curve #1728

y² + xy = x³ − 46516972372758360375x + 125424758308464262026060419241

a-invariants: [1, 0, 0, -46516972372758360375, 125424758308464262026060419241]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 1273798114327323858
discriminant (Δ): -354047152389528622933339511721714955274205756173990240452608
Faltings height: 10.2024
naive height: 147.5262
primes of bad reduction: 2, 3, 7, 13, 23, 31, 41, 189599, 420919
regulator: 7476.6226570438125782404905284687714770019380378702
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:16:57 UTC
last updated: 2026-09-25 06:16:57 UTC

(2456405910, 161188020066549)
(621356694, 311064026888181)
(3079911702, 106638930504309)
(-6316712262, 408924759189513)
(3669906198, 64332494579829)
(334833366, 331491707557941)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:16:57 UTC · history