curve #322

y² + xy + y = x³ − x² − 866215048931314001543961797x + 8949093843799245559606590167545608201021

a-invariants: [1, -1, 1, -866215048931314001543961797, 8949093843799245559606590167545608201021]
c-invariants: [41578322348703072074110166241, -7732017081042361061049524740935071989934289]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 629075100185133502304654857112050123902296131370484653081175510
discriminant (Δ): 6999261033381807498715075353191558357314891369639817057660849291454800800012800000
Faltings height: 14.4418
naive height: 197.6921
primes of bad reduction: 2, 3, 5, 7, 23, 37, 41, 61, 229189, 722311, 2834005545627250868066627215215067318560613
regulator: 260186996102572644.1061300963495749986522343224222018987815177082798076075663
submitted by: Andrii Prokhorenkov
submitted at: 2026-08-24 13:27:14 UTC
last updated: 2026-08-24 13:30:05 UTC

(8503317341951, 46885352853607361664)
(26000280171311, -63275822568411297456)
(26662230402911, 69335180753046087744)
(11981625767711, -17044177212649515456)
(342225260480591, 6308192168746725711024)
(10939625677461, -27968374033219071756)
(7093840420511, -56225289775862213856)
(29133780222671, 91875237436143615024)
(-26981968177369, -112595235049536969096)
(20957086216841, 302292708024253524)
(-29055238261849, -97921110431200273416)
(377802281963599/9, 5825927145576584632288/27)
(25855412108831, 61944721748922485664)
(25026486343241, -54272374522331423916)
(10925164643531, 28099300132545395604)
(2852032251759, -80633860743942649216)
(22385640429311, -27859262849915523456)
(20963505824511, 1729637585817078144)
(-29932836172129, -89768039726434562496)

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