604177936934703434021757162],
[38103636827775818703924, -602871947522626544944984085585562],
[38103636827775818703924, 602871947484522908117208266881638],
[68296730574863543357124, 12016869604109640204128570478400038],
[-33996677631715214031096, -13798582675772076357211584512226522],
[35789871977060457781044, -140716133689780813211626644447642],
[-33996677631715214031096, 13798582675806073034843299726257618]
Independent points of infinite order:
P1 = [361243379744142215129852527239924/3120898225, 6012669857285842283310181552043596122238190252502/174348979339625]
P2 = [623469207553150775662270048809381320413608410155609936677195292136387663461845707340323692030005431116039279689898068525791906685762155093267639547990655145700906127415961480948/
29053764185031846239953827338951812744909563651903616922744097286824134536915329701549359019205308949736990206420138729104137804572870023083273702232155249,
22496323674846710832763682668621469660048398874917815287094923055950651929969255764628735349014611612695806707430246106839626611333028643482538521703141762647528877078220359502136667681752669796849575911876056145020554425119207410400957698636264718789238259190302870/
4952261975639611725168252400601100954299595114961655640328597263983630645562373445673780306231315911571560033944711537819972265326926642456732422130887487513155156739224421208539682551835525483661103410691604438686382430338830850057]
P3 = [11003135127375533667284155005327273502789464167435956102346709640200948234424490589853430474592315209239731545569796479961953629050549640797389166246242574904519274830535126916297578510255866028970221671109631239004445928353126090517100879322043112055776711148021570785060311238334120937628604166608328468/
15167523715174927989066199782521256985564678273109667417036387039734731523960696397053822231376879333142924834288516343363712738149940858982761010010327139465513478089918411089647726840810594767222757205244042164255970284477163538828485868117873165845033779390527448098066549736409,
1149990388888748221965328246499964849646061085509687250830024729719371365565313698875573631649034829548030669567777022083511172157015842352687375677084418672789476275508213539822454517505320121367368243751935187881169036433770770848938999296446746231626774129378746445444689028492297181136227807007991175420479572249099606203389419426696555123773444908716538103887641556761210086572422450694140249808942605368179827216698587774006247333625663625819138957170/
1867979148155268117146358320198832299903747970382135866480406897803256568200650355697950764228164548707594876539327480850916581883142282940732360529543681140235050315488298806020204541117907608343985459485794850355015425141489022434778024934857363477697268561531955301699015074117602965118935455058695390337042785695542048955942398784131389060484519816710876043450961545946100864679192109810469638480236094226812867433827]
| High rank curves with prescribed torsion | Andrej Dujella home page |