curve #4342

y² + xy = x³ − 137122640473570747595x + 618033296161044458569780563537

a-invariants: [1, 0, 0, -137122640473570747595, 618033296161044458569780563537]
c-invariants: [6581886742731395884561, -533980767893015242318387500722809]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 49929225145586332590
discriminant (Δ): -6191259139898331909348140654099893024449747475341900000
Faltings height: 10.0403
naive height: 150.7158
primes of bad reduction: 2, 3, 5, 11, 19, 31, 43, 71, 14951, 5627669
regulator: 34724.557653622708988039162119398685534027147147528
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:34 UTC
last updated: 2026-10-17 10:05:34 UTC

(6890476564, 18532999191793)
(27148189711/4, 29982295413329/8)
(7133115114, 53513811501093)
(371713248064, 226515910332832393)
(251782843567036/37249, 1500585175627702051/7189057)
(36053040308536/5329, 262796560402946071/389017)

BASE torsion/torsion_Z5.tsv.gz:2102 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:34 UTC · history