curve #1850

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y² + xy = x³ − 216202252224465267823290017974015335x + 37932309716061316952299289621231919867576178486689225

a-invariants: [1, 0, 0, -216202252224465267823290017974015335, 37932309716061316952299289621231919867576178486689225]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 4259286975258245779727908683651134093360721419194605595172673543934354879950690
discriminant (Δ): 25198434689487938751754051542246659382515773296189395645802873563541829056898049959016965220900812800000000
Faltings height: 19.2035
naive height: 255.6982
primes of bad reduction: 2, 3, 5, 7, 19, 29, 41, 47, 71, 139, 21727, 1254737945271752553372201020672235947264362080365986453601509
regulator: 2303817202789960272727.876975407768894405085132659049579836882950611369981368135463
submitted by: Ritik Jain
submitted at: 2026-09-25 17:11:21 UTC
last updated: 2026-09-25 17:11:21 UTC

Witness: 22 independent points log in to add more points →

(5014379691372129248174905702626378641159030/13210032139352953744327489, 4933498838325862122918040551049146773300528053601025340404740005/48012664854052005566156205409850112737)
(34569628568366685934/225, 308241173524670094654319863643/3375)
(604615240782797382, -358100589644419706545467243)
(3057061777940299780/9, -1639017098374707404520881945/27)
(-12276489233525514586/25, 20033813340902262752546042353/125)
(141929083609849397040/49, 1670265652212904942424720305275/343)
(-831604607264559583938/1681, -10636252660826402799432066359739/68921)
(-118453941691771668024/361, -1860111236636606507406342838887/6859)
(9699909120559571802630/1369, 953317517497684404852804625155345/50653)
(447450744084956502, -175435272625972026808245243)
(-371724012838328430, -258719002085483575954830435)
(8094120798708033270, -22990706859196954882097656635)
(309324203542113270, 25540409925537591001303365)
(-229942081266852570, 274751697026237993527558005)
(379438412522923438062/5041, 53189381522280260822721453274971/357911)
(-91304699270588955176700/534361, 103263292553411331698833358608572165/390617891)
(-21130865749457239902702527370/772902964201, 142245102338033021393157409636111058688531945/679496868074344949)
(319696912626117378870/2209, 10211557342193697755183500681995/103823)
(-442002043867278090, 217122226600945260352006725)
(-533097467293751850, 41068996490723176699029285)
(665014474086611297618130/4190209, 748594092397186398955934475277063395/8577357823)
(249913306837129828974630/1471369, 139512112714194639013694870186518905/1784770597)

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