curve #386

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y² + xy = x³ − 1959597671778012400793716956575363x + 31215574828451091811944359784635933468091823313217

a-invariants: [1, 0, 0, -1959597671778012400793716956575363, 31215574828451091811944359784635933468091823313217]
c-invariants: [94060688245344595238098413915617425, -26970256651781743466610959221942339373578956216045625]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 25246684796811036252777646363342404565866601836392096658908773540967371070389350
discriminant (Δ): 60647580435148424172780206611022636141024640438942596472220122798620409181838326420560229945344000000
Faltings height: 18.0847
naive height: 241.5877
primes of bad reduction: 2, 3, 5, 17, 19, 37, 10453, 1347311144368061238779164520703467246930066740304199494519539164790843
regulator: 115647624484908285478219.613705515294016893615729801007725245168775310971978950
submitted by: y011d4
submitted at: 2026-08-27 04:15:47 UTC
last updated: 2026-08-27 04:15:47 UTC

Witness: 20 independent points log in to add more points →

(12759174177114381969466138324/49941969529, -1420801005011344398061128117976877290384313/11160881524432333)
(143343498034928136001042/373321, 53924079351692132727071808413291819/228099131)
(123994884515558633644878163/17960824324, 10216962109355402040889558157706109396883/2407073754253832)
(94937909808324002302/8281, 2413372543136659406781368028859/753571)
(2345667548301553850478/9409, -111916489022228080511974870044183/912673)
(307719165880242137494384702/369062521, -5390519197741863696707211599835231252661/7090060090931)
(15753291881802493657451053/82664464, -60959982644478171047396199387405673813/751585306688)
(244374131139084111773278/1408969, -117176627974870982392399424635382893/1672446203)
(811926181919147290474798/734449, 731023567996961116732324085747132657/629422793)
(2478384721070530500901918/1324801, 3900609730641407055183651770314252055/1524845951)
(5036985323030537969307742/1042441, 11304148697104087372754721598687663309/1064332261)
(923735826437352448/49, -338411313813498947931618743/343)
(1270839969037045926507502078/77803618489, -40978720401020249725019644017210666006187/21701996715992237)
(1982396018821593257498932/33028009, -2162784790213061871051978742168924189/189811967723)
(36502550152514542, -2884888329748180938898871)
(-3871900526628038, -6224539824336630274311131)
(79416890594372206, 19402992668734623168854089)
(8148520772514538895795038/634384969, 45654899402384548776771304668592289747/15978254214203)
(-219015393039764732/9, -216827642038748047650974527/27)
(7351872307346926, 4148039516897531738485705)

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