curve #4471

y² + y = x³ − 220280389x + 937214745522

a-invariants: [0, 0, 1, -220280389, 937214745522]
c-invariants: [10573458672, -809753540131224]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 304624442109032000008541749
discriminant (Δ): 304624442109032000008541749
Faltings height: 3.7910
naive height: 69.2448
primes of bad reduction: 803832833, 378964916090995253
regulator: 186162770.39657213770720468452770607057089665876721534650867680
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:27 UTC
last updated: 2026-10-17 10:30:27 UTC

(-65943/4, 2375953/8)
(-7435, 1471053)
(-1281, 1103309)
(-611, 1035170)
(944, 854465)
(2979, 554469)
(4109, 318525)
(4663, 106946)
(12335, 311213)
(12950, 506291)
(16245, 1282893)
(65617/4, 10546819/8)

BASE records/rank_12.md#16 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:27 UTC · history