Torsion group Z/10Z, rank = 4


Dujella (2005)

y2 + xy = x3 - 127381738643041574974581021420318985x 
         + 17495594046612039766866496413577998621609407092547225

	Torsion points: 

O, [203769462231968570, -101884731115984285], 
[332051686763374970, -108672604320573158012454685], 
[332051686763374970, 108672603988521471249079715], 
[211631902068128570, -4017107787421614740944285], 
[211631902068128570, 4017107575789712672815715], 
[-154358229273495310, -182975962921722514975647685], 
[181819753779296570, 18594407565319705343407715], 
[181819753779296570, -18594407747139459122704285], 
[-154358229273495310, 182975963076080744249142995]
 
	Independent points of infinite order:

P1 = [193451723581658570, 9645265473564776734225715]
P2 = [78048873853088570, 89604896036482666170415715]
P3 = [172482359782680170, 25609953801231675965701715]
P4 = [16869046220129031866, 69269070346323710817037659107]

Dujella (2005)

y2 + xy = x3 - 3913976067656937637459249967383835x 
         + 80614222594310898664080091661625700445673557913297

	Torsion points: 

O, [147142093317455134, 51869518732561519802251633], 
[51911781939882334, -4162491938312861445081167], 
[147142093317455134, -51869518879703613119706767], 
[51911781939882334, 4162491886401079505198833], 
[6719521341454534, 7390370520775308774976033], 
[-53529705016637666, -11693700018005632879041167], 
[6719521341454534, -7390370527494830116430567], 
[-53529705016637666, 11693700071535337895678833], 
[24231785515134238, -12115892757567119]

	Independent points of infinite order:

P1 = [8185642345602334, 7008872315854122124478833]
P2 = [-12386639730434786, -11278065707632343668729487]
P3 = [-71051466385703906, -134428832419254188216207]
P4 = [145126829591796568531936/528529, 53943123228441855079366471262433889/384240583]

Elkies (2006)

y2 + xy = x3 - 2494386716254257179900313435657471298255x 
         + 47950428811853578302303100075736441050437846119869139884025

	Torsion points: 

O, [36156127476023797910, -70913501850678806447693493955], 
[29842628588842318070, -9417785990496683805276877555], [95894680496915196410, 831011029592655545712147948545], 
[28980779476046125010, 1302386777882843703111209045], [28980779476046125010, -1302386806863623179157334055], 
[36156127476023797910, 70913501814522678971669696045], [95894680496915196410, -831011029688550226209063144955], 
[29842628588842318070, 9417785960654055216434559485], [115502981116810136015/4, -115502981116810136015/8]

	Independent points of infinite order:

P1 = [28509015942778302410, 3003281534671521511510019045]
P2 = [-4710087341394312480646/289, 1426248104611211485908211687075441/4913]
P3 = [651746601062048885608610/27889, 229159071225334021088598309104574895/4657463]
P4 = [2474363018938566848121587468060/27532433041, 3386940458446040733191786369680733084310244255/4568429082060089]

Dujella (2008)

y2 + xy = x3 - 186734461375182851611482374885236743900x 
         + 979124235576847382684597033191041431087287234552438410000

	Torsion points: 

O, [-63094581573040382401/4, 63094581573040382401/8], 
[8573169226738886280, -2887808798032547052801252780], [8573169226738886280, 2887808789459377826062366500], 
[17027292432893204700, 52309105344304937748235343700], [17027292432893204700, -52309105361332230181128548400], 
[1289562023800530900, -27211451062399196171540251500], [7214544821242258920, -2726660508888088403470129500], 
[7214544821242258920, 2726660501673543582227870580], [1289562023800530900, 27211451061109634147739720600]

	Independent points of infinite order:

P1 = [-5710514747140022400, -43119071959774152308676399900]
P2 = [35512172342223738248711400/361201, 209680437320717911654215167303833570500/217081801]
P3 = [520496225635820845011448680/55965361, 2866472932142118340340507801774393572500/418676865641]
P4 = [17134135927565201341566386400/19997636569, 80967502846094281568437665397281398037119700/2827925780131997]

Dujella (2008)

y2 + xy = x3 - 349960450236374537044731366104096847315x 
         + 2334228106621384646411703013971250553516398106559474797217

	Torsion points: 

O, [38424785173813772874, -213588130419282591543267852687], 
[14348396161361511774, 16335669926093284317941973513], [14348396161361511774, -16335669940441680479303485287], 
[38424785173813772874, 213588130380857806369454079813], [-4265357259315208686, -61231802571123461140858098867], 
[7282624064329309374, 13108906365745448613906164313], [7282624064329309374, -13108906373028072678235473687], 
[-4265357259315208686, 61231802575388818400173307553], [-85689871598856534129/4, 85689871598856534129/8]

	Independent points of infinite order:

P1 = [27871728089570766822518550306/1952137489, 1358573678733666234270912721506451253111211/86251290676487]
P2 = [79683221958290183275583671483164/9703418130961, 113757749527935178347203593091878214202979830333/30226448283905574791]
P3 = [33026790339998050436047234709581888880376212714/9804544701240252493986308161, 
      33540608912457629088874029577586902533526527356898735736949738801518267/970825435725653250476084979911365621664159]
P4 = [736337187123421188570624534418924717252369265410496142/9168290659335385099399214430138049, 
      615933984744210480360486565011634252817560601953373667789965845887943908189546873/877874753963421185196947919583452248308798801730593]

Dujella (2008)

y2 + xy = x3 - 112990215345279616192969388342207278250x 
         + 450679052475043122152258628678943621649365601242615639716

	Torsion points: 

O, [6914743098109976052, -3457371549054988026], 
[7415784844735440628, -4537686145522182699673929722], [9664667086490694964, -16167934331629706360092471610], 
[67689720828780820840, -550408775499983374795283571374], [17988067714340499076, -65104630511870775146410571594], 
[17988067714340499076, 65104630493882707432070072518], [7415784844735440628, 4537686138106397854938489094], 
[9664667086490694964, 16167934321965039273601776646], [67689720828780820840, 550408775432293653966502750534]

	Independent points of infinite order:

P1 = [6696939383407955213350/961, 38890862058136309460245936458886/29791]
P2 = [-19899650118231499878584462/5583769, -375078398943804846695701003020808811092/13194446147]
P3 = [-783182741540466218088295340/96609241, -27421032732829902302805535229052268364114/949572229789]
P4 = [2392646277865369447057271336404/457967553289, 533825670332370617931227995532001114296175902/309921756239924837]

Fisher (2016)

y2 + xy = x3 - 606341743349993803027157758323354789555x 
         + 5746776413116429159936198290812862370694589715823570957025

	Torsion points: 

O, [14228641123808966610, 76851077269708933130462145], 
[14228641123808966610, -76851091498350056939428755], [15663335916942468510, 9606574937818397457316520745], 
[15663335916942468510, -9606574953481733374258989255], [14204716681319919510, 76807979922555818618804745], 
[12817478361673950720, 8986597712071399356442778895], [12817478361673950720, -8986597724888877718116729615], 
[14204716681319919510, -76807994127272499938724255], [-28433354560106741490, 14216677280053370745]

	Independent points of infinite order:

P1 = [14159039853988504230, 375892386063512187316850025]
P2 = [9532815941956270465860/361, 619175762512013804758050935039955/6859]
P3 = [41690465093237831038497620644181358099360/2478711087682235406961, 
      2160684371858685499456685311034334429688985694068464371135705/123406735549303475878679163059959]
P4 = [327798947530195390706439516059276804112990/72528395434563328141249, 
      1087302369591792703704633853772367786994149994370664824994675465/19532692105853429139638818685297057]

Fisher (2016)

y2 + xy = x3 - 19194775548787283845230607299614214311678x 
         + 1023582059693167156639765281299410390763594972426927678761572

	Torsion points: 

O, [319985493971327392543/4, -319985493971327392543/8], 
[86583336157569340138, -103544239683123829017620701040], [173821983693041492032, 1714345288520094326004263382454], 
[80525261753473723102, -8313897596683466945983776986], [80033503730719266616, 678429316864861779373467514], 
[80033503730719266616, -678429396898365510092734130], [86583336157569340138, 103544239596540492860051360902], 
[173821983693041492032, -1714345288693916309697304874486], [80525261753473723102, 8313897516158205192510053884]

	Independent points of infinite order:

P1 = [-72916487552680553369672/529, -12470497160653492460311828196091562/12167]
P2 = [3800850833657108380680857998/413449, 234299952032482293627366132672200635358548/265847707]
P3 = [1038663796752458552287654/9025, 499085422584595640129514287454205868/857375]
P4 = [9299986225503696073397435648430959777336325444966169329232/118582088494247866469775586700363663089, 
      31154049781500818599931128211014876857065379953409468100300331357090737532995533586570/1291304434505042263235924994206689677621210701220944773687]

Fisher (2016)

y2 + xy = x3 - 6235503349706099317232119038151880529845x 
         + 189419104701643513972219165960187230267385337379886707205025

	Torsion points: 

O, [-39661218201337509410, -611832642451356186385139438045], 
[38261919201068874370, -82772289430854573693968042825], [38261919201068874370, 82772289392592654492899168455], 
[47496820397170921990, -20071784166441023187239599445], [-39661218201337509410, 611832642491017404586476947455], 
[47496820397170921990, 20071784118944202790068677455], [80858256886686541090, 462474996717189911580819524455], 
[80858256886686541090, -462474996798048168467506065545], [178913345320035258735/4, -178913345320035258735/8]

	Independent points of infinite order:

P1 = [17589807360712156090, 291856320210123832159665884455]
P2 = [32254945713754125363142410/169, 183186909473224164721735686310561219635/2197]
P3 = [3568054094929294949476685410/859329, 213092992005335904580831819367952379418665/796597983]
P4 = [103201476065683018372809559484742207512444260180660/698317240262928282290790194449, 
      921872016140031983045959981157221175214685946760439597841749424753905185935/583551441562923065277439175513892774989278457]

Fisher (2016)

y2 + xy = x3 - 10473660140875584389345540158685974580330x 
         + 404522597629437110022875275775819960239486284577507418898852

	Torsion points: 

O, [166116778145690582644, -1802395219858149389309149108922], 
[32070550811449751944, 318765992799379080513741532678], [52214884248122398068, -26107442124061199034], 
[166116778145690582644, 1802395219692032611163458526278], [70154413248824267524, -122572433489628945717969667082], 
[70154413248824267524, 122572433419474532469145399558], [-75685783024209737036, -873885597929491731063295506362], 
[32070550811449751944, -318765992831449631325191284622], [-75685783024209737036, 873885598005177514087505243398]

	Independent points of infinite order:

P1 = [26334418483966623604, 383363808519334137611332032838]
P2 = [438464495825389901844471796/874225, 9003098982004211137467325385159329345226/817400375]
P3 = [34148940294054927865131323498356/3114421249, 199547823697490389280906999090863265935393274554/173806506642943]
P4 = [389791926546015494683490223364/49126081, 243339889827286771363228875842882003641694662/344324701729]

Fisher (2016)

y2 + xy = x3 - 750317650367394301235970310370497308826620x 
         + 250157454864721027465417103055839870833708995946817266393040400

	Torsion points: 

O, [479324287994569225260, 798490056558363246074532089760], 
[-185964280020627366360, -19576991267600973158764632845820], [1996576092274320591935/4, -1996576092274320591935/8], 
[644624427391107643140, -5861059993138170744023389607820], [644624427391107643140, 5861059992493546316632281964680], 
[503352676005832676040, -120262390051700333441620829820], [503352676005832676040, 120262389548347657435788153780], 
[479324287994569225260, -798490057037687534069101315020], [-185964280020627366360, 19576991267786937438785260212180]

	Independent points of infinite order:

P1 = [17760263894000822086514356290/37442161, 226532742271018774631384862712751240571120/229108583159]
P2 = [350567486458718720405225319497034217440/669960651643360081, 495290473212199696701820612009068834520669710828639069180/548370324397775349309170521]
P3 = [1530451596008647220909458187462668626068160/3066234367489948068241, 1057420170110265567532271510484889764084769939474810832791140/169788401885295860993826984340039]
P4 = [280334710629211670592640053482279953405109861696485836461666884152120257341860/501817799873780422540987267295127211834713308129625628849, 
      25975410418297962202363841869199655415723075473006962560844935953987170356511143908042793632875561734493663048342760/11241366131686945263495520264586685947493477023144222601543788490144017129564436177257]

Fisher (2016)

y2 + xy = x3 - 1839418161391200701592417510440894309468480x 
         + 960215688236954682587978137650987794043787450549032912088829952

	Torsion points: 

O, [3132697862812686052351/4, -3132697862812686052351/8], 
[783791195416249294144, -36141606247358988068235625472], [1867230873180813559744, -63527893295747656968361809303872], 
[790998349970805817984, -386693032261232888779094341952], [868626879654326575744, -4223458822251636750997834647872], 
[868626879654326575744, 4223458821383009871343508072128], [783791195416249294144, 36141605463567792651986331328], 
[790998349970805817984, 386693031470234538808288523968], [1867230873180813559744, 63527893293880426095180995744128]

	Independent points of infinite order:

P1 = [1339831623999885208192, 30015032432629679138800811685568]
P2 = [35060976084292128793030624/44521, 2042162827960677237467425856272111168/9393931]
P3 = [4083558211828702873168841406208/5218184169, 8165718244228589745635950339848838597027264/376945969816053]
P4 = [20628622910332260248990458428251990700858561162985355499893096656419949421408116/30810196638269105617759683937975880239922665560465851819689, 
      29020782216830490207555707026277845339275558301612912326239505694390955941708687893469387077787443525345738040695097036/5408062538913847296988804230456239148726163474036664547352459762847684270086036032351637]

Fisher (2016)

y2 + xy = x3 - 1137101178706193150632089206340193771499355x 
         + 466728543369983412885999265867724342532601525048077866954666577

	Torsion points: 

O, [607330742739688136094, -382580276868252007745778685647], 
[886619819591467721454, 12470735604448607007853904394513], [624032392217905716894, -386055500358275213146575556047], 
[379370269861485727134, 9483976754164218051446803437873], [379370269861485727134, -9483976754543588321308289165007], 
[624032392217905716894, 386055499734242820928669839153], [607330742739688136094, 382580276260921265006090549553], 
[886619819591467721454, -12470735605335226827445372115967], [-1231319839060116714082, 615659919530058357041]

	Independent points of infinite order:

P1 = [4888700976154389482523100993866414/1070937289321, 333218665157664518682701926706040599001624357641733/1108271234164019381]
P2 = [-1129714921185379377769157862443848785006/933945978381528025, -7675229542871124961891877699507809291670355601754161489707/902573616902248332714260125]
P3 = [73723016993027038899580064555267075893944412014/91302191071306008881248681, 7556488409199072723264683987635467300493857081130821157829882211817563/872412339773155779314629325514398728171]
P4 = [1653059201802442799669785377394726014196667406/2679926248083932548421449, 642370142892105107856851146793289260864048428817124160941385965771/4387167981334433134396316226987563707]

Fisher (2016)

y2 + xy = x3 - 4040631189456765959525697667769593962529755x 
         + 3172404897992753976431573355142695271191051899906870074173299025

	Torsion points: 

O, [1321165533646275380910, -11837571326800423080843331435455], 
[-2324900972751723202914, 1162450486375861601457], [3125604632279056922610, 145183624156712349265034611255545], 
[1014276299106842450910, -10841203543253495133448886845455], [-91188489526012168290, 59498787294744237108254843309745], 
[-91188489526012168290, -59498787294653048618728831141455], [1321165533646275380910, 11837571325479257547197056054545], 
[3125604632279056922610, -145183624159837953897313668178155], [1014276299106842450910, 10841203542239218834342044394545]

	Independent points of infinite order:

P1 = [-539492724333439443547023133090/360202441, -523519458552011282103457573682911157377244245/6836282127739]
P2 = [-73382284329713655733395764190/381928849, -468612021035064850347092698085576055401777085/7464035496007]
P3 = [4741089398224660756163430630/67081, 326319817317356955224021310091556359573275/17373979]
P4 = [51787762354121268422151403666560684587799486753764310/10955589923192572908721256298241, 
      10860434158009996263836226380829102822967766563691829698587704619868261627072745/36262158498127752324777184821048632878622904961]

Fisher (2016)

y2 + xy = x3 - 47276498134436527849525960367886553344290290x 
         + 125117091786735364804757114439441886224113329551018090356929775492

	Torsion points: 

O, [3983721980257386878084, -1580330729363143506480397035202], 
[3955776015724149452864, -1576626702113537927445585666142], [4821929095038549171524, 96269643511080732729258279072638], 
[3174460396528427666324, 83841453348977665501795648720238], [3174460396528427666324, -83841453352152125898324076386562], 
[3983721980257386878084, 1580330725379421526223010157118], [4821929095038549171524, -96269643515902661824296828244162], 
[3955776015724149452864, 1576626698157761911721436213278], [-7939480428474519917692, 3969740214237259958846]

	Independent points of infinite order:

P1 = [69466270195543235421748/9, 12665319595659586368779455713670346/27]
P2 = [8499691397222699467544996/2209, 1375655106370619551473473016985130434/103823]
P3 = [437789514417683579573879863110195429764/178006802602561, 9160018226241402653551621726518204468434386758858191379842/2374952341772358054559]
P4 = [1646145200291085779032677407739767058001507849449790782370890495271572431075173143880187460455028644/329056059900733624966695035690201737635054835859641675762208114875177576426681, 
      22180101548602810125408138790346599606982138572934779736789063179606776000673212224779215023848716902802094873084962693664511521064894427589793223398/188757770810049865876915208845635553291689837482953371991812342032417699593204583131902062608732499127185769934581421]

Fisher (2016)

y2 + xy = x3 - 1790884818544248483549671834829972593551295x 
         + 922462585059738754152984400543095956097213785601785710185488025

	Torsion points: 

O, [951700416428154151990, -8947842221248404115334626620995], 
[775902719431460903590, 151796316907716978215869001005], [775902719431460903590, -151796317683619697647329904595], 
[951700416428154151990, 8947842220296703698906472469005], [796282966318641785830, -1143640068263658865939250344595], 
[2468111402046793608490, 107410624827822245040251161334005], [2468111402046793608490, -107410624830290356442297954942495], 
[796282966318641785830, 1143640067467375899620608558765], [773507848541288941990, -386753924270644470995]

	Independent points of infinite order:

P1 = [654333564006769891463590/841, 6275522977478825797633717851152945/24389]
P2 = [49473800108565830715310853260/67354849, 1005548067846641628447602815493619481469465/552781245743]
P3 = [11820797499755531616018422464238590049260/15320977351602828049, 1873025318224837460347385996898150764587950522903666682465/59969400298845334216271694343]
P4 = [27398885076486808551565416178241283010/35071352191293961, 2710274810150752201904644618545461562190734392612415065/6567933787384371675220709]

Fisher (2016)

y2 + xy = x3 - 1087058217198170551357239166185336734649205x 
         - 348313390838489017000093754927310755519988091697835549933005023

	Torsion points: 

O, [1360556927988791445794, -26291245089321190267012968007897], 
[17779632387093494157044, -2366587947179336203996427254129147], [2099303840553942581594, -81372071268175346423533203722497], 
[4493465306852264817494, -292396343713617890813867739464197], [4493465306852264817494, 292396343709124425507015474646703], 
[1360556927988791445794, 26291245087960633339024176562103], [2099303840553942581594, 81372071266076042582979261140903], 
[17779632387093494157044, 2366587947161556571609333759972103], [1176102565155133244818, -588051282577566622409, 2]

	Independent points of infinite order:

P1 = [287320482582764465415833864906/72709729, 148101576522913285919789321663002338093019529/619995859183]
P2 = [-15014447753821172763040414/18769, -7869584871975673090064178227698260641/2571353]
P3 = [-10553204600732261606291646310158166/28290495092161, -345904001256842911865363643055603394269051526732377/150473776826288391841]
P4 = [-6927142446393408387155712328003744/15823632719449, -415977019653697006851737892859678587698358408952429/62944717829267140957]

Fisher (2016)

y2 + xy = x3 - 154954755728192832325573450693397812493412614805x 
         + 23477626369643382523699316208284935358727835083046530063998476781660001

	Torsion points: 

O, [907799169750913420899183/4, -907799169750913420899183/8], 
[284930988757250714241426, -49583539249042176833795036159548617], [-70390234977313938059310, -184488914417903424407546169223359369], 
[219427856132629407394194, 6432503081687163711241598028444471], [228416567259135468168018, 910081622092820369215952227453623], 
[228416567259135468168018, -910081622321236936475087695621641], [284930988757250714241426, 49583539248757245845037785445307191], 
[-70390234977313938059310, 184488914417973814642523483161418679], [219427856132629407394194, -6432503081906591567374227435838665]

	Independent points of infinite order:

P1 = [233561164801377941322858, 5212068103995124425659122256334063]
P2 = [237178731981797626189518, 8236941193617003408174436522967859]
P3 = [126835364402431992807367671427779814050/5904807660361, 1428197000149392279096438167836526930836827918574462561491/14348570423331683141]
P4 = [10356870938615705171546705942101297608007353813946309586850/617675876668805159678231749777609, 
      1053717554015927319571807215868606650927644456506576947553817881057710855053966929376877/15351151595311032476983855227019150732504282374523]


Fisher (2016)

y2 + xy = x3 - 1711638225368515268323064650709174068985624420x 
         + 232210627709045907581719449979884580568084565196040134101664308272400

	Torsion points: 

O, [-70687215479339285336760, 35343607739669642668380], 
[-36457859848768718776760, 15689308414232360901570768935468380], [-36457859848768718776760, -15689308414195903041722000216691620], 
[78176308255912406074840, 24003714873789860540787214561340380], [18511325157884094559240, -14382948105049520184374432441547620], 
[317237383937894276533300, -177808450366713109461092793176324480], [78176308255912406074840, -24003714873868036849043126967415220], 
[317237383937894276533300, 177808450366395872077154898899791180], [18511325157884094559240, 14382948105031008859216548346988380]

	Independent points of infinite order:

P1 = [2272326796862398559235400, 3424825827059891418833245875654265180]
P2 = [6416235765293139592099882, 16252180351464472672379050919371248712]
P3 = [466424545165376288842874030436040/3652872721, 10106293860411563511086958265072045603246874169220/220775974384519]
P4 = [-756737464015592670840472530999494549641663862885324065775127473626845056660/76128359012454853678358805620964068044060303908622801, 
      -330946553467425613178702341587923885073719563810002479643329793652943433018493508173614577498651262312460281696120/21004855715260014529450954817787347785343236774634418024391812473386605945874201]

Fisher (2016)

y2 + xy = x3 - 62005296485905798761970207550045463250097454130x 
         + 5789532992807304372367304652589285625132626611081197926062416086663076

	Torsion points: 

O, [72536303475990568303334, -40909031544723405023579167159348360], 
[-188540591040511717372120, -103816623476598435728400887880059614], [-188540591040511717372120, 103816623476786976319441399597431734], 
[72536303475990568303334, 40909031544650868720103176591045026], [174063246688087275161888, -16445681291131630297682623901584006], 
[497910965560885818914783/4, -497910965560885818914783/8], [423298351761132308762546, -235350854091931067140694996260177492], 
[423298351761132308762546, 235350854091507768788933863951414946], [174063246688087275161888, 16445681290957567050994536626422118]

	Independent points of infinite order:

P1 = [194600642663000058273670, 33055619729461870480540793180445016]
P2 = [3366984453505322789870563037416836464/6856076164921, 5497498381975421740928207700046889520602576955011699506/17952025247066960531]
P3 = [15929417918006383262501078519699096/48668330881, 1539459145355492050219553470817331908461545618807254/10736671807326529]
P4 = [232215840423026844434169398297807987878475034560811280699160/11906090425691000324068998161329, 
      111901977718959946456684718535465119617543865281949977981922232167576719307629890414324382/41082206854093166502864559303890375800439528983]

Fisher (2016)

y2 + xy = x3 - 476068293055332770677811963638103223072793289890x 
         + 125919348478903221572038949960367157753104905766938711419921050188845892

	Torsion points: 

O, [889744191935233760272364, -637731642438070670517398444306220442], 
[282687067582586687102684, 118030002634913653494874614315017198], [-439523948983425699747676, -500254891052591599577701887990720562], 
[436934687651298019321124, 36395579983961910729896816115825038], [436934687651298019321124, -36395579984398845417548114135146162], 
[889744191935233760272364, 637731642437180926325463210545948078], [-439523948983425699747676, 500254891053031123526685313690468238], 
[282687067582586687102684, -118030002635196340562457201002119882], [1509973410712173067946207/4, -1509973410712173067946207/8]

	Independent points of infinite order:

P1 = [5007902241714560823361136773560029/172239376, 354292987431014031029542556002178613121946503899097/2260469570624]
P2 = [13853719603250586475609069393550949247440121076/36765567528526273845409, 40861854189757130321733490084850073803827431960177666715968154988894/7049558380378832468186586082050673]
P3 = [4746015867164184441329624338380991493796003574144628/6814628287943055429190125409, 204513196672034694931561947829025452002369751029262399413112203149964294880466/562552757138925994518443100084205919209327]
P4 = [618503758021956273370536426989309376558482689110461/764982589541051489108949904, 10984757689301975218973972314957796604794021817317126123137208801989773219919/21158132209345655306841338587369686742208]

Fisher (2016)

y2 + xy = x3 - 102357121579914188416626387471212281192195487785x 
         + 16882033617390298666180627389186843640259490565173172015051879589003225

	Torsion points: 

O, [-382712265091480194077830, 191356132545740097038915], 
[-126765475239294594077830, -166794264845524096256159821502961085], [934158761769581595328970, -858172649669544618869737071800995885], 
[125970510111231677922170, -77375878558773273679589255294961085], [279879291778368338562170, -100786986188059243858724480738001085], 
[279879291778368338562170, 100786986187779364566946112399438915], [-126765475239294594077830, 166794264845650861731399116097038915], 
[125970510111231677922170, 77375878558647303169478023617038915], [934158761769581595328970, 858172649668610460107967490205666915]

	Independent points of infinite order:

P1 = [74775575676358585287719923518332353612570/104765660341707121, 18801718450453569187888026177738813731505532048059411454942885/33910050150094874057676919]
P2 = [90003989769696709995869587118458918058613770/627394335805635765481, 1127812147091994037885966835586643908218885508586389806400543821215/15714873530543905745148866357621]
P3 = [1936616809856861872980944483695378757274662570/2665372962077600535721, 78579105927091824255879236320058214509395382638984999072706221103135/137605876760176292090468498501269]
P4 = [350537492002857088827276518323790133756211130/2365541663663054431489, 8109535256938197515433662958490568945583662477901946824025236580355/115052458239943350683397434660737]

Fisher (2016)

y2 + xy = x3 - 194244626848842496975852314384487804134488971945x 
         + 37836614076244330213038852559652431783659307125520407574760926787704025

	Torsion points: 

O, [-130829712634551759283210, 247002524887822858043577723035477855], 
[-130829712634551759283210, -247002524887692028330943171276194645], [345330169794619551186890, 109269013666849403654483340038872355], 
[345330169794619551186890, -109269013667194733824277959590059245], [1056810746910743360441150, 1006406867517098320758567557581884155], 
[187841296704831730005290, 89315788439241535784042925528010355], [187841296704831730005290, -89315788439429377080747757258015645], 
[1056810746910743360441150, -1006406867518155131505478300942325305], [-2068478264036700474688465/4, 2068478264036700474688465/8]

	Independent points of infinite order:

P1 = [5628921655134442769196402453878/2093809, 13187300309080087909361711668438811245935636233/3029741623]
P2 = [20961739153079732051792321444130890/42303851041, 2188196939023981090985285526394628009453286746162845/8701013778261839]
P3 = [11837486564224332558829326675533840/824321521, 1287322587758264936846268733358185730199776938806755/23667095189431]
P4 = [-127413531084587359574250276975906367/364922311744, -55372267159529188179078572430067912200497370064403411/220445189456809472]

Fisher (2016)

y2 + xy = x3 - 333869948828740802854329951914653442137141829455x 
         + 74193728707898625969934095384319220186640266881824137259466129698316025

	Torsion points: 

O, [-2668575461961110890446385/4, 2668575461961110890446385/8], 
[113105675730065281426310, -194622946865960122419593260520525155], [350078831371155000277310, -14727669417954919070151066509531155], 
[317274655689845645795150, -14252720268211757947791788014624795], [616256905741191851899910, -320127378372587282781448272893966755], 
[616256905741191851899910, 320127378371971025875707081042066845], [350078831371155000277310, 14727669417604840238779911509253845], 
[113105675730065281426310, 194622946865847016743863195239098845], [317274655689845645795150, 14252720267894483292101942368829645]

	Independent points of infinite order:

P1 = [53622485288130684527887538094065/175085824, 59887605341268815180217189092271696566443190335/2316735623168]
P2 = [12061403751770242202937375495095540/30396876409, 343046059320192921506114688232623159099888562844935/5299604211279923]
P3 = [269330306729887702801934957267577973239585612793910/140190638155155894648804361, 4239582634403504541770990312451507333106214863712283108551194998596679227855/1659886982439502029424625286556564920859]
P4 = [5133416387473238301570456156388030568280245373267260/7327952767414035463028444521, 269140992152647529337224814736253927008067939835509529165037504077258868720945/627298128875251594451182350659114064400181]

Fisher (2016)

y2 + xy = x3 - 87748268296475438293863393504357096119405144407640x 
         + 316582473482499514464268410652046626899764680048107778920719333992577059392

	Torsion points: 

O, [5626947862568814765716224, -995498454944754937492005106181323112], 
[-10817324679410223564373776, 5408662339705111782186888], [5194041630088435602636034, -969291306864937912284091537578005702], 
[9777932654757051274607224, 19835172751994842901473448195054857888], [1966942450190215130727124, 12312453440561444740477694850150428788], 
[1966942450190215130727124, -12312453440563411682927885065281155912], [5626947862568814765716224, 995498454939127989629436291415606888], 
[9777932654757051274607224, -19835172752004620834128205246329465112], [5194041630088435602636034, 969291306859743870654003101975369668]

	Independent points of infinite order:

P1 = [3791844686212452476304112, 6194686278310745251988143735594511368]
P2 = [1944314767955020351429992685747267264/610790703961, 3979880795342722582406184273739662641028237906917380408/477351869657344291]
P3 = [77673261081328146386308804249017657018696457708184542708156273216720386354798576631276732798235193711/18954120425237152980214951481803569859529371540407284243412439753820392656004, 
      13257561538594803013829757742445632725931357715004553436960267855105327110555382659902123318021828165440835802535791620034120189336043871866424250917669/2609488897327402012449019735541896673336446521853139264595756188487913805395224026736634181966272992500501865968008]
P4 = [17204000829356259262764776480023186150044033998292870414895082755096901257180406481727555031987306037294117068314/3102552085623270581280698171777388607805306775566573063855170288919421035696757690795361, 
      123545094665546537722257407109399675456131889604615511149688640139934236704707539527291256413458325349823406553965901750313684271676741152510901449048239371231407698942/172813880279775413444994587914782061769964329787756888563891568275088764893409757478745785388319716231357280767949113986075740789359]

Some curves with torsion group Z/10Z and rank = 3
High rank curves with prescribed torsion Andrej Dujella home page