curve #4466

y² + y = x³ − 1726817617x + 57975709345266

a-invariants: [0, 0, 1, -1726817617, 57975709345266]
c-invariants: [82887245616, -50091012874310040]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 1122482466080847283271138480843
discriminant (Δ): -1122482466080847283271138480843
Faltings height: 4.4556
naive height: 76.9052
primes of bad reduction: 1122482466080847283271138480843
regulator: 2903942132.452011171806205637446490201779203177694613377858737813
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:13 UTC
last updated: 2026-10-17 10:30:13 UTC

(401, 7568574)
(52318, 10527843)
(-29122, 9141443)
(-33509, 8843865)
(893, 7512281)
(30523, 5805593)
(-47872, 5561681)
(-226151/9, 249660170/27)
(-207703/4, 22105873/8)
(-104487/4, 73868697/8)
(35904, 6500753)
(27267, 5582409)
(44289/4, -50731203/8)

BASE records/rank_13.md#18 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:13 UTC · history