Torsion group Z/2Z × Z/4Z, rank = 8


Elkies (2005)

y2 + xy + y = x3 + x2  - 2245321045583713014514387556551626518613389075x 
      + 40951023798706743647147655022412395573869307978556305934134697952785 

	Torsion points:

O, [29763029845850765905683, -699062028100151372099326510447442], 
[29763029845850765905683, 699062028070388342253475744541758], 
[25020708005132605807283, -659819080891533619932483575588242], 
[25020708005132605807283, 659819080866512911927350969780958], 
[27391868925491685856483, -13695934462745842928242], 
[-54715261409445312524061, 27357630704722656262030], 
[109293569935814506670307/4, -109293569935814506670311/8] 

	Independent points of infinite order:

P1 = [27217950144770714592483, 38762407781313186093387207311758]
P2 = [27320269699175805115083, 4282784155038060041953794941758]
P3 = [26418172070836772829603, 267416980432082210201830462862158]
P4 = [10414141517367257310883, 4324048052446654998517502008537358]
P5 = [14754827562060331594233, 3321731136830881492136790818111758]
P6 = [25585681690941092682203, 502030908890298294255957345396638] 
P7 = [986362241207870406575223, 978503144438732243193326482294398358]
P8 = [46128952570662176815171889384353/7777652481, 
     3619335153700852172354561908429346471339075334368/685918949951871]

Eroshkin (2008)

y2 = x3 - x2 - 3600510377430985267434688529347574077140x 
    + 83138379062405631329348360175446817662846629397471808788100

	Torsion points:

O, [34229494755989932566, 0], 
[35055806040511421530, 0], 
[-69285300796501354095, 0], 
[25770428610439666980, -86407241469249848980704067350], 
[25770428610439666980, 86407241469249848980704067350], 
[44341183470583176080, -103288366988754759023178655150], 
[44341183470583176080, 103288366988754759023178655150]

	Independent points of infinite order:

P1 = [27511666916754609030, 70040648032618306626353925000]
P2 = [34229379576265773880, 99263845939143951371702550]
P3 = [10971836682199381472, 212025871290888247368613734722]
P4 = [8338450132387552080, 231722836999797935854676725650]
P5 = [32659973917695474330, 19579215436552380987396572400]
P6 = [-45604229710736283684, 390501827997281792196178261950]
P7 = [-12333515316119324970, 354498531541702609016748618000]
P8 = [19128709204098397905, 145823871611640213929311101000]

Eroshkin (2008)

y2 = x3 + x2 - 23686061832482481624168232900x 
         + 1401294826072670363740983663536729053022048

	Torsion points:

O, [91442724267692, 0], 
[128849323043966, -698954455279281979050], 
[128849323043966, 698954455279281979050], 
[54036125491418, 528367347363098395698], 
[54036125491418, -528367347363098395698], 
[86243530797416, 0], 
[-177686255065109, 0]

	Independent points of infinite order:

P1 = [-19578753643834, 1362913540526632116750]
P2 = [7039133112536, 1111266965543810963160]
P3 = [76748038982126, 188419870198587400230]
P4 = [-32194246291774, 1459616860760570800470]
P5 = [85367453744006, 37417621531734692430]
P6 = [85225678008086, 40788683120841618690]
P7 = [71598493464386, 269159820951235640790]
P8 = [94712810727878, 86857168689634948878]

Dujella - Eroshkin (2008)

y2 = x3 - x2 - 866893152450363503763740085700x 
    + 61220734062068506723288644020689511073795652

	Torsion points:

O, [-964553620677266, 0], 
[-342699560964996, 17834151956634131617730], 
[-342699560964996, -17834151956634131617730], 
[2129738165284264, 88741191035298932908470], 
[2129738165284264, -88741191035298932908470], 
[71034318517633, 0], 
[893519302159634, 0]

	Independent points of infinite order:

P1 = [44067817038164, 4806685314955215492570]
P2 = [-10736855835311, 8398047577801604981580]
P3 = [-130593986210846, 13122671738229868426920]
P4 = [960440019693249, 10703970375598940056760]
P5 = [54120967930564, 3802914955516162348170]
P6 = [-820100918833816, 14852239103603527475850]
P7 = [-6811698256976, 8193011203460150583390]
P8 = [-1950786692688, 7931699078003287923106]

Dujella - Eroshkin (2008)

y2 + xy = x3 - 79803310703487437168280400573137070x 
         + 8580075521385909204798110196185094214069266303840275

	Torsion points:

O, [-325790548478330174, 162895274239165087], 
[176991358629130790, -88495679314565395], 
[595196759396797535/4, -595196759396797535/8], 
[296048119817520815, 104409969138874520663894480], 
[296048119817520815, -104409969434922640481415295], 
[57934597440740765, 64429461731296463071772630], 
[57934597440740765, -64429461789231060512513395]

	Independent points of infinite order:

P1 = [77453929409112770, 53513084916901067806613855]
P2 = [-170797570009527145, -131254762955578219832362360]
P3 = [20353565720999740085/169, 58780040321920278978933581585/2197]
P4 = [-285337308928151965/4, -943518525241689473472819785/8]
P5 = [145355941987959590, 7163889827590147924320605]
P6 = [8299757602781346415/81, 28033456909165933393433537920/729]
P7 = [147942534837381665, 3433476697149808365624605]
P8 = [-427591904897299165/4, -1008423586826373027829927385/8]

Dujella - Peral (2012)

y2 + xy = x3 - 74080202792053037257517366670840x 
         + 245162596325324791545535916283786496196278857792

	Torsion points:

O, [-39749417909825409/4, 39749417909825409/8], 
[4838514709224944, -2419257354612472], 
[5098839768231408, -2549419884115704], 
[7077298298057424, -274524484093231519201752], 
[7077298298057424, 274524477015933221144328], 
[3120381238405392, -210681239779447791084792], 
[3120381238405392, 210681236659066552679400]

	Independent points of infinite order:

P1 = [4788825441078024, 15061463188506846389448] 
P2 = [2502112947834762, 274718423698114510009170]
P3 = [3013816380468554, 221975741815687460563748]
P4 = [-2519466817783248, -644835137924363889045240]
P5 = [5855963060746032, 110300164969468654954440]
P6 = [9872268963343724, 689920984075167459213848]
P7 = [5101321879516304, 3132086030194574751848]
P8 = [-3629653943551056, -682810094828549484558072]

Dujella - Peral (2012)

y2 + xy = x3 - 23240401552546314845230555767250x 
         + 39035737383640548738264240132679708432408668932

	Torsion points:

O, [3456384868058948, -1728192434029474], 
[2050756399368004, -1025378199684002], 
[-22028565069707809/4, 22028565069707809/8], 
[7005946462945604, -469137084920834763101602], 
[7005946462945604, 469137077914888300155998], 
[-93176726827708, 202978799380947536252510], 
[-93176726827708, -202978799287770809424802]

	Independent points of infinite order:

P1 = [2040837862129604, 10294405331164056123998]
P2 = [1546125919559684, 82457093881535497643678]
P3 = [1127689628153444, 119422955102773909527518]
P4 = [1146935474467964, 117852641604632336320958]
P5 = [1559355735815744, 81162787604838366316418]
P6 = [-2633076962819836, -286311249696516774300322]
P7 = [-2051742007175356, -279431456561050060030882]
P8 = [3795308235097924, 74163692520455985675358]

Dujella - Peral (2012)

y2 = x3 - x2 - 7985998165395787304825344219115871830992424400x 
    + 236404979519788048487726074172367159784103845913664502907469980160000

	Torsion points:

O, [34946727318433683466800, 0], 
[66610183201593376904401, 0], 
[-101556910520027060371200, 0],
[139581077077533461761002, 42908643898268573372620204002322698], 
[139581077077533461761002, -42908643898268573372620204002322698], 
[-6360710674346707952200, 16939429081011503482711558394131000], 
[-6360710674346707952200, -16939429081011503482711558394131000] 

	Independent points of infinite order:

P1 = [458123899229555420336240, 304512282591221901172859228550376480]
P2 = [-556527982200795593598800/9, 599973700305364156322329535800120000/27]
P3 = [-715786309836038245516055/9, 518289306622325305901326245913940780/27]
P4 = [399517099142986498309682360/961, 7812282912249909568240108605258847931080/29791]
P5 = [12561119218085308986479600/361, 5558347635312556457817364149250330400/6859]
P6 = [84743544757985701918286640/10609, 14377703424675195049494286957191511079040/1092727]
P7 = [-1121769632634659662085881600/16129, 43712927833230253667993454847264650060800/2048383]
P8 = [-1499273832946650907300886437587680209720289600/1234233672671735151497929, 
     21510748072061462707597175802853760710501757844505409179960017818431200/1371185102581530401574998554059782533]

Dujella - Peral (2012)

y2 = x3 - x2 - 760201942774772669314343562439497825088080x 
    - 95708989342755051877989387613747100171663599927715475233817600

	Torsion points:

O, [-128703865129324730640, 0], 
[-800389895439714968640, 0], 
[929093760569039699281, 0]
[-423475537104904818390, -12258687550978678807712996877750], 
[-423475537104904818390, 12258687550978678807712996877750], 
[2281663058242984216952, -100240076662735612577296047674312], 
[2281663058242984216952, 100240076662735612577296047674312] 

	Independent points of infinite order:

P1 = [-157193238959894394015, 4461548640246165747321657478500]
P2 = [-231279463763557154718, 8230366078822038752394755750922]
P3 = [-30918971892959545270935/64, 6451941899339501705722439539269525/512]
P4 = [73811327267811758064304/9, 19937842805666907625290376343497120/27]
P5 = [-12141397122092928753615/16, 425473553595006671934574757714625/64]
P6 = [-1325202685471468237723108035/3247204, 70839830854339908211026421944809796660975/5851461608]
P7 = [19770075506843467096846246840/16621929, 1770678556263481136405467941938843386474600/67767604533]
P8 = [1324965075013717075651654543156717736347090/79438278586210360569, 
     1523028257174004960038711545968910252749231153916498407654661250/708018713765363550939670649997]

Dujella - Peral (2012)

y2 = x3 - x2 - 66674910963953221381407330155283909120x 
    + 209538273973188523148521241768602534888862671193290502400

	Torsion points:

O, [-9428604807613266960, 0], 
[4745439204255832321, 0], 
[4683165603357434640, 0], 
[3805934675309079552, 3302636858326070874259642992], 
[3805934675309079552, -3302636858326070874259642992], 
[5684943733202585090, 3771537538983328401008271550], 
[5684943733202585090, -3771537538983328401008271550]

	Independent points of infinite order:

P1 = [3076600551220809280, 5790309084727561617990589680]
P2 = [2624966616333845330, 7253003452128121411514474530]
P3 = [3547244722406466320, 4202479459903014363817103360]
P4 = [156321344049512720, 14110966735201664715968076160]
P5 = [4165318991405373040, 2020840253034786431960712000]
P6 = [1465984963007142245, 10721213683005167296487179790]
P7 = [4670014691023768325, 118255811923845410917572470]
P8 = [-4847874993922745910, 20465475152817628426216774050]

Dujella - Peral (2016)

y2 + xy = x3 - 656566580528041526076907434779x 
         + 204763686511453405853594537484357296391508689

	Torsion points:

O, [465701912994078, -232850956497039], 
[469934840672542, -234967420336271], 
[392800653014014, -2733137944404316858031], 
[392800653014014, 2733137551603663844017], 
[-3742547014666481/4, 3742547014666481/8], 
[547069028331070, -3050531011062818067407], 
[547069028331070, 3050530463993789736337]

	Independent points of infinite order:

P1 = [50900064512542, 13094895084332895785329]
P2 = [311089955373442, 5533421800790073001189]
P3 = [334153933123486, 4762417864510138878577]
P4 = [365015487014878, 3706754651255271985201]
P5 = [-371832437144672, -19937078913637958859689]
P6 = [-70309868476526, -15829694250402987332231]
P7 = [469950833947294, 9772969417713770737]
P8 = [464505611873086, 95361784093264808497]

Dujella - Peral (2016)

y2 = x3 - x2 - 155620906905035367584300588900x 
    + 23529944481555251676876571790285671801162500

	Torsion points:

O, [239709676940850, 0], 
[215593160466401, 0], 
[-455302837407250, 0], 
[369175042008980, 4048892965476349009110], 
[369175042008980, -4048892965476349009110], 
[110244311872720, -2777321176871585634290], 
[110244311872720, 2777321176871585634290]

	Independent points of infinite order:

P1 = [-119848234211200, 6360769086691746325950]
P2 = [3704327230850, 4790983672414742751000]
P3 = [402823572798126, 5119285037015739604560]
P4 = [59875247652245, 3798257444515667223090]
P5 = [202535726445532, 565077405802465062962]
P6 = [-321267781161640, 6353496718852216718070]
P7 = [117373386467505, 2623201761704752568340]
P8 = [110898103490818270, 36930350949386712434893640]

Dujella - Peral (2017)

y2 + xy = x3 - 288526127482564603081865455676550120450920x 
           + 59623051117716862080826366200122667467803766340526197695822400

	Torsion points:

O, [417977064399123824920, -3471074446251455159387469426800], 
[417977064399123824920, 3471074445833478094988345601880], 
[213410790596458017160, -2787127288107206789195853969320], 
[213410790596458017160, 2787127287893795998599395952160], 
[315693927497790921040, -157846963748895460520], 
[-2480838089366127969921/4, 2480838089366127969921/8], 
[304515594843741071440, -152257797421870535720]

	Independent points of infinite order:

P1 = [997030173749947569232, 27623735278471448759442366116056]
P2 = [413963578399544283760, 3335110345925788073643624509560]
P3 = [671801458840823936040, 12999474265526367525510729540480]
P4 = [-583845736255021644800, -5390630063513533677952084489880]
P5 = [296829643412456440, 7716048732112295506817467368280]
P6 = [891061571249984810067541630/11449, 26598139248741223248139349341082951895500/1225043]
P7 = [3046005977701180542165608716858/10310980849, 430434866738181115628808016219944459990805484/1047007928350007]
P8 = [9468237027061366679670834319399808959624/497220807651266449, 
     920942907205671079037348877116789554814128361165819442428576/350609711983830878450308793]

Dujella - Peral (2017)

y2 + xy = x3 - 7939605217634187705540375862159757546265372082473930x 
           + 262687218501495524246147585277121803488992761789661749489359754558412306857252

	Torsion points:

O, [-102483292119811810378115532, 51241646059905905189057766], 
[173347262337172499979910751/4, -173347262337172499979910751/8], 
[59146476535518685383137844, -29573238267759342691568922], 
[8596384131391474033319844, 441667947951236732845010649251652033078], 
[8596384131391474033319844, -441667947951245329229142040725685352922], 
[109696568939645896732955844, 843656076371476366250067987134143965078], 
[109696568939645896732955844, -843656076371586062819007633030876920922]

	Independent points of infinite order:

P1 = [-24250697620423967817401256, -664053038142458117205216968715604746522]
P2 = [37964568009153644842707444, 126420678453008692247832868788668995878]
P3 = [26959628584308770666537844, 261214950556169843529505108968194631078]
P4 = [160141730331967096038657744, 1760147617426561065539510821356402377478]
P5 = [-102188643690468869134669656, -83173698354615998133753102032164201422]
P6 = [150223675095909790495187844, 1568467767539049162301994961764145831078]
P7 = [17247598442245118088272416/9, 13431755066553737907658344574547461287266/27]
P8 = [505080000074952960943247927741/8464, 29107449636409824704531256037415244768691789/778688]

Dujella - Peral (2017)

y2 + xy = x3 - 93016379737949678213737945088754x 
           + 248176820329629460414197205085637112817583889284

	Torsion points:

O, [-1706182988880060, -633966073480600841254338], 
[-1706182988880060, 633966075186783830134398], 
[17368222836102084, -1967704693351304009657346], 
[17368222836102084, 1967704675983081173555262], 
[7831019923611012, -3915509961805506], 
[-43091286998379553/4, 43091286998379553/8], 
[2941801825983876, -1470900912991938]

	Independent points of infinite order:

P1 = [724518345330180, 425634897071619210739518]
P2 = [2466343285334784, 183763137126139307726562]
P3 = [-243339027083388, -520381520139590912837826]
P4 = [-3049210233396, -498458069246280103970346]
P5 = [1400661774217218, 347333018067921149283186]
P6 = [4923987111172809716/25, 10913426769918985868266471174/125]
P7 = [-8315627616507174, -668313957994846830984108]
P8 = [189304695352472445/16, 57382453476457944122564163/64]

Torsion group Z/2Z × Z/4Z, rank = 7


Dujella (2005)

y2 + xy + y = x3 + x2  - 99693354254976736309048235x 
             + 367381667413491416441937241575243024665

	Torsion points:

O, [799623476723, -16975741865015910122], 
[799623476723, 16975741065392433398], [12588948901683, 33278580255984806998], 
[12588948901683, -33278592844933708682], [-45905215149213/4, 45905215149209/8], 
[4782017598099, -2391008799050], [6694286189203, -3347143094602]

	Independent points of infinite order:

P1 = [-835742939437, -21215935717377581002]
P2 = [3746954832963, 6814774952116046038]
P3 = [-6096171578085, -27360105846461167706]
P4 = [-2303622473757, -24182904784189102202]
P5 = [2494935489403, 11583755159287549598]
P6 = [1441480579203, 15055590839860301398] 
P7 = [7012677573523, 3623709821741193398]

Dujella (2005)

y2 + xy + y = x3 + x2  - 41959740466267167794021810255839x 
             + 101420623252214369655938971034713774891685508101

	Torsion points:

O, [7800185826861527, 498711103150132601849070], 
[7800185826861527, -498711110950318428710598], [722868763952863, -267333060096424984336010], 
[722868763952863, 267333059373556220383146], [-29816914475444701/4, 29816914475444697/8], 
[3192701323453979, -1596350661726990], [4261527295407195, -2130763647703598]

	Independent points of infinite order:

P1 = [-3445007038526955, -452864909445844203135878]
P2 = [2492198029680029, 111030669509523025660920]
P3 = [4451874811734813, 53419669922106933968746]
P4 = [242687787774531, 302079129136924019524594]
P5 = [6876160157322373, 371502935939782200743776]
P6 = [17054531626317779, 2084765600175066109066650]
P7 = [6575035045258779, 331330290650557906808050]

Dujella (2006)

y2 + xy + y = x3 + x2  - 1165389362066982859390020804572126935x 
             + 479169098415397603082209745065693417368573098611430765

	Torsion points:

O,[1121722398993900383, 763770549022673134993708818],
[1121722398993900383, -763770550144395533987609202],
[227498775902112823, -475203958333468654848954522],
[227498775902112823, 475203958105969878946841698],
[2281899376216052387/4, -2281899376216052391/8],
[-1245085431502019701, 622542715751009850]

	Independent points of infinite order:

P1 = [-219613035643780957, -851182637388769392857068902]
P2 = [-68223999018942087, -747234281532450366676883702]
P3 = [497293734150587235, 150364681171547564975694874]
P4 = [10796967815787170653/16, 404988480627920631161493627/64]
P5 = [1044774651633868835, 634056668621030138238484890]
P6 = [4919976421604836927/9, 1994819697953126282867607346/27]
P7 = [-328470482217806715463/289, -2845674500282729683306185667926/4913]

Dujella (2006)

y2 = x3 - x2 - 23915436403668100957879238210372478564x 
    + 44961725066137056690704922539092621426845072010929824004

	Torsion points:

O, [2903013524470034482, 0], [-5646124833195250962, 0], [2743111308725216481, 0],
[4072212466523820944, 3886146862871075405578563406], 
[4072212466523820944, -3886146862871075405578563406], 
[1733814582416248020, -2951073576030980502660949482], 
[1733814582416248020, 2951073576030980502660949482]

	Independent points of infinite order:

P1 = [1131018313110890882, 4399969306249670626854871960]
P2 = [2728347748849569104, 146952908391872112013369586]
P3 = [261187619128923630, 6223594389290707973165058528]
P4 = [29320876476743932860, 156688551675810110453020536558]
P5 = [-4606042810657217150, 7576090497154110956612194152]
P6 = [-5268512043362633412, 4972046499534700899993247890]
P7 = [12466639899760292984, 41040781435946053834115762026]

Dujella (2006)

y2 = x3 - x2 - 66316100370037243788808101431860x 
    + 207787397329581777063539110158423853553882263492

	Torsion points:

O, [4628372593789489, 0], [4774517796226298, 0], [-9402890390015786, 0], 
[6213948304937164, 188792790675737045056350], 
[6213948304937164, -188792790675737045056350], 
[3335087287515432, -153990087256491803556554], 
[3335087287515432, 153990087256491803556554]

	Independent points of infinite order:

P1 = [2296719982411009, 259986354975552263423820]
P2 = [-754552913305211, 507342881379999424501350]
P3 = [4623547820142394, 3196373093851098851280]
P4 = [4774647845487904, 519325665120008067090]
P5 = [2882111728866944, 201488073470229552730830]
P6 = [4572248586935254, 12595554476372830774560]
P7 = [-14146681940011859/4, 5047542184921547691312855/8]

Dujella (2006)

y2 + xy = x3 - 4352472636817242527981668893860x 
         + 3202806006191278796231716596650711645198790975

	Torsion points:

O, [907667106246270, -453833553123135], 
[1478672062650370, -739336031325185], 
[-9545356675586561/4, 9545356675586561/8], 
[2964249583270165, 127856115668915058245395], 
[2964249583270165, -127856118633164641515560], 
[-6905457969425, -56858257917087837736865], 
[-6905457969425, 56858257923993295706290]

	Independent points of infinite order:

P1 = [-586964814172115, -74534076914908408877600]
P2 = [-2328305178439673, -26738296509185052458918]
P3 = [-419400465474005, -70387952431540002422810]
P4 = [-630447314322050, -75473377079125527624335]
P5 = [-846673128162305, -79252667902607341645985]
P6 = [-268297363924910, -65964004932893602468685]
P7 = [1377377634990063790, 1616512407040009129064037565]

Dujella (2006)

y2 = x3 + x2 - 1974182441851753491140042260957041544x 
    + 1067650302694924098203516167151188617468357911014102916

	Torsion points:

O, [-1622418946354203118, 0], [811326669343979123, 0], [811092277010223994, 0], 
[787442546696709656, -36894683045645829307668798], 
[787442546696709656, 36894683045645829307668798], 
[835210791991248590, -37626009005611049158919916], 
[835210791991248590, 37626009005611049158919916]

	Independent points of infinite order:

P1 = [807173041427965811, 6288993601307198150714928]
P2 = [789278583199907432, 34057398752431372965082590]
P3 = [596369565518553920, 320016850497427999752392094]
P4 = [814421506614155896, 5010768410557123065521538]
P5 = [-981176602679102770, 1435299907571197805711062764]
P6 = [41561092163942585600/49, 19934917122155057779445712078/343]
P7 = [39756857357017556954/49, 54250001709421994662548384/343]

Dujella (2006)

y2 + xy = x3 - 7059202548408453936348405003649460x 
         - 205544995440715384038467753747276578744945665206400

	Torsion points:

O, [-242093366040292161/4, 242093366040292161/8], 
[-35403361017968480, 17701680508984240], 
[95926702528041520, -47963351264020760], 
[239267534900752570, -108642684797447273394364010], 
[239267534900752570, 108642684558179738493611440], 
[-47414129844669530, -4750711426855673634362960], 
[-47414129844669530, 4750711474269803479032490]

	Independent points of infinite order:

P1 = [-40080467944208480, -3606122876978274455995760]
P2 = [408080083130635270, 254697953786456983119660490]
P3 = [95933492675735920, 373533990830032696210840]
P4 = [-962353464408583355/16, -77146422425694624547527515/64]
P5 = [-36340930482348830, -1731722552202363314731760]
P6 = [16892458715992053910/169, 20552422351563850326861544690/2197]
P7 = [95927004352140082, 78749450426831409587536]

Dujella (2006)

y2 + xy = x3 - 3236364326867793561860795581563976590x 
         + 2240038946953594158835601178135288379947620927515076100

	Torsion points:

O, [4085603896699595295/4, -4085603896699595295/8], 
[-2077199566031870404, 1038599783015935202], 
[1055798591856971580, -527899295928485790], 
[727518722182179300, 520179734430437450073364890], 
[727518722182179300, -520179735157956172255544190], 
[1384078461531763860, 641949208250981314550343210], 
[1384078461531763860, -641949209635059776082107070]

	Independent points of infinite order:

P1 = [1005739555669779996, 49163099954291059347164322]
P2 = [518381451900100280, 837655552211056707012286310]
P3 = [-2405859056872500, -1499274881218127124560219310]
P4 = [843602380471211580, 331958679042130626373098210]
P5 = [940105128640111310, 168460532843765869032724460]
P6 = [848175468782248980, 324365423296277587356836010]
P7 = [120130530737617207683/4, 1314369752929665855682758389883/8]

Dujella (2006)

y2 + xy = x3 - 552333041381848469546578260185903690x 
         + 105246264670604440637332918974955977886070209631543475

	Torsion points:

O, [825953971768859295/4, -825953971768859295/8], 
[618112058064791230, -309056029032395615], 
[-824600551007006054, 412300275503503027], 
[-152507502803882195, 431200760645876446118157385], 
[-152507502803882195, -431200760493368943314275190], 
[1388731618933464655, -1420027357952646693708591740], 
[1388731618933464655, 1420027356563915074775127085]

	Independent points of infinite order:

P1 = [703736453716866055, 255090819294844960769724685]
P2 = [39615732830330262145, 249301833834654463541876995270]
P3 = [-2042038215442845405/4, -4033210585603340196533135145/8]
P4 = [669011498243733907, 187517617205695776364821997]
P5 = [-180114161620463585, -445966550007175173221222675]
P6 = [1164418516389907131295/4, 39733995653091626373596729630705/8]
P7 = [-294620693466003965, -492342902235415687643737520]

Eroshkin (2008)

y2 + xy + y = x3 + x2 - 223647057021425547430678972007035x 
         + 1273106313114343201368902765863085728849052445440

	Torsion points:

O, [-68988428135422813/4, 68988428135422809/8], 
[7881912604174649, -3940956302087325], 
[9365194429681053, -4682597214840527], 
[3082397035545098, 782958279826254162287598], 
[3082397035545098, -782958282908651197832697], 
[15647991823817008, -1266902042378890394018832], 
[15647991823817008, 1266902026730898570201823]

	Independent points of infinite order:

P1 = [-8726288912333155, -1600070202750911236143711]
P2 = [6456748016181118, 313453072716873679262383]
P3 = [18713273063365648, 1908160131603999620825503]
P4 = [-6424268512310840, -1563565672503751617925976]
P5 = [7312072950399488, 169508147861449136621823]
P6 = [9461772364824908, 63837523115230204267143]
P7 = [4432663254435236882/169, 8057681617359104719760519331/2197]

Eroshkin (2008)

y2 = x3 + x2 - 4123297792196061474931925360x 
         + 83669201239698270468036960902365235322900

	Torsion points:

O, [105340804361380, -904572509820269840550], 
[105340804361380, 904572509820269840550], 
[-6876184911470, -334210472735844058200], 
[-6876184911470, 334210472735844058200], 
[23398765230714, 0], 
[-72631074955670, 0], 
[49232309724955, 0]

	Independent points of infinite order:

P1 = [7863233370580, 227448753821255216250]
P2 = [-53445032541830, 389075979691181365440]
P3 = [-19322069176277, 395127953404498572804]
P4 = [11983227764095, 189682759293189672510]
P5 = [21829310745364, 63737975851715924730]
P6 = [20867194460260, 81938705576738152230]
P7 = [-10451426017445, 354431812482973625400]

Eroshkin (2008)

y2 = x3 + x2 - 609255875083793261019303912808600x 
         + 5769420440641556969899813369432728161558284302500

	Torsion points:

O, [14909494948028675, 0], 
[-28491289380416726, 0], 
[13581794432388050, 0], 
[7318497402772550, -1304823582135807142909500], 
[7318497402772550, 1304823582135807142909500], 
[22500492493284800, -1858019425995733566315750], 
[22500492493284800, 1858019425995733566315750]

	Independent points of infinite order:

P1 = [-4832356503434830, 2932698150079894286497680]
P2 = [13129331116915280, 183094773963169535400570]
P3 = [-5283378139483450, 2973359875332604804546500]
P4 = [-5015545724269450, 2949406988156065867657500]
P5 = [1786720755936880, 2164845074961685794361530]
P6 = [13326362147583050, 130039828235976803430000]
P7 = [15081385235732810, 105978840319725141328560]

Eroshkin (2008)

y2 + xy + y = x3 + x2 - 8007418165950294717261920x 
         - 870716437481702091977368984017213055

	Torsion points:

O, [-108900008427, 54450004213], 
[2882616151573, -1441308075787], 
[-11094864572589/4, 11094864572585/8], 
[-1230899311627, -2668455376347768587], 
[-1230899311627, 2668456607247080213], 
[6996131614773, 16897925184033057013], 
[6996131614773, -16897932180164671787]

	Independent points of infinite order:

P1 = [-383181597927, -1463323767915288287]
P2 = [3563438686053, 3980478568219330213]
P3 = [-137187778427, -474575037055755787]
P4 = [-109031458027, -32371068443947787]
P5 = [-691731404427, -2082612916549255787]
P6 = [-1049448028427, -2525242524171255787]
P7 = [-183188678427, -768117380830765787]

Dujella - Eroshkin (2008)

y2 = x3 + x2 - 2386801266816420981220x 
         + 44845424005663002738546614573600

	Torsion points:

O, [18270423230, 2708574311641770], 
[18270423230, -2708574311641770], 
[39452756090, -3476857524473970], 
[-56407666421, 0], 
[27546076760, 0], 
[28861589660, 0], 
[39452756090, 3476857524473970]

	Independent points of infinite order:

P1 = [22032102854, 1718678096630670]
P2 = [22764199660, 1519345810983000]
P3 = [4756640090, 5796541328047470]
P4 = [-26758658452, 9463251767513544]
P5 = [-12340124452, 8509977139977456]
P6 = [24822560510, 945284011785750]
P7 = [14209561490, 3714714049911930]

Dujella - Eroshkin (2008)

y2 = x3 + x2 - 5334348061487201120280x 
         + 149721135899592401852463095048100

	Torsion points:

O, [43529258115, 0], 
[-84320610606, 0], 
[40791352490, 0], 
[24819878790, 5710776107645700], 
[62238637440, -7668712654006950], 
[24819878790, -5710776107645700], 
[62238637440, 7668712654006950]

	Independent points of infinite order:

P1 = [5359329240, 11013016898588250]
P2 = [33560492490, 2914994668950000]
P3 = [49198220490, 2522552201778000]
P4 = [40461341130, 355436590214160]
P5 = [16644351690, 8096013181198800]
P6 = [44116137240, 500611414899750]
P7 = [43529729040, 12840247642950]

Torsion group Z/2Z × Z/4Z, rank = 6


Dujella (2001)

y2 = x3 - x2  - 84385099279492765124x 
      + 262973362131816463305769975044 

	Torsion points:

O, [-450024320, 548504848910018], [-450024320, -548504848910018],
[13914569924, 1335239311059654], [13914569924, -1335239311059654],
[-10464902242, 0], [3732629441, 0], [6732272802, 0] 

	Independent points of infinite order:

P1 = [12885805880, 1146827806213782]
P2 = [7979506940, 312565640755122]
P3 = [604008660, 460678184564598]
P4 = [1473384440, 376616759777622]
P5 = [15209138914, 1580409705748016]
P6 = [20163601480277, 90542423098869511770]   

Ansaldi - Ford - George - Mugo - Phifer (2005)

y2 = x3 + x2  - 75345731906887386383040x 
      + 7956141361808560862806122648470388 

	Torsion points:

O, [107886244746, 32910620718406200], [107886244746, -32910620718406200], 
[161469150507, 0], [-316936855054, 0], [155467704546, 0], 
[215052056268, -41212648971204018], [215052056268, 41212648971204018]

	Independent points of infinite order:

P1 = [153985039026, 2285947010756640]
P2 = [162803544546, 2167055919336000]
P3 = [30235962867834/169, 31283143086365619240/2197]
P4 = [32189665272114/169, 49863355519584351360/2197]
P5 = [154625377443516/121, 1881611310019500873450/1331]
P6 = [217002711282, 42715445379794880]  

Ansaldi - Ford - George - Mugo - Phifer (2005)

y2 = x3 - x2  - 1621105850715834564900x 
      + 4979606331160862237085144928452 

	Torsion points:

O, [-41718901791, 0], [38628969058, 0], [3089932734, 0], 
[92065715784, 25220808536003850], [92065715784, -25220808536003850], 
[-14807777668, 5073231297419714], [-14807777668, -5073231297419714]

	Independent points of infinite order:

P1 = [1291128254, 1699618513398080]
P2 = [-9589966542, 4432154369225880]
P3 = [-166732650939/4, 2867877947917125/8]
P4 = [-987086238936/25, 340817455790473662/125]
P5 = [6033839983202, 14821119830299337984]
P6 = [-14560799125208/3721, 761767378800794319954/226981]  

Dujella (2005)

y2 + xy = x3 - 1412825737585924163044x 
         + 15284155642547476371073178165264

	Torsion points:

O, [66149709524, -14535609729112288], 
[66149709524, 14535543579402764], [-5994218500, -4851549910630708], 
[-5994218500, 4851555904849208], [-168549044801/4, 168549044801/8], 
[12059515688, -6029757844], [30077745512, -15038872756]

	Independent points of infinite order:

P1 = [-4710088480, -4672705304733532]
P2 = [10971680384, 1050627482515964]
P3 = [5142674960, 2855599110883388]
P4 = [190936944656, 81893102282965052]
P5 = [188694106912, 80419019486556004]
P6 = [47485021091/4, 3441975241405087/8]   

Dujella (2005)

y2 + xy + y = x3 + x2 - 20174541800058615341705x 
             + 856471220529843128844656290913975

	Torsion points:

O, [-639179005053/4, 639179005049/8], 
[111893780143, -55946890072], [47900971119, -23950485560], 
[-19962627757, -35373042637815172], [-19962627757, 35373062600442928], 
[243750188043, 102083834331329428], [243750188043, -102084078081517472]

	Independent points of infinite order:

P1 = [-85832332857, -44223889042397072]
P2 = [114334829243, 6667410918555328]
P3 = [-51502844857, -41939263761590072]
P4 = [4095391655, 27819366371819600]
P5 = [113157736403, 4744791614680828]
P6 = [40334772162089/256, 163280485878941726915/4096]

Dujella (2005)

y2 = x3 - x2 - 168258761005814873925308660x 
    + 630726626828906815917748614617850058692

	Torsion points:

O, [4183796725814, 0], [-14547043674127, 0], [10363246948314, 0], 
[22770176501164, 92765011772747132350], [22770176501164, -92765011772747132350], 
[-2043682604536, 31081480114842787350], [-2043682604536, -31081480114842787350]

	Independent points of infinite order:

P1 = [-1181620857528, 28773162432111226794]
P2 = [-4080437386136, 35346241790698760950]
P3 = [235082596420931926/9, 113980528024566253238850200/27]
P4 = [12397530832897061/4, 1380381075594638902858965/8]
P5 = [21473097297618184/841, 2778642295098362364452690/24389]
P6 = [17594838020822091901/1387684, 37835298438599399762075368625/1634691752]

Dujella (2005)

y2 + xy + y = x3 + x2 - 26114391257594216192350319x 
             + 39441729062095446183464976447530972981

	Torsion points:

O, [-22972042324701/4, 22972042324697/8], 
[4045286938075, -2022643469038], [1697723643099, -848861821550], 
[8838891842163, 22342036507934785450], [8838891842163, -22342045346826627614], 
[-748317966013, -7652747778169852550], [-748317966013, 7652748526487818562]

	Independent points of infinite order:

P1 = [1682911881033, 509744180039882596]
P2 = [-4350450222813, -8409079383332570750]
P3 = [-2732001972537, -9507631680841759250]
P4 = [838116572907, 4259524325765646130]
P5 = [-8602000453, -6298123877540569838]
P6 = [-5174972297007, -5999620042052044670]

Dujella (2005)

y2 + xy = x3 - 890502303468937724149130x 
         + 251976732409553090006157393210660900

	Torsion points:

O, [742337937460, -371168968730], 
[-4247871397281/4, 4247871397281/8], [319629911860, -159814955930], 
[-130985906660, 605287285332941470], [-130985906660, -605287154347034810], 
[1615661781580, 1740886872995215750], [1615661781580, -1740888488656997330]

	Independent points of infinite order:

P1 = [34804303282, 470133559355108026]
P2 = [287152225570, 141225042040120570]
P3 = [-268025483360, -686585417289749030]
P4 = [-952849293368, -485157848702086574]
P5 = [10019541317440/9, 21606662227037110690/27]
P6 = [-501429434660, -756587916758553530]

Dujella (2005)

y2 + xy = x3 - 1009893481532852485509490x 
         + 307126098316462880729754569042548100

	Torsion points:

O, [-134384068060, 663636142416168350], 
[-134384068060, -663636008032100290], [1708894587620, 1889931644827630910], 
[1708894587620, -1889933353722218530], [-4527652164641/4, 4527652164641/8], 
[787255259780, -393627629890], [344657781380, -172328890690]

	Independent points of infinite order:

P1 = [326435595860, 110661301285782830]
P2 = [186678812540, 353703099209895710]
P3 = [-24614318068, -576167519527474978]
P4 = [-644001146800, -830907162445976110]
P5 = [201411568100, 334503195371036990]
P6 = [10088870660, 544920576783541310]

Dujella (2005)

y2 + xy = x3 - 8417650709198283033894x 
         + 273611860820485052415499040073444

	Torsion points:

O, [-419974072161/4, 419974072161/8], 
[40252511948, -20126255974], [64741006092, -32370503046], 
[129212262480, -36650458788184122], [129212262480, 36650329575921642], 
[269749704, 16472438107887342], [269749704, -16472438377637046]

	Independent points of infinite order:

P1 = [31511617284, 6296693126428362]
P2 = [-5242929084, -17821357800987918]
P3 = [11122388942, 13467117330606884]
P4 = [65983525524, 2337990892009122]
P5 = [39733247316, 1370881423554762]
P6 = [14769183135206724, 1794877079819738239098354]

Dujella (2005)

y2 = x3 + x3 - 5881112817909257676180x 
    + 172368599382146998973856168201600

	Torsion points:

O, [47280943140, 0], [-88482565381, 0], [41201622240, 0], 
[76009847310, -12825473417517270], [76009847310, 12825473417517270], 
[18552038970, 8345488101247470], [18552038970, -8345488101247470]

	Independent points of infinite order:

P1 = [-10176865200, 15204140496080760]
P2 = [40557350480, 747648180255240]
P3 = [151220795688651/625, 1775600563187320377024/15625]
P4 = [12647675942690, 44978827414035407850]
P5 = [576449081936/25, 875190476902116984/125]
P6 = [317899098338454/105625, 426961707725012406012858/34328125]

Dujella (2005)

y2 + xy = x3 - 9779547590023543199800x 
         + 348929743858830658241338918280000

	Torsion points:

O, [68394784400, -34197392200], 
[-113388065200, 56694032600], [179973123199/4, -179973123199/8], 
[3172150220, 17830855647907100], [3172150220, -17830858820057320], 
[133617418580, -37785854192696680], [133617418580, 37785720575278100]

	Independent points of infinite order:

P1 = [41083488392, 4061346698069456]
P2 = [35783467310, 6693471246647390]
P3 = [-28150319350, -24534037344300700]
P4 = [-20650075240, -23282438354786560]
P5 = [111698481602, 25498589338688996]
P6 = [1555253472775/36, 574272931872414175/216]

Dujella (2005)

y2 = x3 - x2 - 2791493234428682804020x 
    - 8540150483506656022970369599100

	Torsion points:

O, [-23510055660, 6640291333025350], [-23510055660, -6640291333025350], 
[132115085440, -43916403255002850], [132115085440, 43916403255002850], 
[54302514890, 0], [-51232804154, 0], [-3069710735, 0]

	Independent points of infinite order:

P1 = [-21686024880, 6465110808903890]
P2 = [-49422123688, 2950516494110262]
P3 = [-39769398760, 6290975605864950]
P4 = [59384756340, 5925451375693850]
P5 = [54646601765, 1450070406881250]
P6 = [104111660675932, 1062304460321303000802]

Dujella (2005)

y2 = x3 - x2 - 119517739302760276059242340x 
    + 493654844362203070424193925118382524100

	Torsion points:

O, [-12597763694370, 0], [1761006233960, 16989540678288837610], 
[1761006233960, -16989540678288837610], [12236759929500, -29384630538664589790], 
[12236759929500, 29384630538664589790], [5598880612641, 0], [6998883081730, 0]

	Independent points of infinite order:

P1 = [-3476870613810, 29447783619818152680]
P2 = [8139165312860, 7750319300680322590]
P3 = [-5386320853760, 31323239917146322830]
P4 = [5596804484412, 230135778885179202]
P5 = [15921874465260, 51254272875976138290]
P6 = [402587320153869/25, 6549092839649221847622/125]

Dujella (2005)

y2 + xy = x3 - 7615466123341469335310x 
         + 188640502062497898331796594948100

	Torsion points:

O, [-14471391260, -17199303109311230], 
[-14471391260, 17199317580702490], [27502255420, -13751127710], 
[-390818401761/4, 390818401761/8], [70202345020, -35101172510], 
[154876081300, 52193194636764610], [154876081300, -52193349512845910]

	Independent points of infinite order:

P1 = [25856946970, 3002532673595590]
P2 = [12376378780, 9812453110093090]
P3 = [26592901660, 2220165269728450]
P4 = [-96426304790, -5137739966639600]
P5 = [72646817992, 4335753498466582]
P6 = [7650691149283/4, 21139962430624193831/8]

Dujella (2005)

y2 = x3 - x2 - 2752408299758620522098980x 
    - 1611469491300450666662632159356431100

	Torsion points:

O, [-1175270339890, 0], [1897773720210, 0], [-722503380319, 0], 
[4735418338480, 9567791352271834990], [4735418338480, -9567791352271834990], 
[-939870898060, 381047432275150410], [-939870898060, -381047432275150410]

	Independent points of infinite order:

P1 = [-776632537390, 240225199081098000]
P2 = [-734467503248, 117821749403203538]
P3 = [-1032087420738, 360378113098626168]
P4 = [2829381083540, 3640225029168985110]
P5 = [-334684659337090/289, 743201851722475372920/4913]
P6 = [10794181649645/4, 26061142903976023305/8]

Dujella (2005)

y2 + xy + y = x3 + x2 - 457072288368656979319090x 
             + 117898635812323031230705122524518847

	Torsion points:

O, [-779899861159, 389949930579], 
[1440505578803/4, -1440505578807/8], [419773466457, -209886733229], 
[687274870297, 358324073089235091], [687274870297, -358324760364105389], 
[152272062617, 227661942377971731], [152272062617, -227662094650034349]

	Independent points of infinite order:

P1 = [-151762196263, -428683465936312749]
P2 = [59852557787, 301257504077200551]
P3 = [-115229341223, -411140772541082669]
P4 = [323869348697, 61951644391518291]
P5 = [-2822956775117/4, -2386177249846311447/8]
P6 = [1170517069537, 1089322648822519411]

Dujella (2005)

y2 = x3 - x2 - 601167709096816182426749700x 
    + 5660909342729347649383846361635078811652

	Torsion points:

O, [21520698541184, -51869708377111066750], 
[21520698541184, 51869708377111066750], [7867902807684, 37656793045848495750], 
[7867902807684, -37656793045848495750], [-28304866216191, 0], 
[14694300674434, 0], [13610565541758, 0]

	Independent points of infinite order:

P1 = [-11396797435566, 105033329058893235000]
P2 = [13515239353472, 2168037912942469246]
P3 = [17644481570684, 23384464315261708750]
P4 = [9815545575964, 26566866494642436270]
P5 = [3088064301384, 61918599936671473050]
P6 = [15361168746549, 7139794323331981710]

Dujella (2005)

y2 + xy = x3 - 4970973276415392436529590x 
         + 4261112314439353076826126873509416100

	Torsion points:

O, [1251883897580, -625941948790], 
[-10296649990241/4, 10296649990241/8], [1322278599980, -661139299990], 
[798552706520, -894849197222925190], [798552706520, 894848398670218670], 
[1846004493440, -1172759629054433050], [1846004493440, 1172757783049939610]

	Independent points of infinite order:

P1 = [341512408190, 1613472512467305860]
P2 = [274826813060, 1707545814831601730]
P3 = [1063369297196, 421355992217645162]
P4 = [780021064496, 926411449154533082]
P5 = [-179141249180, -2268450868639669190]
P6 = [679519563830, 1094076774315711710]

Dujella (2005)

y2 = x3 - x2 - 41967143645254581562603277540x 
    + 2499923757202652047177517799000949313532612

	Torsion points:

O, [-229874550646882, 0], [66611176071329, 0], [163263374575554, 0], 
[358193220387164, -5781403049573347524510], [358193220387164, 5781403049573347524510], 
[-31666471236056, -1948620297182521408810], [-31666471236056, 1948620297182521408810]

	Independent points of infinite order:

P1 = [11244440114992, 1424587112757798224066]
P2 = [-12064380792848, 1733342261915366587394]
P3 = [163310459909122, 42310965041794002736]
P4 = [180811017357314, 907187094398719658160]
P5 = [-222648525455948, 898127072944350900794]
P6 = [2819459834400617/16, 48594797208579968891181/64]

Dujella (2005)

y2 + xy + y = x3 + x2 - 24755262175855280781923864788015x 
             + 37265034103619296083235936013507719601892332405

	Torsion points:

O, [-22416053814052573/4, 22416053814052569/8], 
[1705860255937979, -852930127968990], [3898153197575163, -1949076598787582], 
[8462310609348023, 658612408264797695479518], [8462310609348023, -658612416727108304827542], 
[-666004214197697, 231207113399564700704218], [-666004214197697, -231207112733560486506522]

	Independent points of infinite order:

P1 = [288671426882035, 173617258740765416051530]
P2 = [-5570742796939277, -47878956410889819020982]
P3 = [-3215474603382537, -289169963223480703893782]
P4 = [20300351053034403, 2810798012718765226249378]
P5 = [3526052528580254773/121, 6528981776892682037881128408/1331]
P6 = [232261432516477661299/625, 3539377448410546468282674082482/15625]

Dujella (2005)

y2 + xy + y = x3 + x2 - 277997148495295110798222064776730x 
             + 1363430168994747642708704333200845201234817963175

	Torsion points:

O, [13225086556644393, -6612543278322197], 
[-74917888169353549/4, 74917888169353545/8], [5504385485693993, -2752192742846997], 
[-2481969017106967, 1427627798260566831998763], [-2481969017106967, -1427627795778597814891797], 
[28932142130395753, -4187907851021071588297557], [28932142130395753, 4187907822088929457901803]

	Independent points of infinite order:

P1 = [5265008707145513, 213823453339216495759083]
P2 = [-270655797380265, -1199438152550610180794711]
P3 = [88072750892721193, 25691302043561677586804203]
P4 = [-4863993025676647, -1612616483560612937075157]
P5 = [-16767861397425427, -1144716636452792623074777]
P6 = [1644474400624935744755/361, 66686476272493576318143019435221/6859]

Dujella (2005)

y2 = x3 - x2 - 2599204480065528608632618826260x 
    + 1318051470724882702726660094314375188894780100

	Torsion points:

O, [1239173390745770, 0], [583551476582545, 0], [-1822724867328314, 0], 
[2656017629514300, -114678716687042268370610], [2656017629514300, 114678716687042268370610], 
[-177670848022760, 42121797345530930308710], [-177670848022760, -42121797345530930308710]

	Independent points of infinite order:

P1 = [-830334184200470, 53886750371913854675280]
P2 = [-129872323419770, 40662337149274345851120]
P3 = [220805643944552, 27475404640607938652022]
P4 = [-1071708693390075, 53597763775288563330610]
P5 = [2186813100689125, 78049655307987615333510]
P6 = [-1721542237587030, 26278200538452947375200]

Dujella (2005)

y2 = x3 - x2 - 18185256818907344021519822340x 
    + 867781677190111136236716183849682108124100

	Torsion points:

O, [-154302193738770, 0], [59029795192641, 0], [95272398546130, 0], 
[165968924940, 929926606909301658930], [165968924940, -929926606909301658930], 
[190378828167320, 2075042828501670614470], [190378828167320, -2075042828501670614470]

	Independent points of infinite order:

P1 = [33470400122640, 544618823369729207970]
P2 = [57112414857680, 124372888676596974050]
P3 = [41350883653560, 431869113743324817690]
P4 = [18552766500702, 732653268165772489032]
P5 = [58462055900370, 66682017950903589120]
P6 = [1760037576895780/9, 59094775417250330911790/27]

Dujella (2005)

y2 + xy + y = x3 + x2 - 2714685581949176342441469535x 
             + 54440460625181460179771190482209079698565

	Torsion points:

O, [26173285440683, 36304122435932239698], 
[26173285440683, -36304148609217680382], [34166397950923, 39665202267150628978], 
[34166397950923, -39665236433548579902], [-60162865244101, 30081432622050], 
[119972094193187/4, -119972094193191/8], [30169841695803, -15084920847902]

	Independent points of infinite order:

P1 = [14161896260893, 137243080592772202858]
P2 = [25575890162203, 41711126192619972898]
P3 = [29360545844283, 6769298049175234018]
P4 = [29945571659813, 979238465267455488]
P5 = [29973001219003, 596008430486665698]
P6 = [28675816049723, 13222290792458270178]

Dujella (2005)

y2 = x3 + x2 - 265134190444488812450005666073620x 
    + 1374889946621052563466183441951718633784728817600

	Torsion points:

O, [12431169885925460, 0], [-18431709610586821, 0], [6000539724661360, 0], 
[26519028621508070, 3604654089224950144108110], [26519028621508070, -3604654089224950144108110], 
[-1656688849657150, 1345209212594071042391910], [-1656688849657150, -1345209212594071042391910]

	Independent points of infinite order:

P1 = [5387240518134155, 320778317527535807647620]
P2 = [13364159011545550, 467379114205798593393210]
P3 = [16508668537961858, 1223554750360444533377754]
P4 = [6147240338643679402/49, 15117667927972155266195579742/343]
P5 = [-1159827509634813982/121, 2318998591535360087597781726/1331]
P6 = [356156947207798925410/96721, 20145066549572426850639551594250/30080231]

Dujella (2005)

y2 + xy + y = x3 + x2 - 1666737234575129261770056486330225x 
             + 20858552697655280228623937828451081716750394990735

	Torsion points:

O, [-46041064285956161, 23020532142978080], 
[57004492588290307/4, -57004492588290311/8], [31789941138883583, -15894970569441792], 
[-5156829197181237, -5414471066226009163347492], [-5156829197181237, 5414471071382838360528728], 
[68736711474948403, -15200503231987582349424412], [68736711474948403, 15200503163250870874476008]

	Independent points of infinite order:

P1 = [3528584361681783, 3875727521493507661133408]
P2 = [32005321616677603, 546298601836283385271508]
P3 = [75161132508580543, 17893704208546244151802208]
P4 = [14160630547166143, 309904973897683118914208]
P5 = [-17082891368920997, -6659281184658577384901512]
P6 = [113047539153133738247/2809, 648310594134977553865017686016/148877]

Dujella (2006)

y2 = x3 - x2 - 343633641057979504x 
    + 36692720733182921224013824

	Torsion points:

O, [-167543430, 9463783668262], [-167543430, -9463783668262], 
[1213426024, 37501606492824], [1213426024, -37501606492824], 
[110729488, 0], [522941297, 0], [-633670784, 0]

	Independent points of infinite order:

P1 = [-7755736, 6273546526104]
P2 = [69795322, 3612298454310]
P3 = [-607838712, 4581447129560]
P4 = [106344040, 1162747450008]
P5 = [3003675688, 161566995145320]
P6 = [582225800, 5829859131432]

Dujella (2006)

y2 = x3 - x2 - 4664630695650596406400x 
    + 122611657721145018740841654400000

	Torsion points:

O, [31069796800, -2770416472639200], [31069796800, 2770416472639200], 
[48428296002, 3207868011028802], [48428296002, -3207868011028802], 
[39113956000, 0], [-78863002400, 0], [39749046401, 0]

	Independent points of infinite order:

P1 = [28260480960, 3654766624544480]
P2 = [-12857421920, 13433587750450560]
P3 = [13143969210, 7973123554358270]
P4 = [34512505410, 1652834075535170]
P5 = [91860783045, 21662718643569190]
P6 = [38608886722, 260090980468158]

Dujella (2006)

y2 = x3 + x2 - 11275024414184475994040x 
    + 460709013467704417216360284483300

	Torsion points:

O, [-122607564470, 0], [62054292259, 0], [60553272210, 0], 
[78703050448, 7799377153768074], [78703050448, -7799377153768074], 
[45405534070, 6509331476735220], [45405534070, -6509331476735220]

	Independent points of infinite order:

P1 = [60507537238, 113814359125236]
P2 = [-23016513302, 26608786846591824]
P3 = [1090357234, 21175847216507760]
P4 = [-7923414617, 23442445921728834]
P5 = [-23132282480, 26629831414568970]
P6 = [45526382259, 6462063575261700]

Dujella (2006)

y2 = x3 - x2 - 331999964186328512900x 
    + 2327612294831641365690701258052

	Torsion points:

O, [10362752654, 0], [10676113458, 0], [-21038866111, 0], 
[13828609532, 617224053832386], [13828609532, -617224053832386], 
[7523617384, -505613082828490], [7523617384, 505613082828490]

	Independent points of infinite order:

P1 = [11413318654, 158535977399800]
P2 = [2131189889, 1276611581208600]
P3 = [4902393233, 904344727306020]
P4 = [1363681784, 1370184634353990]
P5 = [10210152404, 47137942544550]
P6 = [10832642558, 48416892483960]

Eroshkin (2008)

y2 = x3 + x2 - 2013664127615449300x 
    - 649446586170797281317775552

	Torsion points:

O, [1558929716, 0], [-1216463408, 0], [-342466309, 0], 
[3856128326, -221190362561070],  [-738268894, -20851671782970], 
[-738268894, 20851671782970], [3856128326, 221190362561070], 

	Independent points of infinite order:

P1 = [-378679454, 7667119485690]
P2 = [-362626354, 5751217317510]
P3 = [-348685504, 3208608800040]
P4 = [-471766609, 13983374893950]
P5 = [-391521934, 8884307265750]
P6 = [-984546058, 19461437192190]

Eroshkin (2008)

y2 + xy = x3 - 645065532532048725x 
    + 182854916195163425393625000

	Torsion points:

O, [1399380399/4, -1399380399/8], [-918745000, 459372500], 
[568899900, -284449950], [1139755185, 30466262110500], 
[-1955385, 13568945674500], [-1955385, -13568943719115], 
[1139755185, -30467401865685]

	Independent points of infinite order:

P1 = [205490700, 7679551321350]
P2 = [39533832, 12546485410752]
P3 = [343406775, 1353486075300]
P4 = [264680127, 5537123858196]
P5 = [166770315, 8939458354185]
P6 = [348330705, 650394675300]

Eroshkin (2008)

y2 + xy = x3 - 13050070927054823465x 
    + 16542549296816918233072779225

	Torsion points:

O, [6226715695/4, -6226715695/8], [5183456770, 296928964099795], 
[-37111310, -130486775461925], [-37111310, 130486812573235], 
[5183456770, -296934147556565], [2573172730, -1286586365], 
[-4129851654, 2064925827]

	Independent points of infinite order:

P1 = [1096220890, 59615874435235]
P2 = [899520022, 74374166104447]
P3 = [392536090, 107146475356675]
P4 = [435448162, 104606127424147]
P5 = [686748970, 88905865222435]
P6 = [896843530, 74565188888035]

High rank curves with prescribed torsion Andrej Dujella home page