Eroshkin (2006)
y2 = x3 + x2 - 298337765420974027925404974199074153225x + 2209525297419800283762159062541471723368027978017989315000 Torsion points: O, [4932343693390245825, 29291893581651695450789307975], [4932343693390245825, -29291893581651695450789307975] Independent points of infinite order: P1 = [12582816306572774955, 21161259527567477756392809855] P2 = [-10238901114928946460, 64736234016763296633829049790] P3 = [-7930737095588324325, 63849411541423127439301106625] P4 = [11495083131989372685, 17292569185912354737409456065] P5 = [-4400110027279034376, 58626392520949825159787439240] P6 = [710843695600020675, 44696901079924332333043574625] P7 = [-6124232965906747285, 61700230054196535588270161535] P8 = [14925305818114923000, 32887307382139198660372885800] P9 = [-10825479394428034875, 64579608463195877622328856175] P10 = [-12802868599160550075, 62694036529804395978303380625] P11 = [-4669378572351124797, 59167308170559298781522768031] P12 = [-1894227661029731335, 52610343752060548173493438665]
Eroshkin (2006)
y2 + xy + y = x3 - 81089552755699140908030202688368478038x + 281263936268193464077589295595406966386314342335769150988 Torsion points: O, [4625450842703735354, 2269090345561701691033219560], [4625450842703735354, -2269090350187152533736954915] Independent points of infinite order: P1 = [5741172515907340367, 2224852147461708059604916497] P2 = [-6283260873451047176, -23296171078888629764646328180] P3 = [-4377070887290532121, -23501903154705392080910055465] P4 = [2577560963520055004, 9453862857802006685518121535] P5 = [2012165467991458804, 11235889541275053343944971060] P6 = [5052438574023597248, 733645881558773670043750083] P7 = [2616398712495877619, 9328022441806695951924810555] P8 = [3958074780969203204, 4723772959038114089554236135] P9 = [6205498548772362149, 4126195518911771323234166295] P10 = [-5276925921661264561, -23711315833456709412101226735] P11 = [5589234149317131623, 1624971859309398399443882583] P12 = [3832164828660767909, 5176158037521448409935173015]
Eroshkin (2006)
y2 + xy + y = x3 - 227204253761112793208000940016487352978x + 1318089867386926711140924601590234088488769981566633802648 Torsion points: O, [9146520430865863874, 2269090343301166896952155300], [9146520430865863874, -2269090352447687327818019175] Independent points of infinite order: P1 = [8145244832551235237, 2802136845278504101116818655] P2 = [-2614487012653179451, -43522879055509397420848043025] P3 = [7955909699716289909, 3748942862747705666913785655] P4 = [-1305804858417159701, -40156540233256298925358896025] P5 = [8120355012367564949, 2927152226216520118893211875] P6 = [8806012412343667349, 442884651697222550228202375] P7 = [8760832457062556699, 67105415368154448552857175] P8 = [1723413480817630199, 30522807816313203931685157675] P9 = [8209263705352116389, 2479721714605586058212981115] P10 = [8221419028699601399, 2418353623765018460259967275] P11 = [5015537671883797799, 17455867889605497871382497725] P12 = [-4345785245986300288, -47152909934632349816986147545]
Eroshkin (2006)
y2 + xy + y = x3 - 2061966282312748415211387989253532899918x + 36079330409584890827203029261000439483009603580628519854608 Torsion points: O, [22898259700584047894, 29498174510918422610714110140], [22898259700584047894, -29498174533816682311298158035] Independent points of infinite order: P1 = [32108239270224712709, 54542283280378129719770629785] P2 = [26962907377126366529, -9204040020243165214050504975] P3 = [29251246559798375369, 28154024182174591974149785065] P4 = [25493183133877482137, -9018143487402250631685901203] P5 = [26108053542756440369, -6438078003708091583745780435] P6 = [26021870731648428569, -6595568383037854439551154835] P7 = [-49871157374901107131, -121966418059392151469935087935] P8 = [18483472222146972869, 65434732112323934885849947065] P9 = [25935621501012332069, -6834967387480344717682947735] P10 = [26752295552864584817, -7951360755245895938491306323] P11 = [25026126671698282244, 12261311424145861787090253315] P12 = [24898439153453520769, -13226275131687532126996461235]
Eroshkin (2006)
y2 + xy + y = x3 - 69993120101005305009860092170583378x + 7639258120193164015870793100033493923516729761682248 Torsion points: O, [84445978180236274, 48278517997658438832968825], [84445978180236274, -48278518082104417013205100] Independent points of infinite order: P1 = [171777816398125539, 26167670979268269042638245] P2 = [169740137584324909, 25477845876425289117707135] P3 = [149332975795951549, 22740998019085332334924775] P4 = [235735302889811599, -65111340369741228518429275] P5 = [140624626342500187, 24029021933798151088331855] P6 = [29075000559302299, 75025241273474528659949525] P7 = [147635813086825357, 22884193456036867524732515] P8 = [160487006141243383, 23233334933109112425738323] P9 = [457571992790515204, 267236203879055542974358715] P10 = [-21296509469728001, 95499782305256485473234875] P11 = [26669222671152124, 76102328670260618345498000] P12 = [161956158824337094, -23484430563596793664294915]
Eroshkin (2006)
y2 + xy + y = x3 - 51012395091150795883443767656668298x + 76434974688414573638384904319711864744626666727159256 Torsion points: O, [2839813206318970, 276206683329981852839709377], [2839813206318970, -276206683332821666046028348] Independent points of infinite order: P1 = [457917641278676257, 386128984291844301517862723] P2 = [270901045199761935, 287221831349545531747622527] P3 = [-397254005700385953, 184415027696538474481219633] P4 = [331187106878779291, 309623241474837135248838809] P5 = [272065748698447585, 287566503142636601677121387] P6 = [-419789818786899680, 154507705600056059101944152] P7 = [768976913240434780, 701372420641720230475880867] P8 = [95702143817093695, 269127303497606029751993777] P9 = [-351066191606211200, 225999296032216298947768472] P10 = [-221402129973000095, 277265825716404359585558867] P11 = [329196849140580055, 308734681486552150048900727] P12 = [183025514774816392, 270609415057442326162910063]
Eroshkin (2006)
y2 + xy = x3 - 15075739125931590120183633247999865x + 719481272914731335170056334451666685290651887623417 Torsion points: O, [53124380663862874, 8277655824923614118134963], [53124380663862874, -8277655878047994781997837] Independent points of infinite order: P1 = [89804331152227354, 9479988398821069756793203] P2 = [-62701899104078726, -37659586597332022817662637] P3 = [-13211903879226806, -30271344415900117440882077] P4 = [-10977722414604866, -29726345592837952853574677] P5 = [86749319841487474, 8031086365180078649558563] P6 = [76996051410701074, 3895081239712605109656163] P7 = [76763044815074074, 3814822332867371404251763] P8 = [76160708262893074, 3615100101120986165178763] P9 = [90468440519765674, 9800261165197851637034563] P10 = [6275050034321434, 25002546738193716541475443] P11 = [12762046847775514, 23003533123328924393108083] P12 = [-17295822293641526, -31225864445576588088555437]
Eroshkin (2007)
y2 + xy = x3 - 420123886323242988442406904384921148985x +14547746280073821301806145504809500759831594126734723275897 Torsion points: O, [1026250449144166234, 118817821851820512660319757683], [1026250449144166234, -118817821852846763109463923917] Independent points of infinite order: P1 = [30660270495414485914, 174610677242694886680521951923] P2 = [-27751044875610449636, 69533982916346344707296560273] P3 = [80265229592403732634, 705645602324169346229354703283] P4 = [25462531704105141634, 142683984969460557005691585283] P5 = [62209773870344426314, 478714153470297354327191030563] P6 = [77369542854586528534, 667218561061651312960497227983] P7 = [7611285268038426634, 108586361707872928552354808083] P8 = [1204020729424715528314, 41772437377979978301951301099123] P9 = [-3756642886530059846, 126779282893774465971084696403] P10 = [476226013166193361114, 10383561539853147479038665421363] P11 = [25934726315159755354, 145244295192942091588704117043] P12 = [11390807473140285528634, 1215713015403696823110293448560083]
Eroshkin (2007)
y2 + xy = x3 - 2274412631042746230240014920326936789445x + 41861448474250945269536760003663301866430401503884473151937 Torsion points: O, [22935589249135150514, 41970474374182395872085761543], [22935589249135150514, -41970474397117985121220912057] Independent points of infinite order: P1 = [29092047839687511794, 17779258075082697894047718023] P2 = [-40042222833789788686, 262166172995985021961841950343] P3 = [12749333601877491314, 122215179045634694783184958343] P4 = [16413671046029425094, 94614860436193229223216411323 P5 = [34231124382078831914, 64161882695108616251348629943] P6 = [184459149322898168414, 2428699358856826709350842982643] P7 = [-44298691225405686286, 235975315425044672490727505543] P8 = [16889375335100119778, 90916176066253752082469675111] P9 = [-20672826778209059836, 282922477635927184125760441943] P10 = [19785262531937505914, 67872448967870615838814873943] P11 = [28528319860348946564, 13945589112868893015324845093] P12 = [29117718101778919154, 17970883254639240872733936263]
Eroshkin (2007)
y2 + xy = x3 - 3460212184869409462879787098424302220365x + 76725332182289401244480579162479048671720653011227833006225 Torsion points: O, [46627887868145828930, 129458223785945094358421180735], [46627887868145828930, -129458223832572982226567009665] Independent points of infinite order: P1 = [10105607718142501250, 206856963386201917943798521535] P2 = [-13009857994099020670, 345745859768995019046066150335] P3 = [28976934109135016690, 28104140780973505497462530975] P4 = [22373995425270287330, 102503101634127369791658258335] P5 = [-53363024164255686118, 330780156751016363506359596471] P6 = [24999947745865277780, 76453321659288905279671764335] P7 = [20906847293512979330, 116282024692195140609164550335] P8 = [-67729462416577636990, 19739037236318087978172159935] P9 = [38091918964547592830, 13797353499110074433329467335] P10 = [38299291670039711150, 19504522661314717583193861035] P11 = [29117728961170881002, 25671954825563261656393399247] P12 = [-27346770928406869870, 388458224524004677675308091535]
Eroshkin (2007)
y2 + xy = x3 - 5915232167158349511943570504558263178160x + 189989838940979212731233721328707449324240816328756166793472 Torsion points: O, [23628255529510549984, 251822846302087015215164745808], [23628255529510549984, -251822846325715270744675295792] Independent points of infinite order: P1 = [-89519732833201272536, 46132069718947335099772316488] P2 = [84691875391497876064, 544507404023764849497002816848] P3 = [45970901032972411744, 123339705593822530812696363088] P4 = [-57127814943564887456, 584356500482526458711993489488] P5 = [100781099570779355794, 785787971074967111000920421218] P6 = [403846687831081059904, 7979057989786159612197872334928] P7 = [412126705956115260904, 8231113852951392740039735265928] P8 = [59425667905190826184, 219839975510776823289040042408] P9 = [93986866492572171184, 681374792998977476568890161408] P10 = [-46025836157323353776, 603939769734558083592818509648] P11 = [52315483791428293684, 153994704354157120312282501408] P12 = [221794131787439765464, 3128684107727828196905846489488]
Eroshkin (2007)
y2 + xy = x3 - 2930856110646876366568351217006462280065x + 61162147490056987962447877881747110669389916249870892297225 Torsion points: O, [26933945442536577130, 41970474372183217775385048235], [26933945442536577130, -41970474399117163217921625365] Independent points of infinite order: P1 = [-40235999407913384390, 337562702986720130719858556155] P2 = [44707073688835602730, 139603648537041562948391294635] P3 = [32087052019039392970, 12480663538868816838967321195] P4 = [31528035511767762730, 9869952437945552272618814635] P5 = [-2651803878244516310, 262517724044421919452063662635] P6 = [50985119243826724642, 210397287358064083790394170947] P7 = [78131376617041716730, 555989435091996521706297986635] P8 = [-21386746977088898720, 337729889632422785641062096835] P9 = [128227595750239630330, 1339292426618763632469963887035] P10 = [445902862569267147730, 9349484855879169740480431667635] P11 = [33615911520963816730, 25014390445822677658407626635] P12 = [304589704490274688170, 5237053493530840603650300449835]
Eroshkin (2007)
y2 + xy = x3 - 1604115720432703747645854436115825419710x + 24854471963630464651375308856010948374447644530671142636100 Torsion points: O, [18399347760464240220, 39605940608244872081398493490], [18399347760464240220, -39605940626644219841862733710] Independent points of infinite order: P1 = [33959885299314421020, 97693051842804472247186693490] P2 = [-41545117463335066980, 140680164997460409038803589490] P3 = [-9174361359411383940, 196974651376491328835587458450] P4 = [-46183272832717250580, 20826151013849617443427335090] P5 = [30899189560960660716, 69209131284197626008455306082] P6 = [180624464887584204060, 2372344986496528817720837550450] P7 = [27006994203855343020, 35077461214397158037804099490] P8 = [24660095404027993560, 17121039832417463073774918450] P9 = [27325131129439513020, 37741995642991621184505617490] P10 = [60354618219869892660, 384566297479682544533572034490] P11 = [37276788414939323670, 129832525945243340323635807990] P12 = [26994959517410041500, 34977300506696000086569912690]
Eroshkin (2007)
y2 + xy = x3 - 435143747768370112106161383366802254050x - 1718988230824332939656053494953243446622485861836978983868 Torsion points: O, [33624478289064400804, 147192227053989133160632318798], [33624478289064400804, -147192227087613611449696719602] Independent points of infinite order: P1 = [-16628901140393603996, 30310798695492477365141969998] P2 = [-18281748975241043996, 11226375646978704018619073998] P3 = [-18120188830565924036, 14706913979321483142093261358] P4 = [-11720178835264088396, 42083965709751428011846582798] P5 = [-14795543899109216996, 38475128378435732798601362998] P6 = [-4273399721615984036, 7906601566687286327464882678] P7 = [-5536028259149890436, 22810388529597166759825074478] P8 = [194437378280745414244, 2695283237214064642263975036238] P9 = [75692504667782440504, 631674870120181974483487621498] P10 = [22627717884668796004, 4516799350135623773217233998] P11 = [26892917340098748004, 77643188526643345552629713998] P12 = [113711726980224511204, 1191273802614516606072894037198]
Eroshkin (2007)
y2 + xy = x3 - 9961897895877072436363696377038852218385x + 386641226009676505641094591224658839288977045345666728365225 Torsion points: O, [42985521501155122570, 194552215642803468217376764315], [42985521501155122570, -194552215685788989718531886885] Independent points of infinite order: P1 = [86006937761814759370, 407503179290727132395383756315] P2 = [257537050800611271370, 3860351532566427118874999500315] P3 = [-47636031804866054660, 867808291817112587252415481915] P4 = [126186608735304687250, 1067173877208511473292263447235] P5 = [7987084975889469130, 554602763521880669996015811355] P6 = [570049510686960737050, 13414511860509253690265185331515] P7 = [-84492898325929220150, 790665439693907320113017087515] P8 = [57759465938964442270, 62784609544384827153200068915] P9 = [71086828408411911370, 194183449779612402337287340315] P10 = [69187816955840072170, 169109893321039996359466787515] P11 = [-74967801385490523830, 843878502711079387679916143515] P12 = [1002185439564440266, 613725153108493160747144097307]
Eroshkin (2007)
y2 + xy = x3 - 4296561733833813622211765271899645505485x + 110491051080034418321885623194222767606021500012097359146897 Torsion points: O, [26223340349492762434, 125911423143838901315213629183], [26223340349492762434, -125911423170062241664706391617] Independent points of infinite order: P1 = [-66335161885466989466, 321878849982494645592135800983] P2 = [43130574497326462594, 73562038494881453388816313663] P3 = [62500645297143948034, 293430327832772473627293425983] P4 = [39724630583973479284, 49990286460186219613552775983] P5 = [52832646183411684394, 175964436870295185202888378063] P6 = [40152375753476762734, 52039247228172469251933608683] P7 = [-43021119583048421246, 464445625850749479637376423743] P8 = [153607000090204783234, 1753534496181588293632680229183] P9 = [118284677678737657474, 1121260852277368266767215651903] P10 = [154293008929717511014, 1766553792553501566858185182723] P11 = [-36517228798129793756, 467646834983113396146797102863] P12 = [65891296272938921134, 336842436424133652476023884583]
Eroshkin (2007)
y2 + xy = x3 - 12639274175693629669246799362435207748655x + 546025924766214300252759666836267029730941947556294567508025 Torsion points: O, [74922305077099245510, 140098625728723286161546726845], [74922305077099245510, -140098625803645591238645972355] Independent points of infinite order: P1 = [62404916143288979550, 17353244355641300882904733005] P2 = [56276436815756921970, 113851600823870891463914866485] P3 = [62531566218939297840, 13529345076882993325316878965] P4 = [51182707218235510662, 182196139172293920440128655421] P5 = [-123867936409446284290, 459443226430915765703642501645] P6 = [60618127466215160586, 51005678040053921720440874097] P7 = [-127187469539387764290, 310025383890038138131817502645] P8 = [25521611479838189460, 489974335234694949980396822895] P9 = [67239902885857680870, 12950322288230406443644134045] P10 = [62116378179347057310, 24343049461826315636280381645] P11 = [357795446003224168320, 6467446075259235162330804622635] P12 = [55800806143121197110, 120386373477442685338038375645]
Eroshkin (2007)
y2 + xy = x3 - 6822056808999168202154285328075085085610x + 220557528518736836412923854565947623298384352585736677636772 Torsion points: O, [33597116630822085684, 171112189663847522584115050758], [33597116630822085684, -171112189697444639214937136442] Independent points of infinite order: P1 = [108627574395471512724, 872521622980212548899508902278] P2 = [114514187165976087924, 970060268305152231750877519878] P3 = [216357056754008293284, 2978642740267652747017153454358] P4 = [-89798247197031297036, 330239130732818562816044808198] P5 = [-58658584952057101788, 647221393889295451414622620998] P6 = [254956008985391713524, 3879952072334244308419153212678] P7 = [48497740467581546484, 61411470632628481940457111558] P8 = [83529709333896481284, 483236613887851803796032674358] P9 = [48488203694843207484, 61393403651322347995436444958] P10 = [135873991883978443284, 1342418703213815188287580052358] P11 = [-19427775789555083916, 588015415298039058142649281158 P12 = [41805113563993625034, 91772043806874993968808258108]
Eroshkin (2007)
y2 + xy = x3 - 12330133292485949436592445464751904238410x + 526068270853525264701322899592369976900342938683261805191972 Torsion points: O, [74184882325187335284, 140098625729091997537502681958], [74184882325187335284, -140098625803276879862690017242] Independent points of infinite order: P1 = [4905857288241651324, 682419568870385061776935663998] P2 = [34359554411510493132, 378119759804359472985568201158] P3 = [-123551365829723864268, 404312866407648058578378398310] P4 = [10573197557735714484, 629985190214737097356430163558] P5 = [50496972003071345334, 179438945385893124021529037808] P6 = [240637491252319647684, 3390195758311167639456901381158] P7 = [-54066540977993417676, 1017186860794534459636769104998] P8 = [-127405192710395498316, 170116430525758365494958061158] P9 = [153470113559116816044, 1499484753154575992628934619718] P10 = [133467655369957502484, 1121577336373929494033258787558] P11 = [133352576988517939764, 1119468654460961408048670372198] P12 = [-35142395903241602316, 957067531429956634361875381158]
Eroshkin (2007)
y2 + xy = x3 + 1211947908078559188213163163805214393450x + 12487523185136437111960490242590614939802936818380403902500 Torsion points: O, [7218786168825388300, 147011881271311887688419583450], [7218786168825388300, -147011881278530673857244971750] Independent points of infinite order: P1 = [174094593215162577100, 2345229516490102683769073767450] P2 = [-8035801177852010420, 47219128802467687802481165850] P3 = [26074175133613931740, 248626068460093118029171627210] P4 = [140989496423786047180, 1727991328121643130655269581850] P5 = [106953989353422468400, 1168577570592871806712912288150] P6 = [51717261544505514100, 462053053176382853062507651450] P7 = [24625984926364779100, 239305443017407344954033679450] P8 = [159741400003774698700, 2069361587765377286656166983450] P9 = [835832012784956824780, 24185747504567921047082803917850] P10 = [79712777204662517740, 784602035812828926688901021050] P11 = [-8823809056205042900, 33264214399934792981206807450] P12 = [113723458726001881900, 1273225342616024250739608343450]
Eroshkin (2007)
y2 + xy = x3 - 10550832125564514944256818543885357615825x + 419625737407708712632765113547497120508448337766481231555625 Torsion points: O, [46568389338256803850, 171112189657361886230397691675], [46568389338256803850, -171112189703930275568654495525] Independent points of infinite order: P1 = [79926686962542884170, 294832766376023415742867978075] P2 = [68394704416818080770, 133954751548629569050308352075] P3 = [58781576061642482650, 50374886492965431536600359675] P4 = [57089477649503099710, 57885672002021166531197824015] P5 = [87439631048272000330, 406941151935030924215555061595] P6 = [57055238293350232810, 58115624990308030371508693915] P7 = [-52895681251992268550, 910889430960719041550892841675] P8 = [-41657627788383789350, 887049874192718065508231143675] P9 = [146766331280154663910, 1425663999120670449199218350275] P10 = [-93353275141765100630, 768779667753179092858150774555] P11 = [-28714328596516645250, 836008654504751183851122218575] P12 = [52626044843740954990, 100623234782195569640335616275]
Eroshkin (2007)
y2 + xy = x3 - 347224739173438611349143152475095606405720x + 131243904079630053502971198622754870300832280107569949516942912 Torsion points: O, [86298823828501546864, 10095619191114969361157788748968], [86298823828501546864, -10095619191201268184986290295832] Independent points of infinite order: P1 = [-614749561874797341776, 10600746933282861402536629692328] P2 = [475572648547118323264, 8583313415804625610117065113368] P3 = [1140115197226494169744, 34890699024068910929778689551048] P4 = [2241986579258382073264, 103063692963121940550568634963368] P5 = [1311751861331224953514, 43964683331285560396293198649618] P6 = [-474782825444657910656, 13750465615490121007791640210648] P7 = [5382285515975580852514, 392659898899681462964182663836868] P8 = [8111735896673083257184, 728744793151651671448361112233128] P9 = [514662210343360953904, 9426703177126795738830590218408] P10 = [-223741136935838459336, 14061716080321850957746462801768] P11 = [600560387177739981664, 11803400521273993098007178520568] P12 = [1318878437198782868464, 44355462228166611148551290598568]
Eroshkin (2007)
y2 + xy = x3 - 17843714757132874055011263134593557643365x + 918347652275294697563872916161846113738275813342846617692417 Torsion points: O, [67742206905192793074, 142984158466394799764815818663], [67742206905192793074, -142984158534137006670008611737] Independent points of infinite order: P1 = [91031845232245022514, 219917666655100106137993308903] P2 = [75850129567446638274, 35829302244905203784126713863] P3 = [-137804054554449291726, 872003877048826363953721477863] P4 = [91062395491766900274, 220405073187266395835724037863] P5 = [75682870370568788274, 37252885795807094056920997863] P6 = [-43461201205976781126, 1269552720180201640215358539663] P7 = [78298623351617992242, 35110091367943702503987927783] P8 = [81041969416392215514, 67270935567918458208126201903] P9 = [-77551713161158629726, 1354895382504045581515597267863] P10 = [79109995916346260274, 42810898873578978681203077863] P11 = [-150651515023150645326, 432853048054021516088940124263] P12 = [239250925801094695974, 3216237854232421576479347077563]
Eroshkin (2007)
y2 + xy = x3 - 52511008932588540734880878160900060971565x + 97380634788478317255437122176207105241892655674522315598342225 Torsion points: O, [2361149176057356930, 9861879213742511369857994107935], [2361149176057356930, -9861879213744872519034051464865] Independent points of infinite order: P1 = [-426102705225606443790, 6510838092680261462121208566735] P2 = [3343745689432367507610, 193150195569462104709098100245655] P3 = [427098414979613366850, 12363720848581623589396527790815] P4 = [1202309048647612481730, 42097986533251394009715414903135] P5 = [524692568212638206190, 14638222734209170743127650297675] P6 = [712538705984535824730, 20536030233502363544972515629135] P7 = [873036429752929199730, 26776081191861791519634591171135] P8 = [-496070042618737410348, 1163673112647665178974098749597] P9 = [2788649868203438524530, 147095449923948584602844068726335] P10 = [557822760544244141730, 15545559026343680710275887283135] P11 = [-305618370360821388990, 9213219683852819728026254496735] P12 = [-410787872703756098670, 7045028902450906395063671211135]
Eroshkin (2007)
y2 + xy = x3 + 98978303519591143407307037145293552090x + 794337445180275349451540964168292632664086352466344240100 Torsion points: O, [968989078863982220, 29852238823111767715229889290], [968989078863982220, -29852238824080756794093871510] Independent points of infinite order: P1 = [19182000926554729580, 98746850443195292840030404490] P2 = [14782697749109983100, 74080627834707871017232012490] P3 = [53052008495695613630, 394158649573849157853291834740] P4 = [40489689825849640420, 266798317776257444240802050290] P5 = [-3958480825750074580, 18452805598072851636103785290 P6 = [16484365638831906860, 83098133074569811029689169290] P7 = [6324915932142029420, 40907118970742667385127697290] P8 = [13405385824790184500, 67306657869643798869823900010] P9 = [7149486591756870020, 43213755209129620767690827690] P10 = [8023893831368328650, 45881697604716023179804884110] P11 = [9508937492380105670, 50944215071843473861548398540] P12 = [201069928400514303020, 2854781143660789370924472657290]
Eroshkin (2007)
y2 + xy = x3 + 638371365356923079870386876943741844375x + 20030368902810195212582937188953841745810795518138076948057 Torsion points: O, [1651844044492906554, 145221782263137413170399129923], [1651844044492906554, -145221782264789257214892036477] Independent points of infinite order: P1 = [42441636600850842414, 351530506252767713137151371803] P2 = [41203862702740337274, 341010168386418516658793009283] P3 = [52766998714318953354, 447925694124039097546025914323] P4 = [144504256692915183354, 1769107267404576858141747832323] P5 = [102586174216930268154, 1079410699236925910547920094723] P6 = [270139188022135996854, 4461606841207189046650698889323] P7 = [22100440326298398354, 211974440337439716831646219323] P8 = [517512923870299020954, 11787727249501276437227068473123] P9 = [260910836779080595254, 4236502559399149599355238096223] P10 = [-14421048913218808746, 88460652055944670240153796523] P11 = [12383609688219652634, 172727485338785469085408307363] P12 = [40786313305102460154, 337514693114546744286354270723]
Eroshkin (2007)
y2 + xy = x3 - 347224739173438611349143152475095606405720x + 131243904079630053502971198622754870300832280107569949516942912 Torsion points: O, [86298823828501546864, 10095619191114969361157788748968], [86298823828501546864, -10095619191201268184986290295832] Independent points of infinite order: P1 = [528969904299078404764, 9776660545804345792345227149368] P2 = [-546778707134673603716, 12555087939076320199124253779788] P3 = [1140115197226494169744, 34890699024068910929778689551048] P4 = [427268354754709650784, 7803020112197134899792809319928] P5 = [548042348944682891824, 10273986082656306249184584110248] P6 = [2194751379780455552944, 99705283887981173884650423792808] P7 = [-250452301732960584656, 14230150355063182090558646948008] P8 = [8111735896673083257184, 728744793151651671448361112233128] P9 = [514662210343360953904, 9426703177126795738830590218408] P10 = [-223741136935838459336, 14061716080321850957746462801768] P11 = [600560387177739981664, 11803400521273993098007178520568] P12 = [1318878437198782868464, 44355462228166611148551290598568]
Elkies - Rogers (2004)
y2 + y = x3 + 44182596082121121317135170025680399046545625711306 Torsion points: O, [0, 6646999028292476087078617], [0, -6646999028292476087078618] Independent points of infinite order: P1 = [-30156002278649820, 4093799681127459731025817] P2 = [11364087102067560, 6756491872572362690626342] P3 = [-20835788771691894, 5927660006237675713476241] P4 = [1134264920569989390, 1208031685828825118221478017] P5 = [8907565209691176834, 26585114133655761890666064910] P6 = [111849199886121334, 37992674604901443769570910] P7 = [11724873521668020, 6767159346634715672034457] P8 = [-138658831412368575/4, 12719819443574268333325811/8] P9 = [165971060901522240, 67941788876402816577138982] P10 = [994768217796990, 6647073075327662243966017] P11 = [532896351059436225/16, 576457310785324883248677823/64]
Eroshkin (2006)
y2 + xy = x3 - x2 - 4536184139377606759385840064x + 117756938515259070124029037981449282901220 Torsion points: O, [33618885611941, 57031010525639772307], [33618885611941, -57031044144525384248] Independent points of infinite order: P1 = [-19490912550326, -445832687088207682886] P2 = [99694509539254, -810177524574020786498] P3 = [44209842630586, 60179204272303054492] P4 = [19042989810446, -195653002235648166468] P5 = [39937171925371, 17130985069181971582] P6 = [-5180338033241, -375655273818610196726] P7 = [40648708695664, 23053923614463599554] P8 = [264049839228931, 4162948942598699706502] P9 = [-11554767109984, -410644344382289546298] P10 = [8407403487266, 283220194078161953452] P11 = [37535093077111, 19323726664997391322]
Eroshkin (2006)
y2 = x3 - 2902707625457545077500107175592x + 1904597097766869546326844055645258034709879849 Torsion points: O, [883309903897008, 5458684044929332492275], [883309903897008, -5458684044929332492275] Independent points of infinite order: P1 = [-1918723880006577, 20256036721460643337080] P2 = [-825654663146817, 61142274721662403678500] P3 = [2092061748308938, 70628088871960572792385] P4 = [1167051651989734, 10320991880819300927785] P5 = [164575959418458, 37833038284168124572575] P6 = [3948225371905857/4, 8506371808216432082625/8] P7 = [434719394368308, 26923734542791513147875] P8 = [696962978964658, 14834832809096935264175] P9 = [131064339186060, 39069259603777455479427] P10 = [979980554131023, 1065853725738960152280] P11 = [973568051517558, 1181237636592991511625]
Elkies - Rogers (2004)
y2 = x3 + 4692726937524378378756566939402025 Torsion points: O, [0, 68503481207339955], [0, -68503481207339955] Independent points of infinite order: P1 = [-135797482140, 46781315964225555] P2 = [-150436201545, 35891470127810220] P3 = [-42200591214, 67952721291406041] P4 = [2327642247924, 3551854243978575507] P5 = [5504535148140, 12914782107290941395] P6 = [140506152430, 86409469562070095] P7 = [397507563420, 259814927561209005] P8 = [7162660587075, 19169656506442936830] P9 = [73148794740, 71303068454026605] P10 = [-102758626586, 60063833881519937]
Elkies - Rogers (2004)
y2 + y = x3 + 87299817093221362429969788356520 Torsion points: O, [0, 9343437113462120], [0, -9343437113462121] Independent points of infinite order: P1 = [-34739896854, 6735993625205487] P2 = [59816792760, 17358779174601879] P3 = [-44207258970, 952038792981504] P4 = [6576595440, 9358646559113879] P5 = [55473407808, 16062629859888488] P6 = [-19255568904, 8953228261141352] P7 = [101583478425/4, 81458264395412407/8] P8 = [11986370039488/81, 42053694778844172287/729] P9 = [-2123513196948/49, 833762857240311704/343]
Elkies - Rogers (2004)
y2 = x3 + 30457819633596695100179965225 Torsion points: O, [0, 174521688146765], [0, -174521688146765] Independent points of infinite order: P1 = [-734843410, 173381106196815] P2 = [5130038900, 406775844709485] P3 = [-2676929565, 106184137901590] P4 = [690947990, 175464197227935] P5 = [291207945620, 157146639625792365] P6 = [25120488440, 3985280944128435] P7 = [-872639080, 172607374924365] P8 = [2918890200, 235215923409485] P9 = [-102315705, 174518619468760]
Kulesz - Stahlke (2001)
y2 + xy = x3 - 101802374223975950878048695685575x + 423441144264551283172186925767924238963073455625 Torsion points: O, [3228164584980150, 358395281084675043437925], [3228164584980150, -358395284312839628418075] Independent points of infinite order: P1 = [7954744215743400, 342036905663438696325675] P2 = [6842957560456950, 217349059459739953181925] P3 = [7252229378427006, 258024710976748981568877] P4 = [6805111068044022, 214023876297663843151077] P5 = [7420355659278390, 276782501766541023783525] P6 = [7319642360196150, 265423911498353437421925] P7 = [1428472688645430, 530032149681385991924325] P8 = [1754872493274300, 500195184802880868728175]
Dujella (2001)
y2 + xy + y = x3 - 4213613959455x + 3328416232976793662 Torsion points: O, [1275964, 170749461], [1275964, -172025426] Independent points of infinite order: P1 = [137177, 1659144070] P2 = [-563615, -2350086962] P3 = [1154661, 50052976] P4 = [1115531, 126630386] P5 = [1263107, 145593902] P6 = [1293422, 204910252] P7 = [1199524, 4879029] P8 = [1570524450, 62238798865528]
Dujella (2001)
y2 + xy = x3 - 31931594312439500340x + 69606680279441891519909634192 Torsion points: O, [2747698824, 51116009544588], [2747698824, -51118757243412] Independent points of infinite order: P1 = [2411566104, 81401231483868] P2 = [2241836544, 96375001873908] P3 = [2403574824, 82111946472588] P4 = [3026475564, 26221716181308] P5 = [3020419272, 26737203531180] P6 = [104889704, 257407287746828] P7 = [12145945551/4, 203003701834509/8] P8 = [2959539744, 32031284219148]
Dujella (2001)
y2 + xy = x3 - 286699610291764606928838x + 59110806824657235777329702047745892 Torsion points: O, [280891170252, 27233824468946634], [280891170252, -27234105360116886] Independent points of infinite order: P1 = [318396699432, 10223679281236974] P2 = [-49377625704, -270456927185157570] P3 = [330898542492, 21763968085963194] P4 = [137818873836, 149050012878717930] P5 = [-50858768268, -271220261144527926] P6 = [257135268852, 48904223792122314] P7 = [316883355096, 8962751754738474] P8 = [-473189014188, -298031944920331446]
Elkies - Rogers (2003)
y2 = x3 + 708291392738196762720225 Torsion points: O, [0, 841600494735], [0, -841600494735] Independent points of infinite order: P1 = [-88860785, 81396479060] P2 = [-87348261, 204569627262] P3 = [-63256830, 674665720365] P4 = [-40588401, 800890328532] P5 = [101707060, 1326794024465] P6 = [-35705670, 814107128835] P7 = [-44793980, 786391914385] P8 = [8308684440, 757353550270065]
Elkies - Rogers (2004)
y2 = x3 + 136677874368461861091875625 Torsion points: O, [0, 11690931287475], [0, -11690931287475] Independent points of infinite order: P1 = [-505980450, 2671829766225] P2 = [-241990650, 11068289345025] P3 = [-351203600, 9662247592525] P4 = [259337650, 12414503280025] P5 = [-464466761, 6039764206388] P6 = [73448775, 11707865310600] P7 = [-96861050, 11652000596225] P8 = [-101098316, 11646654527123]
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