curve #4463

y² + y = x³ − 3491340307x + 85062365501016

a-invariants: [0, 0, 1, -3491340307, 85062365501016]
c-invariants: [167584334736, -73493883792878040]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 402099048666566052137511629723
discriminant (Δ): -402099048666566052137511629723
Faltings height: 4.4253
naive height: 77.6720
primes of bad reduction: 748271, 114415993, 4696641350652541
regulator: 1867385003.844404283274207829720325380828306495080275683868918230
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:03 UTC
last updated: 2026-10-17 10:30:03 UTC

(32014, 2470146)
(101, 9203789)
(11355, 6847062)
(59037, 9203789)
(41873, -3505342)
(-65278, -5899690)
(45978, 4661966)
(232009, -108460414)
(152658, -55764634)
(-35901, -12811434)
(32266, -2450050)
(-48106, 11903381)
(3021, 8633805)

BASE records/rank_13.md#30 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:03 UTC · history