curve #323

y² + xy = x³ − 488583200914951350174059380727x + 139655693690206399673338390777234389000152361

a-invariants: [1, 0, 0, -488583200914951350174059380727, 139655693690206399673338390777234389000152361]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 2037198008859408091912035089995835254546406429756696377295787020674158
naive height: 216.8187
Faltings height: 16.0148
discriminant (Δ): -961192558763116104494174560156552740369599525184419354704623810269290750248214752575717376
primes of bad reduction: 2, 3, 7, 11, 13, 43, 10651, 34589, 21411695992716464285409174880925569931884440740356999409
regulator: 4486017426613919654.845745329057243944211442663547329289270425143203989125802
submitted by: 7fff-zip
submitted at: 2026-08-24 13:27:24 UTC
last updated: 2026-08-24 13:30:01 UTC

(361954173154156, 3198574418289927497029)
(768647106610966, 14772895880840825027509)
(516168341912806, -4998711991524590583035)
(-697873969199594, 11863430471317787567029)
(162068521736662, -8045412544552045860107)
(299359341640942, -4496792307029478619955)
(362368495172266, -3192409485898613864675)
(231243811702486, 6248144752647965403445)
(416198269627450, 2898704884530300772681)
(-311503315587266, -16174809570285385285211)
(305901456269992, 4338470108878703551963)
(-771805707709916, 7549480282935051779527)
(178511548975342, 7624071350401148479045)
(124129150345510, -8995602528921686483051)
(568311120023614, 6748343874446503006117)
(-169554131427098, 14752035519175297787653)
(7763536944224182, -681376807212388289427755)
(-12640425608276906/25, -2005583603686937952583807/125)
(299244556408996, -4499597230288805186795)

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