Connell (2000), Dujella (2000)
y2 + xy = x3 - 15745932530829089880x
+ 24028219957095969426339278400
Torsion points:
O, [-4581539664, 2290769832], [-1236230160, 203972501847720],
[2132310660, 12167787556920], [2452514160, 12747996298920],
[9535415580, 860741285907000], [2132310660, -12169919867580],
[-1236230160, -203971265617560], [9535415580, -860750821322580],
[2452514160, -12750448813080], [2346026160, -1173013080],
[1471049760, 63627110794920], [1471049760, -63628581844680],
[3221002560, -82025835631080], [3221002560, 82022614628520],
[8942054015/4, -8942054015/8]
Independent points of infinite order:
P1 = [2188064030, -7124272297330]
P2 = [-2815745040,-214568724545880]
P3 = [3643261410,-122557804465830]
Dujella (2001)
y2 + xy = x3 - 2564530435455464744050430x - 774033544664307864229665861908231100 Torsion points: O, [16618584813010, -67426145676274447880], [2169649474900, -1968552933159520070], [2169649474900, 1968550763510045170] [-447882003740, -533599927551503630], [-1227486286730, -724161720859881290] [-313881055364, 156940527682], [-5684941839585/4, 5684941839585/8] [1735116515260, -867558257630], [-807983468840, 877828928053364470] [-807983468840, -877828120069895630], [16618584813010, 67426129057689634870] [4278216499360, -8158380056050342130], [4278216499360, 8158375777833842770] [-447882003740, 533600375433507370], [-1227486286730, 724162948346168020] Independent points of infinite order: P1 = [-331856672240, -201186308576020130] P2 = [681747812843740/361,-7252543732961516356970/6859] P3 = [6714894088217635/3844,65964362556960760047245/238328]
Campbell - Goins (2003)
y2 + xy = x3 - 18262097056293794050462967800x
+ 947221615382521776843113311413294620840000
Torsion points:
O, [384056732811440, 7112084226340944585800],
[86673191107100, 124488424515112474700], [69584365444100, -115721935078771750300],
[-54632409541840, -1334864242442902982200], [-54632409541840, 1334864297075312524040],
[69584365444100, 115721865494406306200], [86673191107100, -124488511188303581800],
[384056732811440, -7112084610397677397240], [74619273455600, -37309636727800],
[-623977550204801/4, 623977550204801/8], [81375114095600, -40687557047800],
[41329758236000, -512884940394970007800], [41329758236000, 512884899065211771800],
[121420469955200, 721056636920400552200], [121420469955200, -721056758340870507400]
Independent points of infinite order:
P1 = [74021617782920,31794425743000034480]
P2 = [81766735559600,25797576413352528200]
P3 = [8775517172730787722056858700518960/117806438860954586521,
18243142868646417426484039651543006669780183825640/1278655473449200890038991093181]
Rathbun (2003)
y2 + xy = x3 - 1501011456398147086648544266758850x + 22251270940723503314374317274872523646621572635332 Torsion points: O, [-18004996592822356, -6590911844637378629814682], [9895942925525792, -2892482299592193885785902], [9895942925525792, 2892482289696250960260110], [83801916803450591/4, -83801916803450591/8], [23756609930945348, -11878304965472674], [37617276936364904, -4360962447048323352828502], [37617276936364904, 4360962409431046416463598], [-44707089131807996, 22353544565903998], [123637769719875434, -41552778147840818577570412], [25680076681242524, -800204848264852023727882], [-18004996592822356, 6590911862642375222637038], [19156257937164014, 726038019382107000286178], [25680076681242524, 800204822584775342485358], [123637769719875434, 41552778024203048857694978], [19156257937164014, -726038038538364937450192] Independent points of infinite order: P1 = [585150090442017404, 446653884639086830911813998] P2 = [60858503151041321123234/271441, 14802686107078222471948784650679698/141420761] P3 = [288266315903991120130014776246/367947788569, 154585670444642553138450754364572706622327814/223192345224704003]
Campbell - Goins (2003)
y2 + xy = x3 - 590353702194591280765010561772238260x
+ 174588372339329184400865798305984325852297773091859600
Torsion points:
O, [403892642649189720, 45117248361149658382349340],
[403892642649189720, -45117248765042301031539060],
[484536348331430520, -47935326971688922180499460],
[484536348331430520, 47935326487152573849068940],
[999365849872638120, -763352998019322222734115060],
[51562583436942120, -379849048667143531212267060],
[999365849872638120, 763352997019956372861476940],
[447143159545088340, -4027018202173742400995460],
[440073800471053500, -4005683155727988678251640],
[447143159545088340, 4027017755030582855907120],
[442993356443270120, -221496678221635060],
[444214495490310120, -222107247745155060],
[440073800471053500, 4005682715654188207198140],
[51562583436942120, 379849048615580947775324940],
[-3548831407734320961/4, 3548831407734320961/8]
Independent points of infinite order:
P1 = [4043145978848660830/9, 174836140793270820642525880/27]
P2 = [-344320394143837595000245442992956696/814862753036115169,
-434298487065859430358209850792879439798635022311026124/735574559415602783298880303]
P3 = [1451737788330638657633482779601154870036516263378345751837531961063344239611753112849556760/
3155136161424248768625112088369105899244411500618381837275221737203503929,
107360513440730689070029083206307720462995748894071425185832190680260396195579613118258628735894896986022984370130847040150217732224660/
5604374640684366142548869049661504017759384690908932215403119227589334003883898544252546288500646931113819283]
The third independent point found by M. Watkins (March 2005).
Dujella (2006)
y2 + xy = x3 - 30507963373084413759489146596105237240x + 64489450113318178611265574148979256340153096329702465600 Torsion points: O, [11961670643380191359/4, -11961670643380191359/8], [-6373837227150843920, 3186918613575421960], [3383419566305796080, -1691709783152898040], [3654569228870148080, 1343860220552335814092541960], [17525500642981370960, 70090370161258775918222295560], [3654569228870148080, -1343860224206905042962690040], [17525500642981370960, -70090370178784276561203666520], [-2550742205939195920, 11212115863563412748297981960], [2737225434923430800, 1220931235200740144167921160], [2737225434923430800, -1220931237937965579091351960], [-2550742205939195920, -11212115861012670542358786040], [1425200857402653680, -4889206373126912123661339640], [1425200857402653680, 4889206371701711266258685960], [5341638275208938480, 7344415662569582990831357960], [5341638275208938480, -7344415667911221266040296440] Independent points of infinite order: P1 = [10895065363091269280, 32021463711584565201301180760] P2 = [590785466637255702306320/134689, 191846322697158506956592726494653080/49430863] P3 = [1178101453122586514401520/237169, 688303727761229397008667652599805880/115501303]
Dujella (2006)
y2 + xy = x3 - 21015960530302473341210266357147569830x + 17566852216331096945097199161461136733028723845196826852 Torsion points: O, [-3679234914110992316, 6714503169501496894330721098], [9487461106090734544, -25926112660917713498375025722], [9487461106090734544, 25926112651430252392284291178], [337356540704445754, 3242741868948536349422940238], [-1309484890129172408, -6545341463304099143816536082], [-1309484890129172408, 6545341464613584033945708490], [3467515766704545951/4, -3467515766704545951/8], [-4955867049656917556, 2477933524828458778], [4088988107980781068, -2044494053990390534], [-3679234914110992316, -6714503165822261980219728782], [337356540704445754, -3242741869285892890127385992], [36297907350124685614, 216976050617525684940372429838], [36297907350124685614, -216976050653823592290497115452], [4993815447644799124, -6095388090235017959119842782], [4993815447644799124, 6095388085241202511475043658] Independent points of infinite order: P1 = [-323768234654667598073236376174/72977240449, -95528205831866792550988270101905028199626094/19714290666614207] P2 = [14313485330700724862739929253151/16750995468804, 33087135823218327101262727287106584612554256751/68558440752730073592] P3 = [-180780928705551339014149547355608/89374315532401, -6081165188483001212676838107943235738339842820990/844926814805897041399]
Dujella (2006)
y2 + xy = x3 - 15343063417941874422081256126489574987160x + 486503741336910955243717595559583892156442731284430865537600 Torsion points: O, [231617775908238208320, 3059138547705534346041804296040], [231617775908238208320, -3059138547937152121950042504360], [-96756198617687116560, 1032100640555285783204846146920], [20367216277135641420, 427149915439181940159082514040], [124378527470717550420, -708727152937284690857720109960], [20367216277135641420, -427149915459549156436218155460], [-96756198617687116560, -1032100640458529584587159030360], [878481558502786758000, -25786786260942624213939494169240], [878481558502786758000, 25786786260064142655436707411240], [124378527470717550420, 708727152812906163387002559540], [103066938249872815920, -51533469124936407960], [34349987359939375920, -17174993679969687960], [-25483899408492576480, -927876521675299652614082871960], [-25483899408492576480, 927876521700783552022575448440], [-549667702439248767361/4, 549667702439248767361/8] Independent points of infinite order: P1 = [62974185209012301066421176/7392961, 12000885861522378526762014623886832999128/20101460959] P2 = [-33877133035878336982966500/844561, -790534983278326482737332351141316687160/776151559] P3 = [537614203446300716665300020/16900321, 12157075128111066917277688092780713996040/69477219631]
Rathbun (2006)
y2 + xy = x3 - 59654254810332161499933732539083310x
+ 936036113034275895945648528397370958419427728893572
Torsion points:
O, [2172909887011690234, -3182889877373545939206543392],
[291435641750171284, -91124467662809922713619542],
[-197931911432951666, 70633774398514491172482508],
[-11552285349244316, 40294383897701739456074458],
[2172909887011690234, 3182889875200636052194853158],
[291435641750171284, 91124467371374280963448258],
[-197931911432951666, -70633774200582579739530842],
[-11552285349244316, -40294383886149454106830142],
[15756596261393884, -7878298130696942],
[-1006956083242885089/4, 1006956083242885089/8],
[235982424549327388, -117991212274663694],
[563715332994916384, -382678252577154660895909442],
[563715332994916384, 382678252013439327900993058],
[-91750483896261608, -75079780211573372996434430],
[-91750483896261608, 75079780303323856892696038]
Independent points of infinite order:
P1 = [423636398364728130558/32041, 70153524044528407532259723512964/5735339]
P2 = [-212218555436959806104/1369, -4070672727584190624828727982726/50653]
P3 = [8452319722523363921569428256760017402630395565491507482512250164/
59692072868085173675728631193552258578545561,
777075522029540793165779905112440827567904945232388550670644286763642232436234047429573571171782/
461184805928472795689461276558991227050395203450511219660991605059]
Rathbun (2006)
y2 + xy = x3 - 153010567793393992556815434658906721140x
+ 728501166933268696802867483882463385720151113375539573392
Torsion points:
O, [7136668969896945704, 23099419970919959862732428],
[4061538115253562644, -13192513775101300439821482052],
[7136668969896945704, -23099427107588929759678132],
[10738972043545873064, 17994512995789382383525462028],
[7146682296961855484, 23110218372866739764213768],
[4061538115253562644, 13192513771039762324567919408],
[7146682296961855484, -23110225519549036726069252],
[10738972043545873064, -17994513006528354427071335092],
[28565149165049492671/4, -28565149165049492671/8],
[-14283350103904692376, 7141675051952346188],
[7142062812642319208, -3571031406321159604],
[7013160268870079192, 593069146560615481135978700],
[7013160268870079192, -593069153573775750006057892],
[7270965356414559224, 600248550074690269251440588],
[7270965356414559224, -600248557345655625665999812]
Independent points of infinite order:
P1 = [2496091851384905686508344/301401, 896029991220504039247351192716501452/165469149]
P2 = [12615321377550619950231033409256/1776481125409,
442088743692246551824728086371328935967298164/2367777538558009423]
P3 = [3662275643349047922027557491418965900328341380384197044972605735916136/
1079191891412968056127590909185669355748367493207289,
558684560664533643585768362793027922417196104247683786808932066647094821421265579707666093396835958760156/
35452593441841085321192243655271783294098334214638916283068984995773571997837]
Rathbun (2006)
y2 + xy = x3 - 4527869148423161203017834259729075232020x
+ 109150076525339545219757428860519443874479508277436337856400
Torsion points:
O, [1346558508812422040, 321022549679742306432091220780],
[1346558508812422040, -321022549681088864940903642820],
[92497102838720102840, 694056236208390273621157556780],
[92497102838720102840, -694056236300887376459877659620],
[-44931919096104508060, 471045531643856283598463281280],
[24308650067491938920, 115965191469086042869418252780],
[-77095097563239177560, 38547548781619588780],
[336517414957140387560, 6057558211763587718022317449580],
[54094265426352592940, 150027981727538736316323676280],
[120693067557891660479/4, -120693067557891660479/8],
[46921830673766262440, -23460915336883131220],
[-44931919096104508060, -471045531598924364502358773220],
[24308650067491938920, -115965191493394692936910191700],
[336517414957140387560, -6057558212100105132979457837140],
[54094265426352592940, -150027981781633001742676269220]
Independent points of infinite order:
P1 = [21314386723997659557280/81, 3017947060024533467886816450022220/729]
P2 = [14543372431855398965476829823848/485241807649,
6469872485529287755605117414151791334525649452/338016046515639857]
P3 = [-114618670527383598003666132031471822360/2270018301844156081,
-1563732439397792869697558860057776098758211584995180980620/3420141214189747796089893271]
Dujella - Rathbun (2006)
y2 + xy = x3 - 3207498288387657621672732005424372705920328770x
+ 68304282772313573439179636385556451355850337924379829175788684488900
Torsion points:
O, [24746904833392728174940, 2020856876072391701726498934223030],
[7903034194933076287840, 6591579585310336939196188490682130],
[7903034194933076287840, -6591579585318239973391121566969970],
[65448903305619408864040, -11778424027315270370904208754098070],
[65448903305619408864040, 11778424027249821467598589345234030],
[228787792826772566585950, -106348966554149434905241308089137280],
[-32724427516721561041670, 11756854433554349839561625705036740],
[40985343079033901736940, -2385576778341943854696176733178970],
[-32724427516721561041670, -11756854433521625412044904143995070],
[24746904833392728174940, -2020856876097138606559891662397970],
[228787792826772566585950, 106348966553920647112414535522551330],
[40985343079033901736940, 2385576778300958511617142831442030],
[28551814894630863335940, -14275907447315431667970],
[36675968750276242575940, -18337984375138121287970],
[-260911134579628423647521/4, 260911134579628423647521/8]
Independent points of infinite order:
P1 = [22846201954487061296170647421060/7006609,
109183226786723806127509952477976944983711420690/18546494023]
P2 = [8781852554545044756170870387874126010/233658035659129,
3280159061355109729170468052344035819749855878060270490/3571667993147059821133]
P3 = [258286266983032617397787369369373455186295923375620/18695418702921634383283969201,
13190845285796317678557186972781192193361551808962073508112846505160757966030/
2556246873058335351513763793171125613693801]
Dujella - Rathbun (2006)
y2 + xy = x3 - 16188503722614063108729139735755154904562292360x
+ 786863421808206463969913495490892469346874709447053592901366525761600
Torsion points:
O, [126942113771663398101920, 27882680574001240245704236363397240],
[126942113771663398101920, -27882680574128182359475899761499160],
[30228264599630424878720, -18031474247759343557251945104801160],
[30228264599630424878720, 18031474247729115292652314679922440],
[422083239655931288586320, -262963676295121325354530570456161160],
[85392774125986994678180, -5211521754389769127545451481401720],
[-61613633858042970798640, 39375066083178460970956312648094840],
[61906075162778279941820, 4684356135071180542946299694504840],
[85392774125986994678180, 5211521754304376353419464486723540],
[422083239655931288586320, 262963676294699242114874639167574840],
[61906075162778279941820, -4684356135133086618109077974446660],
[-61613633858042970798640, -39375066083116847337098269677296200],
[68209869346874809632016, -34104934673437404816008],
[78585189185646911490320, -39292594592823455745160],
[-587180234130086884489345/4, 587180234130086884489345/8]
Independent points of infinite order:
P1 = [66119657073815781066800, -2355339128918565969721076384104840]
P2 = [401169287265672834550867500080/76335169,
-17669918374394464360754418260810255353172665480/666940371553]
P3 = [289687648221921501808291121532003587972851140280852543070142236950355376437227490536812623183120/
17156914675194799164872812895696296908615977178623591714662702334872955881,
-1617954908834725344870195603458416032731793227363235820394569809657744633819656062208905822304087388210043858968407239618913517436708870237508440/
71065495284003135354842363163578373997823698038097319480954479040616074792502966798554498341539450071275232779]
Flores - Jones - Rollick - Weigandt - Rathbun (2007)
y2 + xy = x3 - 250878395393474545316759183209311840250x
+ 1479979592022167493224960512910755689574299477808903560932
Torsion points:
O, [68156184360686840234, -548620665858774781668749384212],
[19241236869397662104, -61452092383940456995970809102],
[11794281695058898124, -12715881122248678201988334082],
[10456933579800800948, -5228466789900400474],
[11794281695058898124, 12715881110454396506929435958],
[19241236869397662104, 61452092364699220126573146998],
[68156184360686840234, 548620665790618597308062543978],
[7766447618213273204, -3883223809106636602],
[6608547727503159644, -10519135261480367776983634762],
[1672630290203939792, -32634832515464687840622144490],
[-9594066305658249586, -54807180967165504404174184822],
[-72893524792056296609/4, 72893524792056296609/8],
[-9594066305658249586, 54807180976759570709832434408],
[1672630290203939792, 32634832513792057550418204698],
[6608547727503159644, 10519135254871820049480475118]
Independent points of infinite order:
P1 = [621727883860331879066288/80089, -11195733275105659072676635210992274/22665187]
P2 = [-3121826350817955803774630199394084/180524403067969,
61692108418757143009501414171937398097766847203574/2425514506583838201953]
P3 = [62782486665149487218097131208426297104/8547022989099698401,
-144593985742523950403942776316687052257460712416405160202/24987471290251272975616507601]
Flores - Jones - Rollick - Weigandt - Rathbun (2007)
y2 + xy = x3 - 97786754135136291205325201456018300x
+ 6192618544071258703787593919472934977414964438890000
Torsion points:
O, [2412494120994676600, -3716356678419606264093338300],
[631768530962716600, -443365234904237874461378300],
[334018109980616800, -103903016996839909899338300],
[274236048186676600, -137118024093338300],
[334018109980616800, 103903016662821799918721500],
[631768530962716600, 443365234272469343498661700],
[2412494120994676600, 3716356676007112143098661700],
[265237400106587199/4, -265237400106587199/8],
[30252528978676600, -57114004555111060893338300],
[-83296434589363400, -117302903560073060125298300],
[-249690636103103600, -122645788091838955199258300],
[-340545398213323400, 170272699106661700],
[-249690636103103600, 122645788341529591302361900],
[-83296434589363400, 117302903643369494714661700],
[30252528978676600, 57114004524858531914661700]
Independent points of infinite order:
P1 = [274887906914724556, -9147492786135424992704588]
P2 = [62718943759824249209034178076092600/1241034587031947761,
-51354834432149065162729129239810440358544450486369700/1382534023431602612057272759]
P3 = [30248369105401958555069911173485380/89681232159126001,
2890206598473212141332130140412636902647519116897480/26856681562855952889842249]
Flores - Jones - Rollick - Weigandt - Rathbun (2007)
y2 + xy = x3 - 1621197495376612287530904105233724120x
+ 792688598791865073857094426358748343551798168746190400
Torsion points:
O, [3511162314817559160, -6195718344276089217794183520]
[1122265697094317040, -621888891456815245393207320]
[810503350065758640, -105522308003205826390735320]
[763710149262110640, -381855074631055320]
[810503350065758640, 105522307192702476324976680]
[1122265697094317040, 621888890334549548298890280]
[3511162314817559160, 6195718340764926902976624360]
[2824604703815991935/4, -2824604703815991935/8]
[661499287147697640, -98627247357463778323642320]
[405154601429904240, -449843532173591237050240920]
[-494102163653747280, -1213712154536757787182077400]
[-1469861325216108624, 734930662608054312]
[-494102163653747280, 1213712155030859950835824680]
[405154601429904240, 449843531768436635620336680]
[661499287147697640, 98627246695964491175944680]
Independent points of infinite order:
P1 = [184265049963459555715756173360/183152329369,
33252887250675563312176497099144406413258360/78382420333745347]
P2 = [82783276094283429032303138646750640/107935148321592201,
747042050857350584081590197310444933406960306538680/35460457871497193838297051]
P3 = [883193138665626092244648865044768278534403013785057249004972327632/
1015272818993790179595312025606995606967976322481,
-206355224855206696230997552878641266346125995941713540380329699739899409129414382783494501582099048/
1022996479223612825011249658698109282807737802426954717854552678271406871]
Dujella (2008)
y2 + xy = x3 - 7508232300031068945507236861692000278143017800x
+ 98536599045907325394109218811543289797912305023169446880249900840000
Torsion points:
O, [185352940682152660141200, 71237602613763561900439287907356600],
[185352940682152660141200, -71237602613948914841121440567497800],
[3460036467683584106640, -8520520202765373489564002189488200],
[3460036467683584106640, 8520520202761913453096318605381560],
[-69924386382988012520400, 16782593821935533274965810748658200],
[-27072934080976642950000, 16791769980466891774929961350607800],
[-27072934080976642950000, -16791769980439818840848984707657800],
[-69924386382988012520400, -16782593821865608888582822736137800],
[710878746324524962206960, -594981232775976968162883906137836200],
[710878746324524962206960, 594981232775266089416559381175629240],
[96997366319390106771600, 16818338245586195529874878358966200],
[96997366319390106771600, -16818338245683192896194268465737800],
[-370350832816127451268225/4, 370350832816127451268225/8],
[13447704903443854221456, -6723852451721927110728],
[79140003300588008595600, -39570001650294004297800]
Independent points of infinite order:
P1 = [-2694568576987041495959178450/942841, -10027582070704208948409204659888495021260500/915498611]
P2 = [3970465520942714626939047462365658730422096528/1812535448603270689,
250185504316803131532134327979586853605556137590939217382022442783176/2440224389796887379083798863]
P3 = [-667104712607831226657178167710669443876760614892400/22554833887350579603456918721,
58153301912038353051602983895232189994148255513921056042552709247894836911800/3387345138491485663907457308101563095956769]
Fisher (2009)
y2 + xy = x3 - 87306660786172655975387678466748290400x
+ 217110378089173582243961228486559615973771263335020160000
Torsion points:
O, [1669735329772740800, -8717029941391454078378370400],
[-7254150279199829800, -21649782187993296417273344800],
[64987362627595365800, 518659939811183754051030629600],
[1669735329772740800, 8717029939721718748605629600],
[-7254150279199829800, 21649782195247446696473174600],
[9252777066556126400, 14193219739781876098850429600],
[2716314313200741056, -1358157156600370528],
[-41603973793557927425/4, 41603973793557927425/8],
[64987362627595365800, -518659939876171116678625995400],
[9252777066556126400, -14193219749034653165406556000],
[7684679135188740800, -3842339567594370400],
[17163931186181100800, 61441745972443707605574269600],
[17163931186181100800, -61441745989607638791755370400],
[-1794572915803619200, 19183564301517113491461989600],
[-1794572915803619200, -19183564299722540575658370400]
Independent points of infinite order:
P1 = [3888389281477760302164731675/1675592356, 356417057891849547266702905721618838031525/68588697500504]
P2 = [2496696667790212491908498894596171695618200/1012027927012975570430329,
4165195691283669818126200299930369868594696169603332876320143200/1018096033886874322960381838946301517]
P3 = [475895390891232373643072236932203983456664030946407307250/7346994645556866599186914246742747289,
10277278351192944745357620448527902233008836938952787496189272376269085022422349633050/19914278893564478018170895166925797756827801313841227837]
Fisher (2009)
y2 + xy = x3 - 28496542442921974135365803597630606183560x
+ 930028463295087397876426818791882627215096824737621502785600
Torsion points:
O, [-46478876034243941680, 1467688000093609913464456747640],
[-46478876034243941680, -1467688000047131037430212805960],
[1318220985222820328720, -47476800119387027399063701588360],
[1318220985222820328720, 47476800118068806413840881259640],
[181967197668850693400, 1330376430063649842385809091760],
[181967197668850693400, -1330376430245617040054659785160],
[14531285838585704720, 720420336183260170122559723640],
[14531285838585704720, -720420336197791455961145428360],
[-135127039181894266360, -1520971552898403767348893122760],
[-135127039181894266360, 1520971553033530806530787389120],
[344898107387090615120, 5668234058802281195223213355640],
[344898107387090615120, -5668234059147179302610303970760],
[-183227597275753303280, 91613798637876651640],
[136071926397319866239/4, -136071926397319866239/8],
[149209615676423336720, -74604807838211668360]
Independent points of infinite order:
P1 = [1454325638141897038414999312/9728161, 3185388268925722131952833060406220088584/30342134159]
P2 = [12144380016386165873956187029418761765638815/22403640429430752412804,
40347016554723133291863623548476431413478755244280572590806919255/3353342326134477042752517776041592]
P3 = [ -41554486788060054850941013197009849645082098385776680594908666706428165839680/456984738121549624533615308869333699622697646624523348601,
16257165155727704525354598119671254058036601043363698765103525012871018751600667532594056111158669097852229731896360/
9769054766720221536148677821713361495748633903749184319614900927829658669292495398349]
Fisher (2009)
y2 + xy = x3 - 1020063221452742528711237053898259919109330x
+ 394868843305477898697900385068741989177100444077780447528592900
Torsion points:
O, [509472723693937984060, -2722948228698735171582685818530],
[3055457350785280330060, -160634080651079471553909367338530],
[658849064841141888430, -2965758418130310030348595010030],
[3055457350785280330060, 160634080648024014203124087008470],
[658849064841141888430, 2965758417471460965507453121600],
[509472723693937984060, 2722948228189262447888747834470],
[-441617925558624786710, 27553945205231124474551726403940],
[-441617925558624786710, -27553945204789506548993101617230],
[281996897304422100160, 11385921464251141371819260249470],
[281996897304422100160, -11385921464533138269123682349630],
[945540303440433853960, 16604665656425297433098783813470],
[945540303440433853960, -16604665657370837736539217667430],
[2207643843335110743519/4, -2207643843335110743519/8],
[613768600372427977060, -306884300186213988530],
[-1165679561206205662940, 582839780603102831470]
Independent points of infinite order:
P1 = [579134216025701576839700860/361201, 11652219128690792038256499913392424136470/217081801]
P2 = [143323974816385441734934161845362823946206810003795773811006467438204090/7948964884044315755199660547148122820476145414569,
54176447873373332160916231000719058215537311649154649248789744992316899999673360540222886844741121571845990/
22411239028772254693265853844917900376122276293008869707453469040609696747]
P3 = [430933266422085631969362497494548572081451961867991799978235392833909967813894605444847310/37450355616357571401354257954458754421597835044552961483731714886201,
281833328827024533501859613504123436027656029363155377491439480558717225038613105042812668958632937089083722503447075305829963214679530/
229183801560450093419805152181230046095710149288529478432080974993176067771023568176008608819939411949]
Fisher (2009)
y2 + xy = x3 - 2008408366171799322006725680352504756640960x
+ 1088347028183149020228866231691755600541724741509337773822873600
Torsion points:
O, [3053938585582027027455/4, -3053938585582027027455/8],
[871743521241881819520, -435871760620940909760],
[-1635228167637388576384, 817614083818694288192],
[695824370267989395840, 5267438503757198834553720640320],
[4601511405809971931520, -298795261999516580916761185901760],
[-671021622901317882480, 46194064023854910751828279752240],
[1392706028827395553920, 31504905937655278283136973611840],
[1392706028827395553920, -31504905939047984311964369165760],
[4601511405809971931520, 298795261994915069510951213970240],
[944509962132938770800, 5829388970516230931694453967440],
[944509962132938770800, -5829388971460740893827392738240],
[350781013656368085120, -20663934019089673131175540071360],
[350781013656368085120, 20663934018738892117519171986240],
[695824370267989395840, -5267438504453023204821710036160],
[-671021622901317882480, -46194064023183889128926961869760]
Independent points of infinite order:
P1 = [871842613747313354520, 164071869245135467114538235240]
P2 = [-410817964422770871621437343129527235520498279231413424471788480/857847006594646675719999335580571562220121,
34998776697295432541092329560771686852923273751984948676408382261636162471451920470188576467840/794538159898072605034784281027980145244450632749428862426631331]
P3 = [-525085435402319949885392341257799180258824002345638474594062320822714730/361767309951804886153929043055737875902870712633241,
211601536457830537100089521791516074418316961471243894677538636372819215707958780804053519513386942444185060/
6880879949866383030199538005700923073636003189492531396047821220370553417539]
Fisher (2009)
y2 + xy = x3 - 151659336416513610120941619754231911069120x
+ 22664749439132439148133088299158455435686131311858534821990400
Torsion points:
O, [-159393769516885084800, -6541306067480576947105262239680],
[199942708737595601640, -578530836240195601516490281320],
[-159393769516885084800, 6541306067639970716622147324480],
[199942708737595601640, 578530836040252892778894679680],
[352039472636288802240, -3592152380668412467637470648320],
[214723992423504661376, -107361996211752330688],
[234806882742480800640, -117403441371240400320],
[-1798123500663941848065/4, 1798123500663941848065/8],
[117574292848672799040, -2541421579410793642523330512320],
[117574292848672799040, 2541421579293219349674657713280],
[352039472636288802240, 3592152380316372995001181846080],
[1117227315755487584640, 35323454535688730203369213039680],
[1117227315755487584640, -35323454536805957519124700624320],
[250381635568957107480, -623460261013343243760813106560],
[250381635568957107480, 623460260762961608191855999080]
Independent points of infinite order:
P1 = [9565362468639540463644849360/39980329, 69273511220115334638960130718296831012560/252795620267]
P2 = [7946033077221090047610008376597275280/27748416318516481, 7620022167008954790909819253714149186428389766511226320/4622291204870560422730879]
P3 = [547496038437564954084383615571937485870742069706003569253760/2143125636953964412929416979206307389089,
76426580794187972576232170491340624898413911982337258326017725664328085680948232728331840/99213654566255402344682711715957276003296518493756459539313]
Fisher (2009)
y2 + xy = x3 - 9978082456644606532120457534482336270x
+ 12118558737989607267350601135758073759160572299571620612
Torsion points:
O, [2606786632889821664, 1954947376794955237818321218],
[2606786632889821664, -1954947379401741870708142882],
[1137975723366891992, 1495797075462005600929148678],
[1137975723366891992, -1495797076599981324296040670],
[7812838707763063844, 20274629216554632033751810298],
[1963174079061117134, 309873841744961716541294828],
[7812838707763063844, -20274629224367470741514874142],
[1963174079061117134, -309873843708135795602411962],
[-1035786544098165676, -4619791638612546445032590902],
[1686920288833271354, -294615287026185664042676992],
[-1035786544098165676, 4619791639648332989130756578],
[1686920288833271354, 294615285339265375209405638],
[-14588174365020454369/4, 14588174365020454369/8],
[1774662413126756764, -887331206563378382],
[1872381178128356828, -936190589064178414]
Independent points of infinite order:
P1 = [64935066190938207177379921809620324336417876/38334673696173434639203369,
65856901684133496078852002264730967351861454596251807552291945974/237349136666849357523634570372143855403]
P2 = [12778692524551274601846592078841174742602753512/1745809761812003076444759729,
1327613229257136573838681932815478197257627319929587909972495605591642/72944974419623675473252095060997029084567]
P3 = [359051941184400968436675916287612822567566985575036/33554076578440432506346355899225,
65354844147837104087026866\12744978642320928319784476158335695253889445283914/194364943774259187095447069125475692174244412125]
Fisher (2009)
y2 + xy = x3 - 1365976977965875684692597442214807543360x
+ 18275400146363694880998794973679939881728339383321437081600
Torsion points:
O, [49507414261719233920, 268311937045162364773521826240],
[49507414261719233920, -268311937094669779035241060160],
[13817765426026376320, 45154019775964812751357243840],
[-24228484401136594640, 192739099074419526727266253840],
[29219548405715258320, 57526467445969554974803177840],
[179220827616271895680, 2351607043209729079666903929280],
[179220827616271895680, -2351607043388949907283175824960],
[25458109597317512320, -12729054798658756160],
[-42392002557843161984, 21196001278921580992],
[13817765426026376320, -45154019789782578177383620160],
[-24228484401136594640, -192739099050191042326129659200],
[67735571842102598655/4, -67735571842102598655/8],
[29219548405715258320, -57526467475189103380518436160],
[1408804932915790720, 127881981297901038291292987840],
[1408804932915790720, -127881981299309843224208778560]
Independent points of infinite order:
P1 = [-28925660493007923778753001979117008/745150831097401,
2301812386537434799394254097252369862652645709600176/20340718299490580024851]
P2 = [4858713561949175021004650887477280518480/590734188869803267249,
1251422333929718305649458089342982178716579297249330432642880/14357808604429252520186572742807]
P3 = [94599801245197236670533717691501242841684676927370643387429857496192/1864388863284238312382345623195552284825142519201,
718229405600637042918975805609126607115846335546517632274099729028455832471003132415297652495662447168/
2545685507172487454419154834888121191096787138928134722184802519165981199]
Fisher (2009)
y2 + xy = x3 - 8891010899996290917768386447341722080650x
+ 321386381817072190725452682772958817656542992462808507422500
Torsion points:
O, [47693008455673008830, -76360594613080145517017489080],
[61375591786575104300, -83035691204262474207356093650],
[283065133628641885370, -4526090062980968168907888569620],
[-40850050216775061700, -785122320411823802443499927650],
[-40850050216775061700, 785122320452673852660274989350],
[47693008455673008830, 76360594565387137061344480250],
[57232463480470841300, -28616231740235420650],
[26644006047412948400, -321572534610368227648797037750],
[206392542778223829599/4, -206392542778223829599/8],
[283065133628641885370, 4526090062697903035279246684250],
[61375591786575104300, 83035691142886882420780989350],
[-108830599175026798700, 54415299587513399350],
[87820920913528734200, -466786580771766177646363443550],
[87820920913528734200, 466786580683945256732834709350],
[26644006047412948400, 321572534583724221601384089350]
Independent points of infinite order:
P1 = [89392066756214910630356189257873946534835729701683869800/719855804601419024567869162141064281,
649891980421647813178126367716785302478832479581922219643353993764872869770681868850/610756737355000227681876924815936698859521920190897571]
P2 = [-368968435313200649585277199506744864617553759922024264847699139109203544632772/
4328444403164795848014330325123657974314266346524105155169,
193116610303288450722489965773295721915902917509902894328305820872359766087275734756646629572879483893657265252931194/
284772314739312089482009570306037437294313894114004262504453611673597510272416409118447]
P3 = [28766481459430656391643599852237810701636893603466567009949133003753092441487540/
266896153729967253930054573164461436524854233618070584417449,
10814728207349576632047809364\ 0030793764931844567497537177312592069943394199538114828302672199934012535673141770846634350/
137883872685203149277045439575375309781049990438645576453334801987530478392777718420294293]
Fisher (2009)
y2 + xy = x3 - 226080057256506952334475656854112608140907120x
+ 1267994298469520992966682807972243164162876870777885816396482310400
Torsion points:
O, [64127947741843644038780, -15826854119140567725521657741491420],
[11149900468413737620640, -365216258475351806832299578358320],
[-9049507335513485605600, 1603998396136898559402421904174480],
[6317043640266678795140, 303180790883885995030238054931680],
[6317043640266678795140, -303180790890203038670504733726820],
[64127947741843644038780, 15826854119076439777779814097452640],
[11149900468413737620640, 365216258464201906363885840737680],
[-9049507335513485605600, -1603998396127849052066908418568880],
[18136346128752643712240, -1770102531933242873835420002216320],
[18136346128752643712240, 1770102531915106527706667358504080],
[-17302176339777887630624, 8651088169888943815312],
[29614638961227403335935/4, -29614638961227403335935/8],
[9898516599471036796640, -4949258299735518398320],
[1660687070189429881040, 947167381605507567444913299009680],
[1660687070189429881040, -947167381607168254515102728890720]
Independent points of infinite order:
P1 = [2959245473855045297342061137004403010608715682200560/54970030243379457721914930729,
1552531046526601909251244062\ 89582335237748170657141246708140365470301381282560/12888101979441798948948361629424584241409067]
P2 = [512060347260917001788897959490078633706407935806451924989807029600/21723534311246731949065076064137651776489,
366422076289658597796685682052465142560027502594185698660484137029482725810616171521324170523168560/
3201811250688816818399832322863564884695482292523644085386763]
P3 = [2316413969889418181857636132838130408011087929900872718224632414569742240/1252241975537292661717925870338466433350657521321,
3525412655267690774723055357378893060889284546269953836508539101560452647105084875371306547704758154636744720/
1401304078636720722341028521039490272260202406946754212294789859421758869]
Fisher (2009)
y2 + xy = x3 - 19561489879503521317374605750139081505164135760x
+ 1053053816008115892520186610673109502267446427439678234588062250809600
Torsion points:
O, [86491205836884310595120, -2859058070681364861322707234542560],
[86491205836884310595120, 2859058070594873655485822923947440],
[75140875867650824975120, -2728201165775701836322389089492560],
[75140875867650824975120, 2728201165700560960454738264517440],
[81186738501862181258720, -212853508690366586591486546262160],
[167699509462983989097620, -49888234138275568930656661346455060],
[16765378630475005239020, 27015003412279923299186979474193940],
[80313196752216066785120, 212087347811157498775615681107440],
[80313196752216066785120, -212087347891470695527831747892560],
[16765378630475005239020, -27015003412296688677817454479432960],
[167699509462983989097620, 49888234138107869421193677357357440],
[81186738501862181258720, 212853508609179848089624365003440],
[80816040852267567785120, -40408020426133783892560],
[-645996663980770291750145/4, 645996663980770291750145/8],
[80683125142925005152416, -40341562571462502576208]
Independent points of infinite order:
P1 = [18389011576013576110535089896131116628936320/334599617050432933761,
73442362420341288201734911223121612522399900224898360724596166960/6120517716199288291152078573759]
P2 = [100084535783919486416594465617917942017455517319874621700/1282373198315859466972893183512641,
60739235924036877684532635971124904613272353892307419209443834658700548769055146240/
45922090380097879912184213308295068868582072622689]
P3 = [3988632811003945475457820367627269144522422973510230831416315/277911900908203826154319692901316644,
7965545835899844821401221485175360369850548792500085284448877663702570574565541471709803195/
146507789969456491753262383159020425879060822911698728]
Rathbun (2013)
y2 + xy = x3 - 18247941180734920258951141060855042640x
+ 30003290659312870154250577706243953923873222960556857600
Torsion points:
O, [996308377714867360, -3579340715205085404723893840],
[2466856489630878880, -1233428244815439440],
[2465748079099038880, -1232874039549519440],
[-19730418274919671041/4, 19730418274919671041/8],
[4300761278960164000, 5574270123073723913554659760],
[4300761278960164000, -5574270127374485192514823760],
[2471328717750216880, -13593622749641886074607440],
[2557419399075237280, -249363871234053165261653840],
[2557419399075237280, 249363868676633766186416560],
[2471328717750216880, 13593620278313168324390560],
[2376293580186520480, 243333683104098404951734960],
[2376293580186520480, -243333685480391985138255440],
[2461279221875700880, -13575171870191526761349440],
[2461279221875700880, 13575169408912304885648560],
[996308377714867360, 3579340714208777027009026480]
Independent points of infinite order:
P1 = [2465691851312622880, 696043088391848153696560]
P2 = [299526139374311133233496416291788297474720/121494563208085746024241,
89760059383324119916982236967929464095424322071022523698480/42348230280965451005863362419157289]
P3 = [255527827197603823692011696953948551106951690366701807000824460296857544191109177529553040490611277793232865334429328712723331209912026266560051735874593651678513697145420096520365957390391994740532194386646007444478507059729407124477574209059308535275984445648944973857230/
103741345948284136600850705022998442002558109152508256758777623996807608081546842897751883462637271251523924738965290989759687615869601630298197558014492384361761785748086947557477806560219345196436037328416193242420156187936018082106090908492627291349969,
8992236068738592977199417717217168961723342142250581399387476637407351248957542689994258388798686468751719255160174869873244536035971856742110190408345123771373528044331860080447724136172230521346777659126418571630040991933558343397019934246107684499084537550620360793967011092035209774250967253346849204690975758718990696148201123874043382645837168758139928716460061585885269278104241162284541200977586790/
1056641873779396328820827179162484245273675046949791318104395249215045001870176172014452659115627601514048849596922228268202511367527045717849698016863150848882070412107024720247414591543688472144146764400298035859221663365795113018416176468950462518263225824616334743029549356055831440152227797493555339799615879533493978750678783291869212439586700180038166469129665579881151478297]
AttarBashi - Rathbun - Voznyy (2022)
y2 + xy = x3 - 125773582955215019659843433869443803612902341280x
+ 16545780427234453690755618162313665193883053063142475175813942418662400
Torsion points:
O, [688126701950298648696319/4, -688126701950298648696319/8],
[-407850282648179707407040, 203925141324089853703520],
[235818607160605045232960, -117909303580302522616480],
[266831171860285833988400, -44537029049170329996154289429771680],
[145376686492857867248960, 36519583324321003055253152267527520],
[-218148570793522572860080, 183307608456812383125815508347566160],
[438445514293612125738560, 213741099911300965512928098672391520],
[438445514293612125738560, -213741099911739411027221710798130080],
[33191700027597964727360, -111389893255934718881687790974142880],
[33191700027597964727360, 111389893255901527181660193009415520],
[1559722769614827374576960, -1901253853474287899397549963942136480],
[266831171860285833988400, 44537029048903498824294003595783280],
[1559722769614827374576960, 1901253853472728176627935136567559520],
[145376686492857867248960, -36519583324466379741746010134776480],
[-218148570793522572860080, -183307608456594234555021985774706080]
Independent points of infinite order:
P1 = [17717758251775551568432211692130/11826721, 72647213627225410774571287094067419960845481630/40672093519]
P2 = [25265559967028327078951230840698576830305880147058149718725154949874724706640/79079121352075128626675914808286270045501129127855369,
2106765868893950319477043345162195244251673901514805587788796833551378947204881017290520143806121408680205865582560/22237847765349441402932354050123832518291985845196712414473193627807627771447653]
P3 = [70440632474491509358601505333374697559627120913877270699767960770057102728566271816968/458764568668965671187860203132419455526027087024508722511106089,
287137721296870635647508363102248521295314501242303658986223599143593344666205275813631008027047008967522227301908578787419498104/9826181994367085850590085023465427811589979116750497045847031843961893432948406446334709108437]
AttarBashi - Fisher - Rathbun - Voznyy (2022)
y2 + xy = x3 - 1838240947808931779471337512024228981876240x
+ 921461984057272856046796380467851357126401246620999428758585600
Torsion points:
O, [1698282517030146755680, -51939714878803585549024985602640],
[1698282517030146755680, 51939714877105303031994838846960],
[-843317719119107957480, 43265788155833053037417990651320],
[548203033826212418080, 8859023363157682728560396158960],
[114698615762746432480, 26685712296889101793868001598960],
[114698615762746432480, -26685712297003800409630748031440],
[906490566396446594080, -453245283198223297040],
[2608687489045914607359/4, -2608687489045914607359/8],
[1028140048932469632040, 10877079705541676850721406713000],
[-1558662438657925245920, 779331219328962622960],
[6060104704481012930080, 460801563518640858779411367166960],
[1028140048932469632040, -10877079706569816899653876345040],
[6060104704481012930080, -460801563524700963483892380097040],
[548203033826212418080, -8859023363705885762386608577040],
[-843317719119107957480, -43265788154989735318298882693840]
Independent points of infinite order:
P1 = [111823554122815353700, 26782487680948992150930816781660]
P2 = [2846493948913024746796151810601680949083199943803452877505947398480376407395749298/385437270178537590809301640057603670285886595010448946609249,
149463052866341158396250370144545301337641382391230698461235710452194621043089868594072163066316515737966586434896035308546/239293311737428169848268879957618648703260283201339036363610394959506234549638159640498193]
P3 = [8951076024529984559839800162331503511399833129118948121366461329233604656027205761605162911327504785901141341985796469944471967894158276856083747603910577873020323048899162705785210720489656399997036396909889590637954309220/
8677435659478096544303636222722370929199321864074814035909684181245837893301435373524668067216473855569818703534662806232486583756478648663291654820783139388425149533937842535696324489370652115350712009,
8960094092050674060257905442430609837387337005873484851135338041310480058067426324757903838078304187350698954610608807948726420345162865785179804538470473081151052346968009604595402912641720217104804081153604948138565594718428971644856703430817317238522330662282907671087223321590501542484335425887543713446969951785803105404905590080/
808327033143181928557638958895248881222209187136396935696047862310458067585764451260606600921231771945917914516325691583646524184604641940885442793196703423503362022876719392262065083181101236620246568917982876171607087214135821533715054038985113930499188283255193215280882809683408761725789321553795973]
AttarBashi - Fisher - Voznyy (2022)
y2 + xy = x3 - 11264359913045241515885165571773370893291111440x
+ 460158968817054512110718150453672468135110101257480852599104548110592
Torsion points:
O, [245105112071370287382271/4, -245105112071370287382271/8],
[-122552627677766574378976, 61276313838883287189488],
[61276349659924002533408, -30638174829962001266704],
[61277747739625833295904, -614599481365527945518916089872],
[70696335191865523223744, -4141049988961593155298418164540592],
[61274879949318372569984, 614589832215916433677957361648],
[52315476333367394168864, 3747174367307296151347290466535408],
[61161589516303724252192, -49173018042862162009800112690192],
[61161589516303724252192, 49173017981700572493496388438000],
[61391109803544280814624, 49234451469919170163370657531888],
[61391109803544280814624, -49234451531310279966914938346512],
[61274879949318372569984, -614589893490796382996329931632],
[52315476333367394168864, -3747174367359611627680657860704272],
[61277747739625833295904, 614599420087780205893082793968],
[70696335191865523223744, 4141049988890896820106552641316848]
Independent points of infinite order:
P1 = [204058843410958138779652435345396634581800858388770318252596/3330135349432565123769725772644868529,
318844402438487780343624605525494203870851505161317305051494769918607985043923941204/6077050255838130552450126090678349082494868070087010583]
P2 = [1741156378705309461900485120338292112209931137403277735898820093340066249483932044806923489377824/
25185266333151405228993923892060076775197393242758365860724467309387117121,
434816808825654791906811161931928167967805899076630772212017656517755556402470232617400311554071039087332025058211815632955906764160515583643152/
126392068598998650082590661727908566437291371021466725735040265277193938152848741226192139729219743039924661919]
P3 = [114186298974454246183850797495125187918533117595195598464045983123338593713040246293938790022923520450847973322106206742714/
1211159924532077082243619343449533909599225001887160505476600963813810255331480055578946819568853561,
647746793237953511389663829142849610090500517086028776802319749475309781180978090602095727970212458423805209261090633038033046129585227774648833866856686039295620669293072958453732292/
42150452215549165492581275492322057512689282064964287722900754689041210569832690155273480795701822316152214854240409614335239133002164907534276183059]
Rathbun (2022)
y2 + xy = x3 - 34367500816998636494776063447511909557400138210x
+ 2428414475449601891165493234304079149949238206638756110690470656655172
Torsion points:
O, [126317702433070182382714, 10135899111371470924818510061068388],
[642771234573338073672604, 495885100577448586123549721633412118],
[88402287273527556761644, -9006082547311107638974802807085362],
[-93817409178807394302626, -69476118802845013046388197588418302],
[393163751494739631142111/4, -393163751494739631142111/8],
[115541110558671377817988, -57770555279335688908994],
[-213832048432356285603516, 106916024216178142801758],
[642771234573338073672604, -495885100578091357358123059707084722],
[126317702433070182382714, -10135899111497788627251580243451102],
[88402287273527556761644, 9006082547222705351701275250323718],
[-93817409178807394302626, 69476118802938830455567004982720928],
[190918453775282104628584, 53159895651243331611757581855326158],
[190918453775282104628584, -53159895651434250065532863959954742],
[40163767342060651007392, -33359788286380015348999013324638862],
[40163767342060651007392, 33359788286339851581656952673631470]
Independent points of infinite order:
P1 = [1467573457112531463097985423925394/12662775841, 2047152512188701368938694464172515282391618187362/1424929502611889]
P2 = [-153566205473666174802934136594267607914305604/2466097008820838224225,
-8055842151855873644664059334031726905996218406205124966372038055126/122465915841674230086410498443375]
P3 = [5381145474732415373469610512728260670241700988497188452617147735026779002943896533295506447268108730647899998927525056715265602026658810600716935998543144494126624108566046872363710263492485528867645400744/
66123736268110931959231904013331937640642823374919022581445265970145617989586978031598793354917579933351532531588554817618739967040650718717142401914295770113550724351283497954280401,
7021891620040226388782074831494052780677397827549962237903109594154381111509933674383029219316431619454968445034727425008862425094465611400045470934809998097483494426178292758909450559202020920863018376388747319420963853690469627603574447555056421255982136508504403442889713527062829038018351374904611666938/
537695098506243780177008122047840683809383072900653427394632962594928748807982173028800111811597594795956539452653939909419567100958569634515927374839268781463533399174644832323005423484738729290837571729255693151883036956978408960758477452317011630811174727551554811480601]
AttarBashi - Rathbun - Voznyy (2022)
y2 + xy = x3 - 12309388820268938951640127082057175888180422513100x
+ 16621666663619443929559236921024628861736270712422298926274118237343610000
Torsion points:
O, [-430312151982682857613800, 4673207247708111230248946573428806900],
[6147224823277152954886200, -13162321636277838075542174374883693100],
[1973116399311447170782200, 124593125686133113270071889526310900],
[2078518675423120965490200, -126773021656105871555526194464697100],
[8049030224871061044154175/4, -8049030224871061044154175/8],
[2038949786698981142386200, -1019474893349490571193100],
[-4051207342916746403424744, 2025603671458373201712372],
[1635762636890702726386200, -929123337741886106735399794555193100],
[1635762636890702726386200, 929123337740250344098509091828806900],
[1973116399311447170782200, -124593125688106229669383336697093100],
[-430312151982682857613800, -4673207247707680918096963890571193100],
[2442136936507259558386200, 1060866811573644112557933063412806900],
[2442136936507259558386200, -1060866811576086249494440322971193100],
[6147224823277152954886200, 13162321636271690850718897221928806900],
[2078518675423120965490200, 126773021654027352880103073499206900]
Independent points of infinite order:
P1 = [-122513562213947519038750025610264/63760225, -2932652195361495649186199659120918986496673458764/509125396625]
P2 = [109207489010930233771594175240133670164624543614774959971480/5632065813520203201100646635969,
36089313861780663285393134789831001680226737910813163727131333948102073903890566062604660/13366003843409619551783448260094926078225755297]
P3 = [2811243076973303737567941759608158151554044657647696821022496144778518213005587297698056247462152128984544382812679093886881543988205592444943959308766070877688827016133046629178308186536595444697557484350787483128801673358006238485/
48446272409269668159936719171775507881192704781493664269239790512290014047207402935557035708891538300469824653543304514105893311113247296136642598574744075618349950948355197070252585646220790381841710500137616,
42529717792764420817560959019018631237480555062040784681184765606350947084260253113078359466389412076635217024111580036952670009671958767747669826396520143197543712991825218751267249632282926553134948553761735823052445412869398071001188613804308478284212118887187533945743870755505442148619688300727882436572285275905197357496218257949812334520662935/
10663273544141057676164293510298763441006126798323579751223441902721982424902753511504913678021691389499053510712351199538469465439820249912502308566061288298194031742467978400352145239337709479327490903068140964710106971898549055634266718363307809000824699445909561840023151273184236309790521618314781922951865664]
Rathbun (2022)
y2 + xy = x3 - 71813598680248384341084284771096244120x
+ 234238430204114181370252185964622864112853337413958990400
Torsion points:
O, [4890977488804319640, -6333800249700801466384320],
[3209815766258725680, -6066339521171184412796804760],
[6793371071343566640, 7739207808589340925333304680],
[4894290445110381000, 6335225122993928798046480],
[3209815766258725680, 6066339517961368646538079080],
[4890977488804319640, 6333795358723312662064680],
[4894290445110381000, -6335230017284373908427480],
[6793371071343566640, -7739207815382711996676871320],
[4892533141966211376, -2446266570983105688],
[4892734605697550640, -2446367302848775320],
[-39141070990655048065/4, 39141070990655048065/8],
[4838355518515853040, 207564664507336331490554280],
[4838355518515853040, -207564669345691850006407320],
[4947113692879248240, 209108355358171008191455080],
[4947113692879248240, -209108360305284701070703320]
Independent points of infinite order:
P1 = [-7598178717919023024, -18472425486358616520979672728]
P2 = [33107518580292000780450278609381760/14540188262786209, 15927641392698942846938889124910803029530512142688360/1753295202855635392342927]
P3 = [7169614805036899134023153141153196990357085683379828079536284782724510447167404998785943150358684964695631101220588376852024665148311485010003860968019856902280419518976437129290556590850089313845905282923159362906272145175547483113113434925455756281408466044338573822926291239208328847688535383453315074754703503870640/
1465359420784521666593500820186204902125635491276180880963545711302043111411259819241169254910223808848889344495128879930179197148977231505337456585096880170139704564540736082118825425137138526515935888308875853360197443623012513977237432276380370788511664976968599329069550249184249712258350070642441,
19051956978166304106636802088573262331706506956418638803175373798556054649348985168693779338395235722904756284015499488031502683118919663470431161407332137187392725048764386690185043801909176315114878304901822975091839245263866757314049094445831863647075924599883755663792503434157502890358923060353677352313056482590085663504087943683812759287294776392715727203942616363548265111224826270514490852966164516961806584087137112284509501589805618445202272808534774622659622920/
1773847340225989184102723728772942402900199513803075093987876252175123264698561137394357540918127507323976256544741489648744105911018442006995904686890599231975654318272238013197969903824088190545915378633831874382204500133419698516514042948690030046152357181320303410975906192377697645691396346590434092119917768862526923404926749336715099054169544666172146667440727804515415014025670218232007675920182529293676086193703390984841249073895986347173989]
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