curve #4409

y² + xy = x³ − x² − 79922404x + 945333881884

a-invariants: [1, -1, 0, -79922404, 945333881884]
c-invariants: [3836275401, -816751210708485]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 176685196983131610721395454
discriminant (Δ): -353370393966263221442790908
Faltings height: 3.7777
naive height: 68.6727
primes of bad reduction: 2, 2591, 405817, 84018035046416041
regulator: 1148969791.1244749612426545129182136618374691084407099438458414
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:40 UTC
last updated: 2026-10-17 10:22:40 UTC

(-9628, 911598)
(-8582, 1003842)
(-8020, 1038618)
(-3478, 1088580)
(-2261, 1056818)
(-1990, 1048132)
(-1445, 1029218)
(-618, 997550)
(170, 965188)
(251, 961794)
(6414, 831388)
(7490, 871962)

BASE records/rank_12.md#11 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:40 UTC · history