curve #4404

y² + xy = x³ − x² − 25949190094x + 1608685635288664

a-invariants: [1, -1, 0, -25949190094, 1608685635288664]
c-invariants: [1245561124521, -1389898783864345365]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 165782089380280872920512734806
discriminant (Δ): 331564178760561745841025469612
Faltings height: 4.6708
naive height: 83.5518
primes of bad reduction: 2, 82891044690140436460256367403
regulator: 477082448584.5023698442136980744238392598814349325820167190001854
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:22:16 UTC
last updated: 2026-10-17 10:22:16 UTC

(-120149, 54759245)
(-100654, 56626110)
(-1434, 40570334)
(-308, 40208088)
(15758, 34686372)
(132103/4, 224397919/8)
(69578, 11798350)
(103747, 5710205)
(124943, 17740860)
(133006, 22521764)
(1376179/4, 1460773185/8)
(20177011/196, 14458679971/2744)
(1686891884/13225, 29316901631272/1520875)

BASE records/rank_13.md#38 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:22:16 UTC · history