curve #4468

y² + y = x³ − 190719817x + 1221345067746

a-invariants: [0, 0, 1, -190719817, 1221345067746]
c-invariants: [9154551216, -1055242138532760]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 200423269507421539440359243
discriminant (Δ): -200423269507421539440359243
Faltings height: 3.7638
naive height: 69.1851
primes of bad reduction: 2179, 91979472008913051601817
regulator: 158496530.78897596828224581122158933494917097347507718511166754
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:19 UTC
last updated: 2026-10-17 10:30:19 UTC

(-15980, 434037)
(-1782, 1247216)
(-1752, 1245033)
(-118, 1115279)
(5419, 589038)
(8623, 466841)
(9134, 491283)
(9278, 500508)
(10094, 569811)
(12145, 834537)
(25270, 3540987)
(47686, 10028084)

BASE records/rank_12.md#14 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:19 UTC · history