curve #633

y² + xy = x³ − 481805499201840655499181572455161540354946707875943545595x + 3787996708319455803688125189783802656028376487166414974768271061303274667935154635537

a-invariants: [1, 0, 0, -481805499201840655499181572455161540354946707875943545595, 3787996708319455803688125189783802656028376487166414974768271061303274667935154635537]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 23727944441030864096387213834241233762298678396410694856785493478043111120631688163839202091071874835260952486380923333121424867763048615510
discriminant (Δ): 959325274574349035172855059523013726376419182426964249365279253580507069051245828224353946745544229122092494235923478613464653556024357401055854920726612835722027520000000
Faltings height: 31.5527
naive height: 403.1650
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 61, 2326213, 1090103210268297832166736343, 1187649827402758944777770290888217788786197111743684246462657964572153633268054931909852799285383
regulator: 28246253120457840564234056558843820.24889934408825780257282227338593219387293734215533893057523
submitted by: 7fff-zip
submitted at: 2026-09-07 23:04:27 UTC
last updated: 2026-09-07 23:04:27 UTC

Witness: 28 independent points log in to add more points →

(-5030557969202041568769805986, -2466666033103699497813579954570405824753007)
(-13330385101524796871693565186, -2800330557091905653059249778085715879958607)
(18874756543359950688711518514, -1190919258038873007063041426319583913226507)
(9838925072495701984741702014, 445828088305126381716874722595898130993)
(15897005849758023435243785742, -382283197766764490017955850041643597037647)
(9732959892835515496571821662, -143566521564562084134460411529288540532975)
(4536451925083593407969608014, -1302177662556781778426522289726257771387007)
(16890495640267696615369883934, 684640769353872041627548763311014584628753)
(9057244713477080063570435214, 408858812498608043244029071208154267926193)
(5819217226160826649751154137454/361, 3143639339040798582596238035413638506005090587/6859)
(2001800416460434509568733154, 1682718004841167114744476248589040004698533)
(37573181763369772614130398790138014/4879681, 7881736215612645347407958099012740895441289683504817/10779215329)
(4050223562605207769311149382014, -8151023183145666494018301927963158303806553007)
(-39440331810460955485439467874/9, -65109958261754785928968978826669066801927189/27)
(-18031611030983056288197333666, 2571564922166951024440952365137010267693713)
(-81841104665081238368795543217/4, -18032379979177667818711137227937674709986055/8)
(36905830779936147891064447134, 6022773031960963795545324546427503737802513)
(49193227880102142623072448414, 9956542832134583177033871686802245726445393)
(43006132871869880890693007688294/7921, -813663434148816056982378180583280577243248733183/704969)
(9375122786089247615842991514, -308249865087690935808627603779269218993507)
(1770964456826009268065506216083204/961, -74521929245407280088228461571789921412260441731787/29791)
(33682545878898396232395394166092608/1885129, 2432838615897071755321301647959549427733904238923405/2588282117)
(374481703627065402516390494, -1899374075895069961302458176327591473577327)
(-18192074787876289776790301736, 2555844751922171030806993002377658088431993)
(566822251975266643947464288604/361, -11949951490288362022664146341415274867370657663/6859)
(16171390079703578401028073814206/289, -60578252746152846129584957057086020018125625471/4913)
(-22442295740975853487199583786, -1815931437670275263503209691625348076387807)
(1279901758816134995231552705610850566/5640625, 1441432899684029337412961710357192965739495716170264511/13396484375)

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