Torsion group Z/12Z, rank = 3


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 = [27275829940946961/64, 33921871382353791771/512]
P3 = [4521513405555635346/10609, 1468974979278800313313851/1092727]

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 = [18544806878885287711971/1100401, 2525379012189745270144071508062566/1154320649]

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 = [-15070131646150604/1369, 5008197756706206553478374/50653]
P2 = [1305969401629420645413875956474459/135245046358958659876,
      125215764064045915446675410093970777956539489160617/1572830964762693483691882033624]
P3 = [8596121480700533171754008730628345610596/182983633308366809525339769,
      -778297336576372972360132509987186690647808138781882441806074/2475246014974504063315049749385456744397]

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 = [971884421153652756/2209, -953816053002038608832905686/103823]
P2 = [-1445919103291960094892146259148929612/43044934449268585976041,
      2181937720132826143505166600670084313929765306151289006/8930650141245625667807035924300661]
P3 = [3303810668524154059063665635722308638369716/23638176679150615390038568809,
      -5760535649413474833654266012598328202719690849743763365679890734/3634301568855472815673105506495008719239627]

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 = [83288442894925642190814618350197590021106984/771398033023790933978902689, 
      755415560956576763580253044892165310840750846759651049456818988916/21424850033510213942168510789477826496113]

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 = [934979980823610014110524/101223721, -73611242501121629122133119338573732/1018411856981]
P2 = [29144405764786543092556/3115225, 542507884099447715383123143294076/5498372125]
P3 = [2605003565366657759223498174554534758058347128274/41617311272936546697245333139121, 
      4095151476202076774705578877962300169604722094348041446777141729706468282/268479436819195442271208844400534452510842048919]

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 = [968981543630496886/25, 1048793083256593049745704201/125]
P2 = [10648645639246599670/9, -34619591821050285851318539505/27]
P3 = [34204154008370590456723994525799331321166734065284830259009029184489577850/
      994834477533461934889468138733951425005969057062180045601,
      313686463773722413950416319252090786262760797866564048418159325795873179686906265218417471114531233033546590385/
      31378071047114376532756775949199573839617764210617741655836490191558965284553473828401]]

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 = [902884410787325961932982598928281378050647838767865965783405167068861564713452160930070381872026164377109372703995257528060773360597437948867826438058871465270531832026583/
      423351634249949322663066331402488896199458918600208730364929495664380678413194021509643700808950452906587144351356777773852044322463390088104584985469444, 
      27129718687582730275261189721952550765909547364002475761409877212477311640661540426819196396934544605888800966219633113297118744957698968198436309564424740812970880135454954449288739619715463791140533990552174089208479449218299551883987640015856988360947309/
      8710676015396243824782467449258040661541270092684566073725276608504991773459396086042534897505744714517864719813444254766813172207946594779377566315061285418686923238378703894894222935777029125039233498768102258912390022035269128

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]
    

High rank curves with prescribed torsion Andrej Dujella home page