curve #4467

y² + y = x³ − 708531019x + 7237725024300

a-invariants: [0, 0, 1, -708531019, 7237725024300]
c-invariants: [34009488912, -6253394420995416]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 134244761086677411732182149
discriminant (Δ): 134244761086677411732182149
Faltings height: 3.8771
naive height: 72.7497
primes of bad reduction: 24439, 5493054588431499313891
regulator: 3636611826.9427570484527069804476225040696665996139819512207127
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:16 UTC
last updated: 2026-10-17 10:30:16 UTC

(-2945, 3049394)
(-2028, 2943855)
(-64, 2698716)
(8569/4, 19149439/8)
(2367, 2360909)
(4033, 2108510)
(64753/4, 805237/8)
(17358, 411110)
(17771, 508578)
(21405, 1370705)
(90313/4, 13267015/8)
(363704/25, 11861983/125)

BASE records/rank_12.md#36 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:16 UTC · history