curve #4667

y² + xy + y = x³ − 477234662647080413x + 126224192527459909865193692

a-invariants: [1, 0, 1, -477234662647080413, 126224192527459909865193692]
c-invariants: [22907263807059859801, -109057702378086257834117139805]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ
conductor (N): 1470210055845288515574478669853106
discriminant (Δ): 73401514113166081736403828843295111016448829604990892
Faltings height: 8.9827
naive height: 133.7340
primes of bad reduction: 2, 3, 19, 43, 53, 71, 101, 109, 193, 227, 331, 997, 3391, 4339, 34033
regulator: 348143192461223825.44240660935341736423284453928444120018392874
submitted by: jesper-petersen
submitted at: 2026-10-20 19:15:44 UTC
last updated: 2026-10-20 19:15:44 UTC

(20282245085170434/6385729, -2825209285060273226461730/16136737183)
(18680932500583719/26399044, -1621276227045591976453399/135638288072)
(75084433036078656/124567921, -10548421587080540303352212/1390302566281)
(81735171707684496/189310081, -2116714738432816091908028/2604717404479)
(18949382884568658/34586161, 1099426173353888683230466/203401212841)
(18728802483527658/22934521, 1841372903569794097363135/109833421069)
(251801017350650832/526381249, -32848647879887046607824403/12076764995807)
(211924158477359232/475981489, -14701250251378379169160085/10384488145513)
(171874387666447264632/13212812809, 2250163283725070068943683585820/1518773193956123)
(28607008971024287309874/47828939727409, -2447654742351305159361175120093346/330777629326982350423)
(836085360919988080663964455444889336472/1112011311665250120888291465289, -16267651853237363687787900583131527939174942605377607060543/1172637578513600408734059306832514145158262587)
(123274468933965116456410370874/18821500026731325625, -43050853670696701013580766798678142292875743/81654730354383022159473921875)

2-isogenous to ICARM curve #4582

last edited by jesper-petersen at 2026-10-20 19:15:44 UTC · history