curve #4400

y² + y = x³ − 6703514287x + 209526656923296

a-invariants: [0, 0, 1, -6703514287, 209526656923296]
c-invariants: [321768685776, -181031031581727960]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 313723684682894471293495831717
discriminant (Δ): 313723684682894471293495831717
Faltings height: 4.4807
naive height: 79.4913
primes of bad reduction: 3048973844159, 102894842894078363
regulator: 15536996839.05587013817839165149161319282431759622667729989991908
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:05 UTC
last updated: 2026-10-17 10:22:05 UTC

(-12776, 17119736)
(26713, 7036878)
(40823, 1975178)
(41468, 1689228)
(42512, 1173680)
(50836, 349604)
(53094, 1811301)
(53770, 2130542)
(75783, 11693621)
(82753, 14882478)
(218196, 95577444)
(-1076701/25, 2556697218/125)
(16501489/324, 2752651765/5832)

BASE records/rank_13.md#37 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:05 UTC · history