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]
Dujella - Peral (2019)
y2 = x3 - x2 - 656714316746649317774273479510020774526130225263360x
+ 6475018218706997636015243652052679904565591870426948879010401905535258556992
Torsion points:
O, [-29589560787165744408593336, 0],
[15035063692246796967172289, 0],
[14554497094918947441421048, 0],
[10404177822015881468446914, 27724823774782948423741898039663367250],
[10404177822015881468446914, -27724823774782948423741898039663367250],
[19665949562477712465897664, 34145353544600919806994289632981039000],
[19665949562477712465897664, -34145353544600919806994289632981039000]
Independent points of infinite order:
P1 = [12137215183123068824737914, 17096566712239562248011297585941168750]
P2 = [7683864618066291085724234, 43388746531700403433406876494660929330]
P3 = [891503040010757711776264, 76748055060815843470057221702359781600]
P4 = [12946734610308762639319864, 11950614719234625287122929822226327200]
P5 = [5205271989184424113048217344/361, 13144286264614942637957828329740789208440/6859]
P6 = [4699813148311284064914055884424/81, 10188748577926888075268854701476234019078407840/729]
P7 = [-74268018859351637397838568389399/3052009, 478268847608576057381175545651151900523272459000/5331859723]
P8 = [224597167732758338447836106176/12769, 27592891590693854094813442257117456914444520/1442897]
Dujella - Peral (2019)
y2 + xy = x3 - 26063688229376963590087835932610x
+ 50137806027135463507471054481447125468330844100
Torsion points:
O, [10364608439711455/4, -10364608439711455/8],
[-5881220642891484, 2940610321445742],
[3290068532963620, -1645034266481810],
[5821859327127940, -309394649913032351386130],
[5821859327127940, 309394644091173024258190],
[758277738799300, -175528601682103622504210],
[758277738799300, 175528600923825883704910]
Independent points of infinite order:
P1 = [1481665335755740, 121543778319648659823190]
P2 = [1590633017588260, 112714350004850071796590]
P3 = [-937585297049084, -271570501176183017692178]
P4 = [1432584187704766, 125457032879934936033442]
P5 = [2407660419575260, 36634552150980951701590]
P6 = [2523242437805380, 20920363161016029015790]
P7 = [-211328498033180, -235873627583674686622610]
P8 = [-1551632189314490, -294692062672567991257160]
Dujella - Peral (2019)
y2 + xy = x3 - 2864261851997523184312777154989269631330629270x
+ 33127964857714555574072691338532131936542179415959379009782924708900
Torsion points:
O, [46365580824843543956940, -23182790412421771978470],
[-58565505656997034603060, 29282752828498517301530],
[106240779393848513944140, -30462718116469458537952503770074470],
[106240779393848513944140, 30462718116363217758558655256130330],
[48799699328613962584479/4, -48799699328613962584479/8],
[-13509617744161426030260, 8328109650376665784098979750952730],
[-13509617744161426030260, -8328109650363156166354818324922470]
Independent points of infinite order:
P1 = [-8690427864727011588660, -7573855954685394281812001452080870]
P2 = [65364652281144471636349740/841, 408117674246055925205397819242683591170/24389]
P3 = [544269582980331124917260/49, 561879167198394639594973129467986390/343]
P4 = [9844373488568157203641363860/134689, 723503421334934991277993088321603837634990/49430863]
P5 = [5872401332024951965189260/529, 19992144040666274504739659849577315510/12167]
P6 = [8038085799029297189883888300/896809, 2428351943367289076412681562780338068105310/849278123]
P7 = [-1405869572792037847308275425940/34539129, -1841217397729661451651332200127816960965976110/202986461133]
P8 = [59060033040840795238975616497121640/49343069689, 14338712439662575811101365073405444199815871427961170/10960724099226637]
Dujella - Peral (2019)
y2 + xy + y = x3 + x2 - 1239682737774369346053097395785098403410x
+ 11149795415761842323945322718716176770048592941471370462687
Torsion points:
O, [-156214347352089111757/4, 156214347352089111753/8],
[29314323959865617817, -14657161979932808909],
[9739262878156660121, -4869631439078330061],
[65897189209835923577, 464341197647694720930299767251],
[65897189209835923577, -464341197713591910140135690829],
[-7268541290104687943, -140628842143503449574490023789],
[-7268541290104687943, 140628842150771990864594711731]
Independent points of infinite order:
P1 = [9490356704879897497, 15476781335539125467540862771]
P2 = [-23481794662076654695, -165263529672877633490024413389]
P3 = [-30794401910432940283, -141855210335722697488633112109]
P4 = [90412703551515621017, 798837581495912850215092803891]
P5 = [8173867954285501992707/196, 490710472031697559498212024858279/2744]
P6 = [2972098845908648549224481/15625, 5039509916958180631287463706624963871/1953125]
P7 = [-15185674629676486125102077/514089, -54665594742100262442576717087145589357/368601813]
P8 = [1718001284435863459635795557/20079361, 65591989920976180607534548011106034404551/89975616641]
Dujella - Peral (2019)
y2 + xy + y = x3 + x2 - 480426083867972513443731935354799475432800841130x
+ 75469536192704935204061526581527440549482746439665617973818818782952375
Torsion points:
O, [666950271523705736304051/4, -666950271523705736304055/8],
[594550843641477797694793, -297275421820738898847397],
[-761288411522404231770807, 380644205761202115885403],
[1356158375876031283601673, 1384967664200001917316095380606650523],
[1356158375876031283601673, -1384967664201358075691971411890252197],
[-167056688593075688212087, 388671737206066587703560194791533083],
[-167056688593075688212087, -388671737205899531014967119103320997]
Independent points of infinite order:
P1 = [24846143295170286879853143513/6241, 3858976459841994019754227043405973319969717/493039]
P2 = [352205188551819385154209657/49, 6579751718711289520423461090720510075629/343]
P3 = [-774214227808346764303763103/1369, -20655834462920196137953767730371940701041/50653]
P4 = [-3329878523534015452513146047/5041, -115750924228408894710287291545648616181107/357911]
P5 = [648425372549500916287024435495073/1061521561, 3446310856928514958437408247620393408474569999023/34585433978941]
P6 = [10997708278781250231441452891217/247009, 36467067966973366158245174554573880365222092419/122763473]
P7 = [471697883944130121119448855773937/755535169, 2853270532009682547948924897424052673830390653069/20767395190303]
P8 = [259604736532074739052213014793/1560001, 22116250137042240955261695151264181040857147/1948441249]
Dujella - Peral (2019)
y2 + xy + y = x3 + x2 - 43104494813773870952598590167526238603734x
+ 3444236771723137524126232072555163438633628706759427431498451
Torsion points:
O, [120792979052397642145, -60396489526198821073],
[118939192847692235169, -59469596423846117585],
[-958928687600359509261/4, 958928687600359509257/8],
[146645184979263066593, 526067521659892666819437483055],
[146645184979263066593, -526067521806537851798700549649],
[94940773125532217697, 455669991079263393945511453807],
[94940773125532217697, -455669991174204167071043671505]
Independent points of infinite order:
P1 = [78838218231977879969, 732100649885382531590529623855]
P2 = [-105805045895465540967, -2611599750655829716994367660905]
P3 = [146970678108897651969, 532693596942333821370958548655]
P4 = [82165545806876958369, 676200092316771454676549612335]
P5 = [94140986762262241641, 469748849181387635002979248519]
P6 = [143932741416993755169, 471052648569246677665455911215]
P7 = [121892868265423785403, 34275602874909052136049934931]
P8 = [1000317258402458082184121/8281, 1185407553817727004511487995513069/753571]
Dujella - Peral (2019)
y2 + xy = x3 - 10699238570566300322465089876084112731704600x
+ 8906264749635532407888593409743046197407929103665973862298600000
Torsion points:
O, [2726236843322023806000, -1363118421661011903000],
[900719707744771294256, -450359853872385647128],
[-14507826204267180401025/4, 14507826204267180401025/8],
[6131800439423702628720, 416953343185606815410702363349480],
[6131800439423702628720, -416953343191738615850126065978200],
[-679326752779655016720, 125940639784280266723237248730920],
[-679326752779655016720, -125940639783600939970457593714200]
Independent points of infinite order:
P1 = [890826476048176369200, 9057291912391511050183594804200]
P2 = [-13276003132402017600, -95122581622272423447355755442200]
P3 = [17904158929076606023073550/289, 75654168666498276700064182726935177300/4913]
P4 = [5109704134103229297678833712/167281, 363210022269692952051829616054815260018984/68417929]
P5 = [2572400851622008384378344/25, 4123729751502003869211388364238905712/125]
P6 = [376229576985978645234293424/442225, 6023330795604082728830932504789277550888/294079625]
P7 = [-781785023546450248230048240/37834801, -22233569385967543461303256153390269956018760/232721860951]
P8 = [386967740799732804971200/441, 128840794913777155394384298424660600/9261]
Klagsbrun (2020)
y2 = x3 + x2 - 8665851076482178429252004x
+ 9394159653904223016884439949397508576
Torsion points:
O, [1980591661228, 0],
[-3382740935541, 0],
[1402149274312, 0],
[3741948782626, -5418711263910784518],
[3741948782626, 5418711263910784518],
[219234539830, 2739496855695315534],
[219234539830, -2739496855695315534]
Independent points of infinite order:
P1 = [-888210146138, 4048522222598440290]
P2 = [1377082663096, 268339815196759512]
P3 = [1232801012476, 764525081785096632]
P4 = [-1172604283622, 4235970008434474590]
P5 = [-387325528466, 3562661647340056170]
P6 = [3694116400735, 5271929598002127606]
P7 = [26091464591596, 132459174466109758512]
P8 = [614639905276, 2073639745189571832]
Dujella - Peral (2020)
y2 + xy = x3 - 39466246565290947729079823487881122376900x
+ 2326640027674305327779055836964540142971116940216857824650000
Torsion points:
O, [265422646824780529599/4, -265422646824780529599/8],
[156990360979660546600, -78495180489830273300],
[342655849846820311180, -5388465629622220293409254804500],
[342655849846820311180, 5388465629279564443562434493320],
[-28675127887499217980, 1853310875085401094343869694480],
[-28675127887499217980, -1853310875056725966456370476500],
[-223346022685855679000, 111673011342927839500]
Independent points of infinite order:
P1 = [45591067659364687852, 788729875481863741848591814696]
P2 = [27919767943014231520, 1116474548015895551707556378500]
P3 = [49135308823317696000, 711393096560861957030507734500]
P4 = [63076298644070950122142570/97969, 478802044819849411904131580032308182590/30664297]
P5 = [-299897661459733247102152313/2540836, -9359616815348899127191116207467883582671/4050092584]
P6 = [33970371269254987670437923493480/127221335761, 149307847709594321938590067656963761984601795500/45377433260569241]
P7 = [8367250620870577444386079396480/17552805169, 22285395002256857625827661731588451476680373500/2325518498425303]
P8 = [-37112649644620237192777128177284/497421288961, -773073906264025697097867332074168574078590423828/350821784099703041]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 3513468140056336833205231504269852961111935719610x
+ 2534629249354615055221589817535180260358954874997525656769738230503638087
Torsion points:
O, [-8657513563423687121038157/4, 8657513563423687121038153/8],
[1073956580212559980256617, -536978290106279990128309],
[1090421810643361800002921, -545210905321680900001461],
[858924434148711436328617, 387940888736765643437633857627879691],
[858924434148711436328617, -387940888737624567871782569064208309],
[1321919187138012163677225, 447350946660537238555954422932650571],
[1321919187138012163677225, -447350946661859157743092435096327797]
Independent points of infinite order:
P1 = [851745323891969388743617, 399956188809149701101713583436684691]
P2 = [-954532231889735751593183, -2240232840935625486976159723597356109]
P3 = [567484208757545674071817, 850613441696032966272789083250869291]
P4 = [951523510768597282800617, 230191732668614222615812829204159691]
P5 = [1069338012703900611862257, 17745123880039459724679264426858531]
P6 = [1058610915983070727173327, 39665252181619646436941246428555071]
P7 = [1069759339054469818928317, 16747591206766766493449899571402891]
P8 = [27597970301953768460694930357/26896, 437133279700655571247435021318497963238279/4410944]
Voznyy (2021)
y2 + xy = x3 - 24326306716406210217701027657020083359447088224x
+ 1440413667675402568618356272782004730157552823721267651264107094549504
Torsion points:
O, [81311732138569922615488, -40655866069284961307744],
[-719293684481171260229121/4, 719293684481171260229121/8],
[98511688981722892441792, -49255844490861446220896],
[167702381142510678347200, -45577524499200936493884466597790048],
[167702381142510678347200, 45577524499033234112741955919442848],
[29320996820935106536384, 27428998855619839285696957029771424],
[29320996820935106536384, -27428998855649160282517892136307808]
Independent points of infinite order:
P1 = [80464129672253195699392, 1995409534995558008101271589652384]
P2 = [147134143361484875157092653350/966289, 33805975640998978158783093915581413911392226/949862087]
P3 = [13678966112637618586588611360/5041, 1597265219743897656134631894902393088083808/357911]
P4 = [1004657359938085071666969770230/10106041, 68514947005902489760707590367645789074257898/32127104339]
P5 = [-41343546400498479772309682447936/333975625, -308494833127431562741536183586494696723233569312/6103404546875]
P6 = [2525369021223952109692148630920/60949249, 10678252122211116456829410821731092896189219176/475830786943]
P7 = [-35520498024091854923140486412480/637714009, -824713291909984201156708738939943000226475392736/16104191869277]
P8 = [8822854375530426476877222771625606166147910343360/133754428415492071314363289,
17141252792141835318015475422234559064163497673006590102984306738076618016/1546900054253178578291022076038285019837]
Voznyy (2021)
y2 + xy = x3 - 244086541734265235806414620264027878839495000682270x
+ 1218006870777529664070689743626094196017097935641565601671574112133491528900
Torsion points:
O, [-17690083752500523118977060, 8845041876250261559488530],
[23127987711084867283976479/4, -23127987711084867283976479/8],
[11908086824729306297982940, -5954043412364653148991470],
[25373637453708792684131740, -106586754392078736005063609883775916270],
[25373637453708792684131740, 106586754392053362367609901091091784530],
[-1557463804250180088165860, -39929749495887379317404824455625426670],
[-1557463804250180088165860, 39929749495888936781209074635713592530]
Independent points of infinite order:
P1 = [-10316402270102350473838140, -51362886951013582607376736896523142670]
P2 = [268254575039428800160039900, 4386283003949085251859880494363263306770]
P3 = [36795565677208508464020734940, 7058187428706895982423764124385297117376530]
P4 = [355509491732669378770756466420440/10201, 6703116338328831624367221267483556868888154860030/1030301]
P5 = [463758307177938817048266460/169, 52400417154858719875776887286692852379610/2197]
P6 = [-74796317552798864794056466668740/29452329, -6821729099734998657427692458221194485116027030010/159837789483]
P7 = [284491194072801615376501650848860/21687649, 1669876316209758519257709795747310867976361674290/100999381393]
P8 = [705976594964130515934421218001132691229052540/16933571542382999449,
17560271746776600792830965946974364123486877328584498061340801643190/69682359918802977853592799043]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 1696699016246922652836208679383316438330x
+ 26885742899232678127729600383318662389671931858722092489927
Torsion points:
O, [93320933132418632883/4, -93320933132418632887/8],
[24230205859629623401, -12115102929814811701],
[-47560439142734281623, 23780219571367140811],
[32268216294629478425, 75730958295618412223596685323],
[32268216294629478425, -75730958327886628518226163749],
[16192195424629768377, -60480138176948108436655109189],
[16192195424629768377, 60480138160755913012025340811]
Independent points of infinite order:
P1 = [-476426781091357263, -166415106313740499420672258709]
P2 = [8718772717538193897, 112939739379622769109089712331]
P3 = [21677611654354758377, 17090313205621860660367860811]
P4 = [-4589417907493240373, -185946061948762429417836292939]
P5 = [20900928322466447517, 23530914368312831661585537931]
P6 = [2596662837734392377, 149991653186809993388108604811]
P7 = [21950209508921318377, 14788905380859980609376340811]
P8 = [1217007286799103922455/4, 42085627674665006424733237796963/8]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 586359283244100670505525384240022514375765159720x
+ 172819191908793252058129879393088252545259814730032067335477586877666345
Torsion points:
O, [1765420998676131227046611/4, -1765420998676131227046615/8],
[442845879599418444619173, -221422939799709222309587],
[-884201129268451251380827, 442100564634225625690413],
[487322120340371153307173, 52952697976625187934928992434442413],
[487322120340371153307173, -52952697977112510055269363587749587],
[398369638858465735931173, -49518360361903440229077842120869587],
[398369638858465735931173, 49518360361505070590219376384938413]
Independent points of infinite order:
P1 = [388425647331190424139173, 60545244793306918827921120064090413]
P2 = [286484095744506578137923, 168372299795239188017771555121984163]
P3 = [636168592084437985419173, 239290465625759604105399880076890413]
P4 = [18847152601869821357734309, 81755219808274080012332022488417260845]
P5 = [438208215532747626140773, 4393223773686296225180527380616813]
P6 = [418234657316413031179173, 27223516947563905505198034228890413]
P7 = [158831685463971954627649253/361, 15695008882711909467400688945044861767/6859]
P8 = [271854157420754658737706143412505485/564979225801, 19386263996965465409696703481758352647335453453013919/424667200052547451]
Voznyy (2021)
y2 + xy + y = x3 + x2 - 1839926530538856584164329942171450x
+ 29873101006545500680178813099094522047280615853767
Torsion points:
O, [-197754322966598477/4, 197754322966598473/8],
[22112265010879081, -11056132505439541],
[27326315730770537, -13663157865385269],
[7319915162092137, 4098439263819854191088331],
[7319915162092137, -4098439271139769353180469],
[47332716299448937, 6987698953255350181821131],
[47332716299448937, -6987699000588066481270069]
Independent points of infinite order:
P1 = [74478604039690857, 17492152774691205333938891]
P2 = [19030865410291017, 1322946856454299639383371]
P3 = [30274902252940537, 1385122149841520915844731]
P4 = [21934709591986537, 261392959659972909942731]
P5 = [27970127422757481, 540311127564830747685579]
P6 = [-11536576828500983, -7040179091594253740552629]
P7 = [-7032549128278607/9, -151080217417016534407570583/27]
P8 = [27003268326679874557/961, 17843511340482205241180959721/29791]
AttarBashi - Voznyy (2021)
y2 + xy = x3 - 177659495856188795826562585450790806558122070x
+ 911444640108767095519152285975691560683509590941137664365917380900
Torsion points:
O, [30756003222602703877535/4, -30756003222602703877535/8],
[-15390882771957941663924, 7695441385978970831962],
[7701881966307265694540, -3850940983153632847270],
[8247282381230489154140, 84838163949908689094150389534730],
[8247282381230489154140, -84838163958155971475380878688870],
[7156481551384042234940, -80923243360178966569202340439270],
[7156481551384042234940, 80923243353022485017818298204330]
Independent points of infinite order:
P1 = [7546745848284659910476, 22499062555795447211018744548442]
P2 = [6243392766308117282060, 213573844062346788811163043453530]
P3 = [12428087891726592515012, 789358324106886749965235179711226]
P4 = [-15082235743844392229524, -400166256968012032438935602734918]
P5 = [-120433554835435627060, -965835937386657520314985911679270]
P6 = [2652141200700190941774740/361, 360680184631465899266208714755135870/6859]
P7 = [986860702996807194561970382/128881, 265161125370520921540741654624113712498/46268279]
P8 = [-1098584332944644966796640/169, -2940725134562681936964222971039278690/2197]
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]
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 + x2 - 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]
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