curve #4345

y² + xy = x³ − 579289723524480910x + 636279381142291023669700100

a-invariants: [1, 0, 0, -579289723524480910, 636279381142291023669700100]
c-invariants: [27805906729175083681, -549745385348648304544383511921]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 3288058890510109170
discriminant (Δ): -162454478548854530158210764508514528236222869789081600000
Faltings height: 9.4688
naive height: 136.9585
primes of bad reduction: 2, 3, 5, 7, 13, 19, 29, 131, 10601, 1574009
regulator: 10862.745858808895499405039786653284418238656523323
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:39 UTC
last updated: 2026-10-17 10:05:39 UTC

(39563517020/121, -29216345715646010/1331)
(249151179380/529, -263192753603120570/12167)
(8271772820, -749549086034110)
(400666640, 21644610473390)
(-465513220, -28373496292510)
(37196287502, -7172363115874234)

BASE torsion/torsion_Z5.tsv.gz:2084 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:39 UTC · history