Dujella - Lecacheux (2002)
y2 = x3 + x2 - 11849634571550798667743047864720x
+ 15613761915399875450490670165233536220551598068
Torsion points:
O, [2106658439922331, 0], [3316780242030356, 113133244154085840132450],
[3316780242030356, -113133244154085840132450],
[1709475188895326, 18780687692370615107460],
[-1580291531282794, 174336293807843204446500],
[-1580291531282794, -174336293807843204446500],
[1709475188895326, -18780687692370615107460]
Independent points of infinite order:
P1 = [1408739633544836, 41429730450937797313410]
P2 = [-218498788069669, 134879432087724391611000]
P3 = [740396620160686, 85124664142477399663860]
P4 = [1278614340522956, 50527198607648165081250]
P5 = [1650944116469206, 23463118324372658662500]
Dujella - Lecacheux (2003)
y2 + xy = x3 - 304241169811532712979315990x
+ 2065986446448965089594679105215890328100
Torsion points:
O, [18327955577780, -51443996747795938990],
[3624507249380, -31794301049998014790], [3624507249380, 31794297425490765410],
[18327955577780, 51443978419840361210], [10096048933580, 4842002440093973210],
[10096048933580, -4842012536142906790], [-80665991468641/4, 80665991468641/8]
Independent points of infinite order:
P1 = [10070073195332, 4839954434963286146]
P2 = [9371130643052, 6152839124497660826]
P3 = [9726832852580, 5191480617042218210]
P4 = [12667127971346, 15641060126117318462]
P5 = [63419650125532, 487696851536311240522]
Dujella - Lecacheux (2005)
y2 + xy = x3 - 476388667785943389435012002002520620x +
+ 126543502804781110382893072580356730547061880243200400
Torsion points:
O, [493667139543209240, -108057069556113274863099820],
[493667139543209240, 108057069062446135319890580], [1289643093590974640, 1287276137791469192822348180],
[411460148407645400, 13730593880654560995960980], [411460148407645400, -13730594292114709403606380],
[1289643093590974640, -1287276139081112286413322820], [401992113591463640, -200996056795731820]
Independent points of infinite order:
P1 = [402532692356724440, 2212637731387190951391380]
P2 = [324782305006667480, 77974882314020296026529940]
P3 = [1390354700866905935/4, 434594151457905802575483565/8]
P4 = [882656384433521059082840/2337841, 79957957553437414478707133108477620/3574558889]
P5 = [323969654355843125370440/829921, 6039142065890653356117619477905580/756058031]
MacLeod (2012)
y2 + xy = x3 - 3561865423528009610395543810x +
+ 81454964632284157241813402084313871228100
Torsion points:
O, [36321858637220, -18160929318610],
[39035821525220, 43557132138191321390], [182221724405240, 2341587779512438706990],
[56220773709620, -242704319349797055010], [56220773709620, 242704263129023345390],
[39035821525220, -43557171174012846610], [182221724405240, -2341587961734163112230]
Independent points of infinite order:
P1 = [5949581008982, 245914531223693387432]
P2 = [-1195249703128, -292763685098693066518]
P3 = [71998581355220, 445232088662833121390]
P4 = [982331112925220, 30732830735127701753390]
P5 = [56005666625120, 240082528969829449490]
Dujella - Peral (2012)
y2 + xy = x3 - 480510101420343678511903884x +
+ 2444567252166483991593076470098546378640
Torsion points:
O, [-17323159448172, -74632298902171904220],
[2911609363932, -32713800070251167040], [-17323159448172, 74632316225331352392],
[2911609363932, 32713797158641803108], [74812439159615/4, -74812439159615/8],
[42554919910296, 243022828193040306756], [42554919910296, -243022870747960217052]
Independent points of infinite order:
P1 = [152142052528410, 1857687175181176518630]
P2 = [-17446157816898, -74280290007379818960]
P3 = [-13924080691168, -80222356449268800940]
P4 = [135431528216497152/49729, 377069596220028001934128980/11089567]
P5 = [255085146694101509910/6661561, 3446938201295351045754826491120/17193488941]
Dujella - Peral (2012)
y2 + xy = x3 - 4271691045320482126621379967109933780x +
+ 3405752246986521064914214812675778553292700806723712400
Torsion points:
O, [664292095093001960, -928031851917201703610528980],
[1815336257724085460, -1278099655521678025514386480], [664292095093001960, 928031851252909608517527020],
[1815336257724085460, 1278099653706341767790301020], [-2387132903893102040, 1193566451946551020],
[1193861295659147960, 86959002218509523776551020], [1193861295659147960, -86959003412370819435698980]
Independent points of infinite order:
P1 = [228562615660897960, 1562479976749216983222551020]
P2 = [2628972178002762280/9, 39891362539299541650001338340/27]
P3 = [13771595863068107064988/12769, 332774380360754013808140834100424/1442897]
P4 = [1812321581372356897960, 77152963252173815252239446551020]
P5 = [1985568691873065786080874868043200384143612539858960/953193451415560177888969926861601,
55419375596823882813941489864115564434831875747904523564094764380938876625980/29428733696013954912586729933306891107344982747599]
Dujella - Peral (2012)
y2 + xy = x3 - 15431325141995640971648011388750x +
+ 28075861328873003447771017200972297203151562500
Torsion points:
O, [6702248138813500, 475096986293999335425250],
[-310791823591340, 181222987504824626760490], [-4635516169602500, 2317758084801250],
[6702248138813500, -475096992996247474238750], [-310791823591340, -181222987194032803169150],
[2366819535999100, 69363039116735853921250], [2366819535999100, -69363041483555389920350]
Independent points of infinite order:
P1 = [-3933616698398660, -167064625300798315877150]
P2 = [-304174496034500, -180946218395393828126750]
P3 = [30125238846195629500/1089, 163781914453907721439422841250/35937]
P4 = [4704373642915683100/841, 8334771827186805028417366250/24389]
P5 = [3873097779952529057020/3129361, 577240587069060000283078461520850/5535839609]
Dujella - Peral (2012)
y2 + xy = x3 + 36206619016320507513893296274455378004840x +
+ 4164017008409107952186593775986362717428213475209847776897600
Torsion points:
O, [156291840727092030320, -3693315412233862929036112831960],
[156291840727092030320, 3693315412077571088309020801640],
[-23669649321485915080, 1814871361218248759825904571040],
[804202125944347841840, 23524285150866281051240886076520],
[804202125944347841840, -23524285151670483177185233918360],
[-23669649321485915080, -1814871361194579110504418655960],
[-92878370948454608080, 46439185474227304040]
Independent points of infinite order:
P1 = [-67064195467452854080, -1197589614369326142568015345960]
P2 = [-65897305576033403080, -1221450897422362864342649380960]
P3 = [-33136093288424303020, -1711107141606955142785711926220]
P4 = [-1199450455321992953655760/14641, -1426062696163063335753522082921519960/1771561]
P5 = [768239157666096330051444908236512975536/1218306864093433321,
22410342584682979788472958396439186031027846303718850846088/1344729822994914935632410869]
Dujella - Peral (2012)
y2 + xy = x3 - 65757608422928824814414058034068422990x +
+ 205242095780348539295058638592647749404597811660012388100
Torsion points:
O, [5054226848205421180, -1414039306655551068866231390],
[5054226848205421180, 1414039301601324220660810210], [10061040755942099140, -23708149465911097936036953350],
[4686603439366827580, -2343301719683413790], [4711749694270443580, -110927181243547634151829790],
[10061040755942099140, 23708149455850057180094854210], [4711749694270443580, 110927176531797939881386210]
Independent points of infinite order:
P1 = [4690074293979129580, 25268425953526489155394210]
P2 = [3287154859686661180, 4960406666627157383270928610]
P3 = [4691951723573631580, 33542898997926248710906210]
P4 = [610225905796845476925033352/129937201, 76089646070271390795437793082053265274/1481154154199]
P5 = [15080919944248669590143074202285722365730/2033873413244877232681,
1026866614433066076575338431243510157145935662081773735756840/91724611061139147195523546255829]
Dujella - Peral (2012)
y2 + xy = x3 - 19743860929325035502863459210x +
+ 4096735464261663217563807627752085945979172
Torsion points:
O, [-55832256650896, -2241659442641343641722],
[496544119254584, -10803657048771739616542], [-55832256650896, 2241659498473600292618],
[496544119254584, 10803656552227620361958], [-801810746064289/4, 801810746064289/8],
[117037435637684, -1840955102182875899242], [117037435637684, 1840954985145440261558]
Independent points of infinite order:
P1 = [64786343948084, 1757705489176705699958]
P2 = [23596343445404, 1908923949002165628518]
P3 = [-36402206521336, -2183396018286616851502]
P4 = [161860995539084, 2267502458684815282958]
P5 = [7071203454338, 1989340636071804829946]
Dujella - Peral (2012)
y2 + xy = x3 - 3311208879480661613210248501333720x +
+ 90685812410781204721505439347438829261545665934912
Torsion points:
O, [34897371938719664, -4199079831539765277150232],
[34897371938719664, 4199079796642393338430568], [101521894343920424, 28299837729476791710467048],
[-272534946734685569/4, 272534946734685569/8], [-5563403593857736, 10437203092192784495142368],
[101521894343920424, -28299837830998686054387472], [-5563403593857736, -10437203086629380901284632]
Independent points of infinite order:
P1 = [-38545427066733136, -12690504561982447160267032]
P2 = [938042469674528, 9358449831722316580767416]
P3 = [10694702454349364, 7516424878414658923610168]
P4 = [-67602742432698736, -2362041271545037246700632]
P5 = [54226730963098031073802/2241009, 16683461082499484751259653062651108/3354790473]
Dujella - MacLeod - Peral (2013)
y2 + xy = x3 - 14308480358642264809261681298200x
+ 20832355619626831304182830954139201872779240000
Torsion points:
O, [2183978504356400, -1091989252178200],
[2212368006468800, 2307895092736193421800], [2212368006468800, -2307897305104199890600],
[3106181689024880, -79731987895753504301080], [2184852459080900, -75561605897010200200],
[2184852459080900, 75559421044551119300], [3106181689024880, 79731984789571815276200]
Independent points of infinite order:
P1 = [1211191369036400, 72655671639587522661800]
P2 = [2184005996951920, 5205662428129388200]
P3 = [1791360394830560, 30808050954630647143400]
P4 = [2718620200653680, 45011891361086352564200]
P5 = [1332000953825150, 64317318766862744365550]
Dujella - MacLeod - Peral (2013)
y2 + xy = x3 - 18517021882744014923118961383526900x
+ 19572370331271742985622541294683515971125406951610000
Torsion points:
O, [-292346212988066200, 146173106494033100],
[195385170934116200, -153014114040205657487029300],
[195385170934116200, 153014113844820486552913100],
[-97108866171554200, 143020236083801361459793100],
[926077960160596280, 892551120908963174263623500],
[-97108866171554200, -143020235986692495288238900],
[926077960160596280, -892551121835041134424219780]
Independent points of infinite order:
P1 = [-118336470086786200, -141797327820264979482286900]
P2 = [210989399689331300, 158297157992907011362903100]
P3 = [-40713731034438040, -142333341041312150111908660]
P4 = [142209347416659560, 140765930666241784687041740]
P5 = [-282818931441843136473040/1885129, -356522449865003833741985045328757100/2588282117]
Izadi - Khoshnam - MacLeod - Zargar (2016)
y2 + xy + y = x3 + x2 - 102395458352937356410639152133170x
+ 856158496702096425441260926362420647519951478207
Torsion points:
O, [-2879723444279123, -1061672315068051126304749],
[26913300116021317, 4194562462418425206704051],
[-2879723444279123, 1061672317947774570583871],
[26913300116021317, -4194562489331725322725369],
[-51903875988466381/4, 51903875988466377/8],
[7092211186683225, -697626458730384925525437],
[7092211186683225, 697626451638173738842211]
Independent points of infinite order:
P1 = [-7896575981427135, -1082743647577851862986069]
P2 = [137070045628542207361569/7102225, 46626711890018575051636134176228867/18927429625]
P3 = [391116510751635260703649927/6650239401, 7636134805651687303025726440017358353779/542320372912149]
P4 = [3897894206123854765273077373/476703250969, 247527251076001399279606156324559408601703/329133562489283453]
P5 = [225725576468973542959010209417/1368429700401, 107051808263784530981136586223519810630198149/1600787695099389399]
Izadi - Khoshnam - MacLeod - Zargar (2016)
y2 + xy = x3 - 78282589422876534310543926547680x
+ 242679292548703638017812138671209901736667366400
Torsion points:
O, [2988208040525760, 188248494673544728569120],
[-6089783557389480, 702538878072933585669960],
[6311074531469760, -3155537265734880],
[12730295341071360, 1144200942810374295993120],
[12730295341071360, -1144200955540669637064480],
[2988208040525760, -188248497661752769094880],
[-6089783557389480, -702538871983150028280480]
Independent points of infinite order:
P1 = [2066566626072000, 299547636274067229154080]
P2 = [-1550787758431860, -600291110493998418028560]
P3 = [3263855129292810, 148139443657335755220570]
P4 = [97385236225472, 484826409788603375426336]
P5 = [523951619159330520210/1849, 11987463546918439737167965101030/79507]
Voznyy (2021)
y2 + xy = x3 - 644070012118973645465314574075314287811020x
+ 198951702907372043736066956863914940039028666732563778907092112
Torsion points:
O, [464608404381378216984, -46720853879356461475181871372],
[847394632527340617744, -16176074593167775170838467554052],
[463499612322340898328, -231749806161170449164],
[484131135530947544664, 780668562726946574287545818868],
[484131135530947544664, -780668563211077709818493363532],
[464608404381378216984, 46720853414748057093803654388],
[847394632527340617744, 16176074592320380538311126936308]
Independent points of infinite order:
P1 = [430318485836488658664, 1216661618442997651958132964468]
P2 = [463513776777183035928, 2511616658937485818265234676]
P3 = [549455331730917131544, 3308353611364023954636223038708]
P4 = [780251559333328598258904/1681, 2051388671158817677945671635024148/68921]
P5 = [7363253106280067898447365160302232/4411507928881, 569212821815275891923887697960526892713742257985772/9265750381996568279]
Voznyy (2021)
y2 + xy = x3 - 584575908845266159343734320420x
+ 168678688516060008059769081909630373379312400
Torsion points:
O, [862567608330840, -17498928403238007445620],
[862567608330840, 17498927540670399114780],
[2994311607463740, -158949618347782068186120],
[546033089109000, -3504544489102106742180],
[490836097815240, -245418048907620],
[2994311607463740, 158949615353470460722380],
[546033089109000, 3504543943069017633180]
Independent points of infinite order:
P1 = [683483555143560, 9403182830726308713180]
P2 = [358860191188260, 2260953171316277017680]
P3 = [495095124921240, 784422017626985956380]
P4 = [156430788088505610/289, 16180653055535639419514190/4913]
P5 = [576710495535576, 4833078565542270063132]
Voznyy (2021)
y2 + xy = x3 + 42820310190133014404859959117120x
- 23658373478904376028348487001417691080146841600
Torsion points:
O, [548646738892160, -274323369446080],
[7161010153165760, -806346938093295445838080],
[7161010153165760, 806346930932285292672320],
[1928944518028160, -257132064070876368806080],
[32225398366930520, -5900979226356082133534680],
[32225398366930520, 5900979194130683766604160],
[1928944518028160, 257132062141931850777920]
Independent points of infinite order:
P1 = [3583766598604160, 419317671398836215321920]
P2 = [1223655037479752, 174846023675014738846592]
P3 = [640947384659840, 63643555662651358725440]
P4 = [62874734137225770734360/1661521, 15996326148420928636911863464909480/2141700569]
P5 = [492085953534821719525760/383161, 345197059318113216898671922275001280/237176659]
Voznyy (2021)
y2 + xy = x3 - 25694365726134223468550961700190x
+ 1244357548241806570305881372682736936744162214100
Torsion points:
O, [37190196035054470, 7192144058044079446379710],
[-3865902222546110, -1133980937913513600889490],
[37190196035054470, -7192144095234275481434180],
[-3865902222546110, 1133980941779415823435600],
[-46203509310383841/4, 46203509310383841/8],
[7803035335877980, -1232464903876603572635090],
[7803035335877980, 1232464896073568236757110]
Independent points of infinite order:
P1 = [1976747394441958945/64, 2800421403978236525286346595/512]
P2 = [-11925632534076161653220/1058841, -353078592295061166501339154033810/1089547389]
P3 = [14954268181680130, 2050449248751834916947310]
P4 = [8783355036600766560796/1560001, 2202838647358953803865680049260758/1948441249]
P5 = [55726798883897009512830/81848209, 820290594054955525206995060007825330/740480746823]
Voznyy (2021)
y2 + xy = x3 - 132924988960110284908561505621343830x
+ 19609839861137054905194073415471668308216402089412900
Torsion points:
O, [-423371335143733940, 211685667571866970],
[212871443443224460, 30984120064124948170938970],
[212871443443224460, -30984120276996391614163430],
[477409696808353060, 254875240149585972277134970],
[26021868026628940, 127155431356021994044499290],
[477409696808353060, -254875240626995669085488030],
[26021868026628940, -127155431382043862071128230]
Independent points of infinite order:
P1 = [-511726571189940, -140277799297994688929253030]
P2 = [810715530999046060, 666855389471387459433006970]
P3 = [-6262103850246781844/25, -24105720413261402599812442894/125]
P4 = [267334647302070060, 56393329036769416529546970]
P5 = [17214845362831663105804260/61324561, 31915077124450649196891469538884835670/480232637191]
Voznyy (2021)
y2 + xy = x3 - 185319335506607367377807049887126780x
+ 30706420940975930139148108311930139410259103718992400
Torsion points:
O, [112076830095660460, -106509335402461363261035980],
[248157152670287800, -330513100190411815554620],
[248157152670287800, 330512852033259145266820],
[112076830095660460, 106509335290384533165375520],
[248580742906083960, -124290371453041980],
[256184802651671560, -6633209116165015780597580],
[256184802651671560, 6633208859980213128926020]
Independent points of infinite order:
P1 = [245838978098807032, 2329550196715137661083076]
P2 = [248499670632083992, 14603934482332493623492]
P3 = [4461691870842463485/16, 1708966553395734055103137155/64]
P4 = [212262352428711160, 30555656189521412316474820]
P5 = [-180130717604294630, -241336716659233714385605040]
Dujella - Peral (2021)
y2 + xy = x3 - 134431595656132560133244530716630407860x
+ 625733616155978798790926637662143295775524742606237971600
Torsion points:
O, [-13451714120676038680, 6725857060338019340],
[6757547189353401320, 5087769653905080308696419340],
[6757547189353401320, -5087769660662627498049820660],
[1031844985619176520, 22093430195578514123030292140],
[14746758347291961320, 43014357067108209250290019340],
[1031844985619176520, -22093430196610359108649468660],
[14746758347291961320, -43014357081854967597581980660]
Independent points of infinite order:
P1 = [-2869410016515168280, -31430043844795184302826755060]
P2 = [-197703685693149665755/16, -1280344522331690130550505277865/64]
P3 = [267012656285161032620, 4359082550841795629652017252540]
P4 = [120129809640950917822520/17161, 11834977828126275253493661544929940/2248091]
P5 = [6509974383351560660742760008943701433303504922999704497463722543320/324488060916955448990270299293793657761326326201,
14322142693795448678509242638453175437725914713686679803977441232718193862747510123647501575235896660/184840903748262822178558650148337720034665263711211950064190200216095699]
Dujella - MacLeod - Peral (2021)
y2 + xy = x3 - 80023840948742540248145769181338470351039011220x
+ 8713190363697935270810147539075137761870903696728181805707561332544400
Torsion points:
O, [163324284784511185468840, -81662142392255592734420],
[164114887322956097347240, -554298684633824420669700246206420],
[164114887322956097347240, 554298684469709533346744148859180],
[204317333653834172476840, -29871000737915227929307749861662420],
[204317333653834172476840, 29871000737710910595653915689185580],
[163339532549462459787160, 11110810425776092403954975912380],
[163339532549462459787160, -11110810589115624953417435699540]
Independent points of infinite order:
P1 = [129335356758547490398840, 22951098496604684640382012834545580]
P2 = [490588572609213042038440, 295851088803393820057477482076737580]
P3 = [57962882381822455314893208486481960/14039169169, 13922914056439208473956212156892977834598137094930740/1663459037327303]
P4 = [3887037662564895185791657765218673000/23367681684169, 239430041461887975802252401221552747313278087686464860/112959677041134840197]
P5 = [72991749142313160778157898830414531419352926632/1760874089655976818961,
19719712084952795573182033044974759977483025733113666107106506048303692/73891154917998753572721568098041]
Voznyy (2021)
y2 + xy = x3 - 525172469302477123758663339710200x
+ 6031419752234985066818544319600791536479120040000
Torsion points:
O, [14073295568726000, -1194921004196054163575800],
[14073295568726000, 1194920990122758594849800],
[42765410778556400, -7860345000637967441630200],
[-2871439065700240, -2741485912382927645764600],
[-2871439065700240, 2741485915254366711464840],
[42765410778556400, 7860344957872556663073800],
[-27312975626819600, 13656487813409800]
Independent points of infinite order:
P1 = [45280920613362328576/625, 291591505287090241304392669624/15625]
P2 = [2340007199330814865520/19321, 111345281636360990008030982592920/2685619]
P3 = [675272796351690210800/43681, 11573803668424560111146533918600/9129329]
P4 = [494742584583483470680/66049, 26934969915110488454891193029600/16974593]
P5 = [3624586638194547879644553200/2562688129, 218188157900625413304705653540049240759800/129730961154367]
Dujella - Peral (2021)
y2 + xy + y = x3 + x2 - 429440575586127978736749900883644708390678299760120x
+ 3680857663766210745250410883387454041855740711121447921422221341112050495545
Torsion points:
O, [28969426461183899642495023, 124708278575848351992470781125746715513],
[672433647469571270160973, 58244239401552208147049843758434982013],
[-24124988300714218952464027, 12062494150357109476232013],
[12160058287965611961238473, 16028312010319800703382115007156532013],
[12160058287965611961238473, -16028312010331960761670080619117770487],
[672433647469571270160973, -58244239401552880580697313329705142987],
[28969426461183899642495023, -124708278575877321418931965025389210537]
Independent points of infinite order:
P1 = [8419194796990325063522035, 25731114444726568570868847618313007369]
P2 = [-919853878336159052665875392579/471969, -21776034045352514711973156440072590145686584685/324242703]
P3 = [447603296864172435943834179507097/31270464, 3777382119130663644612087655451740164007197226319/174864434688]
P4 = [554279913062262490568641736779721833590725077/15009114489113784649,
11362788305241656669844665704908780507306967081042302468708795920591/58147708632714085144905650107]
P5 = [3374529274718568953867102103728300441892225763/636809415581464146961,
633490652265873087160737682894584898426242502918696448656021793307583/16069938477120832893110421318791]
Dujella - MacLeod - Peral (2021)
y2 + xy = x3 - 160358871823589190660330376693948531315562016302680647360x
+ 781403589697980511946417429593407042215161927414640522217868261495087848009346486272
Torsion points:
O, [6992023098625578649462998864, 44714483988463932813513886965190008195648],
[-2782196334823404060010203216, 1098188299171882581741075186579635642158608],
[-2782196334823404060010203216, -1098188299171879799544740363175575631955392],
[6992023098625578649462998864, -44714483988470924836612512543839471194512],
[9462877207813199563126656384, -333632290407848130615791859640852448505792],
[29627551498497717888143168511/4, -29627551498497717888143168511/8],
[9462877207813199563126656384, 333632290407838667738584046441289321849408]
Independent points of infinite order:
P1 = [1149443819044519078465834944, 773691634354736546265193640421224485793088]
P2 = [7519371448610152623281435184, 27532704035106919645488469105565758483008]
P3 = [21025045777992389118277140500256/2809, 3211627687682556232712727326552922576502557216/148877]
P4 = [20413825608394099205504328875478856192/9332139609, 598735887811507371568252687842910263285246184688312725952/901512682648227]
P5 = [128626837719106491451596732944522075136/16673782129, 126071540308014359455631850886425357420481253102623836864/2153035464971383]
Dujella - MacLeod - Peral (2021)
y2 + xy = x3 - 12197933370978228836092207878933295982373272623660175960x
+ 16397484346944592911810909714353246206641051548880102267971930260543030002851073600
Torsion points:
O, [2017733976405934367365689520, -1008866988202967183682844760],
[498741125002707453796334020, -102166195748404425495122520600666583714760],
[2007320610973786370009532400, -700394297549991869991980220238645065560],
[2143502921899177184651609920, 9986355083668049131739081071073823580840],
[2143502921899177184651609920, -9986355083670192634660980248258475190760],
[2007320610973786370009532400, 700394297547984549381006433868635533160],
[498741125002707453796334020, 102166195748403926753997517893212787380740]
Independent points of infinite order:
P1 = [1642649021065874207756274520, 28158728682661854352258891106188292050240]
P2 = [1494796730514495789958159072, 38782122790431416023619899239089732875432]
P3 = [3583517435024697682920253120, 136762805345877865938455855486464400281240]
P4 = [2036250584909882307236145837699975201580/1015110655729, 827008355294005576510102555307150558068325544069269270920/1022751393634672183]
P5 = [10733967779515905215348449385013819608778290080/350988361077487849,
1105136233006953479793842164384411747402637439416166160497645882118120/207940494762240338021167243]
Dujella - Voznyy (2021)
y2 + xy = x3 - 630459815970173205612451266600281600610x
+ 6084072099613544938374664107082686571998844127230789964100
Torsion points:
O, [14948493605004146820, -7474246802502073410],
[21266132974766907720, 47897856713797303856925520590],
[21266132974766907720, -47897856735063436831692428310],
[-8851861386565520250, -104743608001205922977412343710],
[13271519995975463820, -7380237251084759181278143410],
[13271519995975463820, 7380237237813239185302679590],
[-8851861386565520250, 104743608010057784363977863960]
Independent points of infinite order:
P1 = [11149405358663570820, 20995098325908671212919902590]
P2 = [-7661290491621321330, -102296263846186442483215703760]
P3 = [-113573698704466594365/4, -264676453487844100025703795105/8]
P4 = [57575369407700568300018098460/196756729, 13765864279590894501464941248993591873087810/2759906637683]
P5 = [3745092046275550670589378849796019520/1691942495258116201,
150868902807966623351528496872381619915436475931903239610/2200788953993316853032410699]
Dujella - Voznyy (2021)
y2 + xy = x3 - 3391141250798509511967270831553855310704360x
+ 2403674883583540371167096319613618464254028272332461903241601600
Torsion points:
O, [-2126391781770603845680, 1063195890885301922840],
[1063198282476866259920, -220593837140185184448723318760],
[1063198282476866259920, 220593836076986901971857058840],
[909205611077264058320, 8487016688386964691219945122840],
[1225002840558364258160, 9369932309124892647818772194840],
[1225002840558364258160, -9369932310349895488377136453000],
[909205611077264058320, -8487016689296170302297209181160]
Independent points of infinite order:
P1 = [705730598509285828220, 19024612230191612424907328396840]
P2 = [10718011505618825548910, 1094210772797841653779992239082500]
P3 = [10176391402354078841640365/21904, 98779586683797496406158515720312327155/3241792]
P4 = [3799909762345025328822562706120/3242049721, 1155020879366091663295895758765884451174603360/184599069064019]
P5 = [4946994248828411798004229160535475950197840/4663866397750222957921,
83283002242622613818638258070317483128242888639835090321140120/318507124702437977892943536251281]
Voznyy (2021)
y2 + xy = x3 - 101408808992424985782452137639712780x
- 3391472817358166102261085990351359605480436004447600
Torsion points:
O, [334009907101495960, -167004953550747980],
[816999601746655960, 677565705728873698246052020],
[816999601746655960, -677565706545873299992707980],
[-64429550214049640, 53617099122971771285924020],
[-251471879027629040, 78786963530963676522377020],
[-251471879027629040, -78786963279491797494747980],
[-64429550214049640, -53617099058542221071874380]
Independent points of infinite order:
P1 = [-36729887349924290, -16843680901536342222326480]
P2 = [-53280956526459320, -43132682851038688073464700]
P3 = [360458506635967960, 83002131458408071878812020]
P4 = [-233562693790797128648/3721, -11852086226363151707201444307548/226981]
P5 = [361128701869646856709208855440618/99878297051569, 6835752483406153389720459690679781726208499104742/998175011321537099497]
Voznyy (2021)
y2 + xy = x3 - 6846036141864580415461343224x
+ 237743716924884102637037303696937775796288
Torsion points:
O, [-96488338007056, 48244169003528],
[48714836793728, -140879702026921652872],
[48714836793728, 140879653312084859144],
[976337266352, 480687639659894293256],
[119835801103676, 1066892531110613926040],
[119835801103676, -1066892650946415029716],
[976337266352, -480687640636231559608]
Independent points of infinite order:
P1 = [-26582546568208, -633201944397337637368]
P2 = [2024596322851172, 91022951659981520271512]
P3 = [65776693082151506, 16869713582173882655604260]
P4 = [-45826422273095461024/714025, -387630399997951812893481230936/603351125]
P5 = [33822779890951982/841, 4041755866523462414580484/24389]
Voznyy (2021)
y2 + xy = x3 - 191436051908630372802314812811714064x
+ 32005980967190069485527012254498420856923933410476288
Torsion points:
O, [269954201396495904, -134977100698247952],
[434847380898345648, -176030629739521570243381152],
[434847380898345648, 176030629304674189345035504],
[213384203789812596, -29538714708987584326855476],
[-210685038422333088, -250971644447022168041237328],
[-210685038422333088, 250971644657707206463570416],
[213384203789812596, 29538714495603380537042880]
Independent points of infinite order:
P1 = [147722421795489312, 83367677895283073648121072]
P2 = [150733102382856996, 81086112222079203647433024]
P3 = [29617004504123808, 162364397601298217710526448]
P4 = [157147861672922892, 76177765644178017256671156]
P5 = [3576966590582962152, 6716652754657833842283012912]
Voznyy (2021)
y2 + xy = x3 - 9239728054086121448616788529350744x
+ 341849656152392173913918229203374607439357486001728
Torsion points:
O, [54993224372432656, 201833786060696311377064],
[4626444817742512, 17297444565179137619075752],
[55587863507614384, -27793931753807192],
[61092738977357488, 2321030305094679933575848],
[61092738977357488, -2321030366187418910933336],
[4626444817742512, -17297444569805582436818264],
[54993224372432656, -201833841053920683809720]
Independent points of infinite order:
P1 = [51179142518187448, 1738407908092415654662504]
P2 = [-115811743318040528/9, -578213352029580981669496904/27]
P3 = [48971686316718784, 2609552925203560162943128]
P4 = [42957247913466672, 4920005807424227412601512]
P5 = [599715787180070416, 458796070305430951395413320]
Voznyy (2021)
y2 + xy = x3 - 16585394169428486616456261284373291904x
+ 25697719698997169176455177243557890276936174547777961728
Torsion points:
O, [2554618971159605024, -1277309485579802512],
[4284601657199320868, -5769906529523674325874385972],
[4284601657199320868, 5769906525239072668675065104],
[-2118592211962362814, 7164233910170467061423719874],
[1914194223224758952, 981798705670933894115058872],
[1914194223224758952, -981798707585128117339817824],
[-2118592211962362814, -7164233908051874849461357060]
Independent points of infinite order:
P1 = [2625385357200230024, 500526275275392958054227488]
P2 = [180308582606530611075104/15625, 72318565154726422613338314406438192/1953125]
P3 = [158359043660328487736/25, 1652652426528786188798714510344/125]
P4 = [-4559692136545806652, -2553898693216181907249189076]
P5 = [1861783986440828554492424/330625, 2001683282551923248053517337947630632/190109375]
Voznyy (2021)
y2 + xy = x3 - 44188786581366836949413959963555589274220x
+ 4360214883086643901482011104041218976400240596315788315584400
Torsion points:
O, [-248469472365875962024, 124234736182937981012],
[127060086406750561112, 892678899979732451385290928212],
[127060086406750561112, -892678900106792537792041489324],
[-18498571889094978760, 2274052367382000935261232017780],
[-18498571889094978760, -2274052367363502363372137039020],
[364749196690046148440, -6063773126228739106308713672620],
[364749196690046148440, 6063773125863989909618667524180]
Independent points of infinite order:
P1 = [355141377568112993240, 5784401088718206682513935389780]
P2 = [5132119846522226010476, 367356376832551465413828543385412]
P3 = [78923198179431247140116629784/487305625, 12961152618788183724180194715943276706929148/10757271671875]
P4 = [-34336777120693277690726754945360040/279748940135809, -13180204241311199739934756936958012919569596428338860/4678996008782680183873]
P5 = [10142456905309898389634506259517720800/51715173018548209,
21160431503059359434785253385250794329731898110016416340/11760532136741661699871927]
Voznyy (2021)
y2 = x3 + x2 - 61404158581503817437633890217680x
+ 186515003851675448088717607179372272424828554100
Torsion points:
O, [7765886433800110, -421912390610929525872180],
[1918667955489670, -275252573682316636000980],
[-9055448668569381, 0],
[4531283579685940, 36250080974957609194050],
[4531283579685940, -36250080974957609194050],
[7765886433800110, 421912390610929525872180],
[1918667955489670, 275252573682316636000980]
Independent points of infinite order:
P1 = [565266824554894, 389853674976579324962220]
P2 = [4382204100769110, 39799964943905804433180]
P3 = [3480968061862500, 122263901449886456778210]
P4 = [556157440793020, 390559406275329804776670]
P5 = [1506544924703710675/361, 371998389656371343326209840/6859]
Dujella - Voznyy (2021)
y2 + xy = x3 - 885470498073167713002317184212739304x
+ 315787360224933400897171748517120652503410335938363968
Torsion points:
O, [597338215050655184, -298669107525327592],
[1027417662835062368, 700405677952492275462424088],
[1027417662835062368, -700405678979909938297486456],
[-511747331490133744, -796809516055550094423058216],
[430562683637904932, -119817926733257962880024908],
[430562683637904932, 119817926302695279242119976],
[-511747331490133744, 796809516567297425913191960]
Independent points of infinite order:
P1 = [42508064591618698307/4, 276092936295411470521358194279/8]
P2 = [599374740625834784, 19599322409773593395085848]
P3 = [10336853054556809957726/17161, 70062162564408079452147216745594/2248091]
P4 = [591692205104801344504/729, 7145486943380724822069002563720/19683]
P5 = [31207315512700919990861160205048461703358374278620437702635535252739296354266705346529925962/4817243728090299166338796143704937948812120388662168566804089530091841,
174335010844107162806218243922661818528969270596382913586470158591464350356902856932197144309837491627275921521183698072532673344913990786/334347384314038704438439286259585813176959095130461867098086595489462204861075787877306740895555220923361]
Voznyy (2021)
y2 + xy = x3 - 206869411970121067085375228840614910x
+ 46865891532735641011875107363843945504248030434380100
Torsion points:
O, [-541657238392148580, 270828619196074290],
[278896403813957020, 104231532348191480286890290],
[278896403813957020, -104231532627087884100847310],
[-55565658970492580, -241224305129224233754101710],
[843489734404205980, -687383057850298269811275470],
[843489734404205980, 687383057006808535407069490],
[-55565658970492580, 241224305184789892724594290]
Independent points of infinite order:
P1 = [53964410917875100, 189365937909838261230045490]
P2 = [233928117020126620, 106181067287462557922167090]
P3 = [51443423450380172380/49, 340739368367933402593267817470/343]
P4 = [168429082040582899900/121, 2085892634896410372507804883190/1331]
P5 = [63090003790854842620/361, 868963121732974304781437075110/6859]
Voznyy (2021)
y2 + xy = x3 + 52278318878383976040306906753953105490x
+ 3858419689880916350645078181835422891835763361277172100
Torsion points:
O, [-73797663420677380, 36898831710338690],
[7157706824841985020, 27290299105437995152946332290],
[7157706824841985020, -27290299112595701977788317310],
[33109929867918460620, 195018277258477611795577578690],
[1502115021927142140, 9261520626856379357329948290],
[1502115021927142140, -9261520628358494379257090430],
[33109929867918460620, -195018277291587541663496039310]
Independent points of infinite order:
P1 = [9791670038731911120, 38138490779648221188705746190]
P2 = [7192151618343783420, 27420444287370000939852546690]
P3 = [23944057508216211881520/121, 3707545051391378965039098289438890/1331]
P4 = [67511989953087997352700/5329, 20211972521978689658863485440038770/389017]
P5 = [62255168689262323016351543196/51768025, 15533559000032325369035280586920153537707334/372470939875]
Voznyy (2021)
y2 + xy = x3 - 11738786090386022311517985017910856950x
+ 14652210278015259379956498818254648835113813674044302500
Torsion points:
O, [4508475858018679500, 7305412745352143114819653050],
[4508475858018679500, -7305412749860618972838332550],
[16262384939811957900, 64222938659920334144192869050],
[2678303733302183940, 1557074498704199186182357410],
[16262384939811957900, -64222938676182719084004826950],
[2678303733302183940, -1557074501382502919484541350],
[2340776648437173900, -1170388324218586950]
Independent points of infinite order:
P1 = [2365569799298052300, 347610266131084815066334650]
P2 = [2387499294548114700, 484745036623095894031112250]
P3 = [-1974693584602872180, -5489313850955299230675603270]
P4 = [2400518458160769900, 553171296095616404052373050]
P5 = [324358371214187452500/361, 15074633004417181342480756832550/6859]
Voznyy (2021)
y2 + xy = x3 - 4186358928804393919177782905016061088528284x
+ 422035090178971262140554156219228753446930469576304147579078928
Torsion points:
O, [4775320855270935054008, -298874155696234635157406752986076],
[4775320855270935054008, 298874155691459314302135817932068],
[-1657109236765268922328, 52998574601952566661175280788532],
[-125801795196176292424, 30768419004205835321416603252004],
[-1657109236765268922328, -52998574600295457424410011866204],
[-125801795196176292424, -30768419004080033526220426959580],
[1993657458285542421944, -996828729142771210972]
Independent points of infinite order:
P1 = [-173627171743178062608776/169, -132524939709827700932312479745458700/2197]
P2 = [344472448906341544096/9, 436915948425913507622391153226316/27]
P3 = [-1590630199594624573188065746/1380625, -98888712181131541943780296681054990752608/1622234375]
P4 = [-792794031363225387011522248/3129361, -211983613241968543660421446429999403281916/5535839609]
P5 = [6366710877141934775808993649624/218064289, 16025343314160667276979130005765199792347994940/3220155355663]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 176132532328195119342725602311244797550130x
+ 28451650278592405087423772199490845990666987542393208382968527
Torsion points:
O, [105326379822211046727, 3326965867209162869968446786361],
[241889790618131896827, 11082540222082899444380771311],
[241889790618131896827, -11082540463972690062512668139],
[105326379822211046727, -3326965867314489249790657833089],
[969384883537247465779/4, -969384883537247465783/8],
[250254444612046926425, 215541551470039453626830849623],
[250254444612046926425, -215541551720293898238877776049]
Independent points of infinite order:
P1 = [243520324530782787767, 32822002418878623545707709951]
P2 = [396734453639824876496503/4, 249888341566479656475402886505582383/8]
P3 = [709458754162246187375705/2401, 174751640596407634013863926282036247/117649]
P4 = [4653498476630305663907084315170086775655707503293/19192387128716238603680427664,
11245474076985644877002528481403160881943908153293929085952541255819783/2658847891701076876172740490723903809348288]
P5 = [134618835172916132264305975758425467829181041315253703546075883141344307024359619253806540873/418781685862130943710814171559969173142040396696365443105406109993508049,
609000437358291615310747069772936066893823550445103153362744280188431317511467698980399780907975317415309483982033575979922797502452115527/271007631911862510621469216454866709156584885305578922079082592238571022290678904020331256449712568386165657]
Voznyy (2021)
y2 = x3 + x2 - 12609309345160750750457843057361610140309840x
+ 17233959290653280972910695342981773859913373622222347431468163188
Torsion points:
O, [2052623233095151790196, 194229516385620101521987992450],
[2052623233095151790196, -194229516385620101521987992450],
[2050171932567804609006, -1947417078969561312512818380],
[2301963439672287963846, -20148860362349621516537554195500],
[2050171932567804609006, 1947417078969561312512818380],
[2301963439672287963846, 20148860362349621516537554195500],
[2050147594194843610971, 0]
Independent points of infinite order:
P1 = [2018615382763314397596, 2466519681163281528414363990750]
P2 = [32874222248157037463073/16, 22553374082305610628440215631847/64]
P3 = [2050402695234320839932, 20045687794083748716678641250]
P4 = [474467281023900929260806, 326811458827807582215530957434826220]
P5 = [7865368416787659541462697687181164/128161852009, 696412640268862405415483753973937803114064746758550/45881558533665973]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 + 91311863801771994810899476107896537703738132960x
+ 48897924433164703403538266070233307232490010678071139675626138325844992
Torsion points:
O, [-284177101563485488608192, 142088550781742744304096],
[293388253146128853935424, 317713134191594999313085327268395488],
[293388253146128853935424, -317713134191888387566231456122330912],
[1522419365590192889216064, 1927826933703964113893313365891893728],
[-99530588063762997593616, 197037096225677355242089738305150768],
[1522419365590192889216064, -1927826933705486533258903558781109792],
[-99530588063762997593616, -197037096225577824654025975307557152]
Independent points of infinite order:
P1 = [66781177172999014451798031936/24649, 17385711227555528422885224478314182361762144/3869893]
P2 = [820343623927302861912553536/289, 23653710957481627860960033823192441573344/4913]
P3 = [-608962821715989620836209988416/2163841, -96073482688496750819866953169059641946644832/3183010111]
P4 = [2302440852713568653137644371736/5929225, 5457975967123124371590689680084120803444407136/14437662875]
P5 = [421790422804535444287948113114081/2100572224, 26423377634632023734735775985034146799943321617589/96273426170368]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 873259287201344211823411893843646842703450x
+ 301507940348246298011213837679811554851398594884019513453253732
Torsion points:
O, [1173504813855777355604, 29879480266724657872318811290598],
[1173504813855777355604, -29879480267898162686174588646202],
[709724005196347479704, -6263276838159821066488553642602],
[4189963180385258225744, -264954153527890709262435224477062],
[709724005196347479704, 6263276837450097061292206162898],
[4189963180385258225744, 264954153523700746082049966251318],
[2501849709836086052191/4, -2501849709836086052191/8]
Independent points of infinite order:
P1 = [773146895950802979752, 9407631152225911512215294683778]
P2 = [676396871194408814804, 4505359925660451714483820356998]
P3 = [4567446347418518942202389/16, 9761304431989278244629296124022367597/64]
P4 = [40520012272175900919713/64, 795190944576111891308700025308451/512]
P5 = [160735588931739702268441406/54289, 1946099333174943411487333754761363805176/12649337]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 176437766116755715593028421000x
+ 28525101373243316234591662405070447436360000
Torsion points:
O, [278825318602000, -1003323333978576776600],
[278825318602000, 1003323055153258174600],
[-17940354796460, -5628914920224885289400],
[238566041102860, -103592856457518901460],
[238566041102860, 103592617891477798600],
[-17940354796460, 5628914938165240085860],
[973500834223999/4, -973500834223999/8]
Independent points of infinite order:
P1 = [117266065309906, 3073679029875028041172]
P2 = [241555047802000, 11200344991211074600]
P3 = [219009368530500, 623205042126650982900]
P4 = [8985470043234687970/38809, 2240578986357384258280099460/7645373]
P5 = [4073801710059160, 258685128952480127236240]
Voznyy (2021)
y2 + xy = x3 - 6930514303590967099509741404348654x
- 220533980179763912112775955032177914660177526059900
Torsion points:
O, [384217497757266975/4, -384217497757266975/8],
[240098861467437436, 109345999924160191998530626],
[240098861467437436, -109346000164259053465968062],
[-45697682413222292, -863127117309814161758318],
[-50319616202518388, -891270032866400881285502],
[-50319616202518388, 891270083186017083803890],
[-45697682413222292, 863127163007496574980610]
Independent points of infinite order:
P1 = [53544985642167931670704/508369, 5351396595507580872562316122744382/362467097]
P2 = [16711399961475372827593756/168870025, 17383251571688564880504242010139687286/2194465974875]
P3 = [-812260028436143852231154093188/16500323319481, -77668642843804819591674333340890327556312858/67025286842807671379]
P4 = [491483026592136118327267664514/2977305387169, 287586767707748175448192207859131204590167688/5137301740590076303]
P5 = [556891987510039086928384451100/8066374969, 415581434774652981507707905835591226683108250/724465335090797]
Voznyy (2021)
y2 = x3 - x2 - 832659955429796607294142447058441440x
+ 31925617474703871158217892755482774498987815838355712
Torsion points:
O, [-62322953757617696, 289097515791333557716808400],
[-738730960839624896, 493856771499967616469128400],
[-62322953757617696, -289097515791333557716808400],
[-738730960839624896, -493856771499967616469128400],
[892690649080602593, 0],
[2140901300147979954, 2839368738778830486156451250],
[2140901300147979954, -2839368738778830486156451250]
Independent points of infinite order:
P1 = [52038111787842660337, 375331974848158960344705788796]
P2 = [1751363066682325954, 1986339260133470854454592750]
P3 = [11455743007920658432626/12769, 120768323273563069630095647271250/1442897]
P4 = [18834141803063567127350529/9265936, 73211212602198367936410352447575869735/28205509184]
P5 = [1898135119877279250818741754721/33656470849, 2614772276309049750356729210499460080595219800/6174515172544993]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 45178223372501125164455335448309366564952693370040x
+ 145986049921384872120248239559143129625060518980160555775387133175479489600
Torsion points:
O, [-31874356195341985977965441/4, 31874356195341985977965441/8],
[11996749175240789518256800, -36477256750633131953151373786072189160],
[4086161504998534750925680, -5441140529147147954755093373972333240],
[4086161504998534750925680, 5441140529143061793250094839221407560],
[11996749175240789518256800, 36477256750621135203976132996553932360],
[-690124277328471210491840, 13297967970334588392395208287286665080],
[-690124277328471210491840, -13297967970333898268117879816076173240]
Independent points of infinite order:
P1 = [15777081022805889178166440, 57968767151941873813071055258017486160]
P2 = [25099653628765073728696266595/4, 3976503265813767221975136468950797240228955/8]
P3 = [1816446242480501519999633230/289, 51604447947308810252453373790697328778910/4913]
P4 = [-164545672703333692918839759412041309831188600/37459679873340234409,
-3694588599810360471009192623977732508260482599236844709177225396080/229269398945376560273171618923]
P5 = [11181829228322599654364009647884444025615152294692398480/1820953455186871918683573437881,
24586089911710324622921972927768587383180324752591419318147556200122047414848540840/2457243911236538079182926691383713164467946029]
Voznyy (2021)
y2 + xy = x3 - 1520381207694697842281446946852419110620x
- 5833184624217326291922774779756600916572239935509460373488
Torsion points:
O, [-7654795243777445036, -73187995401019333292338840232],
[-30847209458980496036, -108229665804022136184958970732],
[-30847209458980496036, 108229665834869345643939466768],
[-7654795243777445036, 73187995408674128536116285268],
[163139425270146375231/4, -163139425270146375231/8],
[99690138821159441464, 912870604575174830426102529268],
[99690138821159441464, -912870604674864969247261970732]
Independent points of infinite order:
P1 = [12256198337795701528534456/529, 42907484613854517393882079334765603756/12167]
P2 = [26231941459196033387070634/167281, 130027881431899013484119506756563727222/68417929]
P3 = [70722373828512850031224/841, 16559250405449780091085700554037252/24389]
P4 = [11664853449099985834474122439/87422500, 1203238099675414086270161043071478585518663/817400375000]
P5 = [608442489831763701546358796506/1533114025, 472283240950493833914107542622132920600397264/60029079648875]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 190737129597279967319718778252721346103470x
+ 32062507524787399895987631784440516042707045886667729857497595
Torsion points:
O, [1010930052508199946611/4, -1010930052508199946615/8],
[282465322904525006673, -850204046494273138677507405837],
[282465322904525006673, 850204046211807815772982399163],
[621644203288444181323, 12398427503539245988930252597763],
[255128858921559122023, 80536671384198605787815517413],
[255128858921559122023, -80536671639327464709374639437],
[621644203288444181323, -12398427504160890192218696779087]
Independent points of infinite order:
P1 = [2198250704697963632380297193/10816, 103065859589211081297694566335160084656457/1124864]
P2 = [7600923152290052848711891983045096353/5288597494889536,
20083062034042829586622877610633673156859507206370749917/384601321739893034806784]
P3 = [1559373608114145177304113127145433/1630266758761, 56038074894820158586637150785752782429364034659897/2081555572654461259]
P4 = [7417131441624066308759979953792344502029540775405/28423157836142509389650912656,
1164641174680472463129927031856409085651970683907225300018805510867431295/4791908206225412369010041094545144896661696]
P5 = [585477031283948814021392699950185521793236560089681423/356246181072843752706609071892001,
433553815158881447847517029242801621015444821206817682850448846914372806503585587/6723963173198708131654542106976391070182018161999]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 26802661929660362969223357383751829126560x
- 421107078006492757434486904855266442082525858677213688060928
Torsion points:
O, [684272414005265638911/4, -684272414005265638911/8],
[418030096886839089984, 7837409178850695829674559648608],
[418030096886839089984, -7837409179268725926561398738592],
[-31779962154344381136, 631334952850288910768828766048],
[-129601395021204605616, 935789863551531329736085289808],
[-31779962154344381136, -631334952818508948614484384912],
[-129601395021204605616, -935789863421929934714880684192]
Independent points of infinite order:
P1 = [-77316087343287309117/4, -2396539142836714290888392859885/8]
P2 = [-18026094087101375088, -237029170101398464191534904560]
P3 = [653241652179332848775887116/2325625, 13370177424080651087475570094621961487636/3546578125]
P4 = [680512945376673113494391526072/27952369, 561364261695299116741912406781719105755377048/147784174903]
P5 = [19183770499846101803767228290816/5546823529, 83928916270633336645108112687971340747914246944/413110775969333]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 + 1200837456129828431133545030365550822920x
+ 1843340155580461232781879471510347444767317963565929230400
Torsion points:
O, [-6128203768866500481/4, 6128203768866500481/8],
[33222502664447192560, -280012489377068041454360178680],
[33222502664447192560, 280012489343845538789912986120],
[6171208820471973280, -97411406174274963437047660280],
[155268970133164325440, -1982823950272472439208643525960],
[155268970133164325440, 1982823950117203469075479200520],
[6171208820471973280, 97411406168103754616575687000]
Independent points of infinite order:
P1 = [179819243495490621712/961, 1354767979633200758908590112344856/29791]
P2 = [84553975825201953598818088/29929, 777559686299960031558206977003635748712/5177717]
P3 = [21875749862642785897750/289, 3564706306818387255173005215815510/4913]
P4 = [1596504113893030452683080/48841, 2976105912659780486911052355541468400/10793861]
P5 = [750309065493528104381375888202130/605209201, 20552293383046498191606590869654025065669692374650/14888751553801]
Voznyy (2021)
y2 + xy = x3 - 202321715027737094276870490159764541960x
+ 1107653093587358506835955916323851397256110776821017153600
Torsion points:
O, [32964613444431187839/4, -32964613444431187839/8],
[8079469415523447840, -641236229847878195558758680],
[-591579728108467200, -35030493653416723353912631560],
[9436189400797781520, 6222631048311858567810011640],
[9436189400797781520, -6222631057748047968607793160],
[-591579728108467200, 35030493654008303082021098760],
[8079469415523447840, 641236221768408780035310840]
Independent points of infinite order:
P1 = [10568553837971347116, 12241433657350951463791321992]
P2 = [4369341809536650330480/529, 2270453210762489044299886461480/12167]
P3 = [92907456421396534000/9, 294727663911369460868127535880/27]
P4 = [12014858145182661928771344/426409, 37125643443482134587501515904290696664/278445077]
P5 = [37815516458618229738267804/6568969, 194692663051744193570969433801257545044/16836267547]
Voznyy (2021)
y2 + xy = x3 - 10977623105578801636718837411109615051400x
+ 442665482446370281727167260471934000859445247893183054920000
Torsion points:
O, [73628451033214422800, -183169010065543972583215375000],
[73628451033214422800, 183169009991915521550000952200],
[-14354904900934872820, 772845520901265214968445107500],
[58793294051910984020, 21972321238539707128359473480],
[-14354904900934872820, -772845520886910310067510234680],
[58793294051910984020, -21972321297333001180270457500],
[243735131692874057599/4, -243735131692874057599/8]
Independent points of infinite order:
P1 = [154057945552273490895624626/2436721, 139205785424125434404161780952752048682/3803721481]
P2 = [61095344313625567400, 5550862428105354826254315800]
P3 = [244519375839429782421018304592213510/2908804408488889,
52941414118189675504084457983103551086109881805183150/156881516794899277237037]
P4 = [1402938083278701945682869796473896305480/20728127401766116929,
9304822118647125402564169394268623740773129573563328977000/94371336134769464023625370783]
P5 = [15556029499949072025332208204771298854693299508200/277112560552274901461295368809,
8410385198075092557561127484820466509349946536376777471299485491961092600/145876158113453172082769414191049241665160373]
Voznyy (2021)
y2 + xy = x3 - 580628028005825067141797351472119971326893000x
+ 5385113903436514918395374195887927495011755831476713047943849000000
Torsion points:
O, [14736011185856253277600, 169994103415088928672279380505400],
[14736011185856253277600, -169994103429824939858135633783000],
[13969327165638910450000, 11613689226688702743952897843000],
[27404127809186281277740, 3170746220847181838321462544009160],
[27404127809186281277740, -3170746220874585966130648825286900],
[13969327165638910450000, -11613689240658029909591808293000],
[13919937784842610906000, -6959968892421305453000]
Independent points of infinite order:
P1 = [12024939917005069959520, 376687143624752354947665595871080]
P2 = [217395249288493421704405/16, 4228311669225926087321980049683405/64]
P3 = [318231182782520331287228650/22801, 31120813129867355457904415097495760750/3442951]
P4 = [543499653110279076003817418605750/3697977721, 12510086251571800104693324537173727477665421179500/224877723191731]
P5 = [-218966030556724199726486954060/31483321, -532512523895067663218812069053929111973626900/176652914131]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 130007696585543304366227250425130x
+ 615151751573662757338863446711631540848623430052
Torsion points:
O, [313516411147944, 757907000367022645853778],
[16074583349698944, 1636728323913154385578278],
[16074583349698944, -1636728339987737735277222],
[313516411147944, -757907000680539057001722],
[-53116134719387553/4, 53116134719387553/8],
[6695713122703092, 211762993970261946068118],
[6695713122703092, -211763000665975068771210]
Independent points of infinite order:
P1 = [4624265727866844, 335925799584753674580678]
P2 = [4631815162328502, 335186152589467972336848]
P3 = [-8060119532790156, -1067426533980528118488522]
P4 = [58831517652288984, 14021096935179941188358598]
P5 = [955350736361611374, 933713167833479284422044058]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 334977127036983589030052824531726877150446600x
+ 2359772760864044970356926429393862697713004581415801780485705248832
Torsion points:
O, [10633466030150230348424, 11715023411560931899773064207808],
[22635718415435644960784, 2524939206466609191667246005166328],
[10577519302955508408848, -5288759651477754204424],
[11398869883527266701904, 150051690017557877876401380825848],
[11398869883527266701904, -150051690028956747759928647527752],
[22635718415435644960784, -2524939206489244910082681650127112],
[10633466030150230348424, -11715023422194397929923294556232]
Independent points of infinite order:
P1 = [10587560749225827328304, 3158283519206960761974075237848]
P2 = [10596331164230586292784, 4891540284585685858398178928888]
P3 = [199725202782949775316800912/17161, 436024830962973084248083185684161253160/2248091]
P4 = [734441370637517074718705984/73441, 1988912737293925342660369255899442472888/19902511]
P5 = [483076207476786905288836622894444/44808845761, 362071778767156199005713844822644140831865232268/9485181279534241]
Dujella - Kazalicki - Peral (2021)
y2 = x3 - x2 - 958595341735422253448874842847626704x
+ 361244367991028420756708447595507191492277326349839008
Torsion points:
O, [563810285993551852, -1901921642955556706231748],
[565271421975081076, -88398726882518052],
[565271421975081076, 88398726882518052],
[563810285993551852, 1901921642955556706231748],
[565271737047922698, -410210312098189651202],
[565271737047922698, 410210312098189651202],
[565271422042992689, 0]
Independent points of infinite order:
P1 = [565237601212634066, 44042207341351033713822]
P2 = [2523381863043230225154/961, 118971517062884738300429680991230/29791]
P3 = [1051191516438152794722/1849, 336559033269697808566620450694/79507]
P4 = [465408004538003962962/841, 375768953991556794748494513098/24389]
P5 = [597965350847321449658258/923521, 97292468679453797994982752355479138/887503681]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 949988329044257762518803992260824x
+ 11270038285843134915076189086326229041239642310208
Torsion points:
O, [17855289389777136, 13814222166325823490600],
[33808383750937092, 4218492749900621074787256],
[33808383750937092, -4218492783709004825724348],
[17855289389777136, -13814240021615213267736],
[17802876409736624, -8901438204868312],
[18718789253195328, 215269624525650157319208],
[18718789253195328, -215269643244439410514536]
Independent points of infinite order:
P1 = [13290324793280832, 995937358447388684567592]
P2 = [17836987542565488, 9528896621835403364904]
P3 = [1071778439022432, 3202045039592906454723192]
P4 = [18153581494133382, 83104044961582700179476]
P5 = [932120224278747628/81, 994707961802535635036237116/729]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 41619883571924461749430110977414620x
+ 3268130612351289717098075397834416729817135226932512
Torsion points:
O, [118682621062103864, -534285320205894743912032],
[118682621062103864, 534285201523273681808168],
[117762357287104274, 13412614010246343274328],
[83915070261583214, 19144272796418006618453018],
[83915070261583214, -19144272880333076880036232],
[117762357287104274, -13412731772603630378602],
[471144350670023231/4, -471144350670023231/8]
Independent points of infinite order:
P1 = [121313113450726214, 2107713418517067564479768]
P2 = [-61540667849691286, -74808929349775001739900232]
P3 = [9822881868560110691/4, 30683351410176387488219952139/8]
P4 = [9700047911142047096/49, 18106889047377596910673384184/343]
P5 = [61471335196041103056986341154/521889211561, 103140151469657055798261567080128830962/377022682326686059]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 1424999206344464644554985206140500x
- 19944217768494572929764341514329357016135259750000
Torsion points:
O, [-24075336456760600, -639161241576052417858900],
[-19245058663781500, -593413202401245856828000],
[-19245058663781500, 593413221646304520609500],
[-24075336456760600, 639161265651388874619500],
[43410096846281000, -21705048423140500],
[108435555847091000, -33174534259273167299390500],
[108435555847091000, 33174534150837611452299500]
Independent points of infinite order:
P1 = [794990678716266560, 708017934439029677050576340]
P2 = [68688257271562072700, 569277056769506244864615849500]
P3 = [-23172978167977880, -796034925685996143288020]
P4 = [251765877393281000, 124818812025185698676859500]
P5 = [-24910657686129688, -308817994988957719934548]
Dujella - Kazalicki - Peral (2021)
y2 + xy = x3 - 4138514127559913332934744150014924x
+ 102469298949950231458725824114397203052249880945808
Torsion points:
O, [44215060406649128, 2433892482473002436686964],
[44215060406649128, -2433892526688062843336092],
[-6611604877721764, 11381674043126708228099264],
[36281184973103192, 277327947061220155561652],
[36281184973103192, -277327983342405128664844],
[-6611604877721764, -11381674036515103350377500],
[37352420510182424, -18676210255091212]
Independent points of infinite order:
P1 = [-64857565578778984, -9902507401572289363143436]
P2 = [756488043262772084/25, 278012716010431403883865492/125]
P3 = [-37323910843850929/4, -94749610348270423377645971/8]
P4 = [612781592850013469452/9801, 9108535990474950426233733876688/970299]
P5 = [2173511843337322575398985498669656/5678493730119961,
99983582442317947334485391803668176945013569087524/427907329936792884844541]
Voznyy (2021)
y2 = x3 + x2 - 1588110657670714141824566980780088800x
+ 766728415851471876036717470571113718121255814086512500
Torsion points:
O, [-561242980292353270, 1217068765936078940841887280],
[632139196677988970, 124194286086494658195858480],
[767755180242338699, 0],
[1192294215781031900, 753762286201332936218944050],
[1192294215781031900, -753762286201332936218944050],
[632139196677988970, -124194286086494658195858480],
[-561242980292353270, -1217068765936078940841887280]
Independent points of infinite order:
P1 = [3544650971722482755402/5329, 26590165495691914525500560368368/389017]
P2 = [1864080474461200083925940/2825761, 372916710661544962049891834210854290/4750104241]
P3 = [-789725393984866385222/22201, 3001268902877591615928902085283056/3307949]
P4 = [3864100248419733467549900/4791721, 1073111040579562836217497354394700550/10489077269]
P5 = [123845609194763187749054924/158734801, 102028022321999931459636734067180678270/1999899757799]
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