curve #4470

y² + y = x³ + x² − 216826410x + 990382874670

a-invariants: [0, 1, 1, -216826410, 990382874670]
c-invariants: [10407667696, -855753249721240]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 228611240971968172580506037
discriminant (Δ): 228611240971968172580506037
Faltings height: 3.7736
naive height: 69.1974
primes of bad reduction: 1361, 24030847, 6989890583646811
regulator: 178054536.58772386987612364116405746454694574938188805229012177
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:24 UTC
last updated: 2026-10-17 10:30:24 UTC

(2241, 718146)
(-16287, 449117)
(-1596, -1154286)
(11400, 15354)
(12579, 503460)
(71777/16, 21031257/64)
(-7063, -1472934)
(11412, -48142)
(11846, 290378)
(4095, -413721)
(4272, 376938)
(12099, -371845)

BASE records/rank_12.md#15 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:24 UTC · history