curve #789

y² = x³ − 1809511249x + 29321959247689

a-invariants: [0, 0, 0, -1809511249, 29321959247689]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 47391988372227480049579076
discriminant (Δ): 7772286093045306728130968464
Faltings height: 4.1634
naive height: 75.5626
primes of bad reduction: 2, 41, 2293, 126025093264302490213
regulator: 56390393.558195852515196441279263960706219981251266119014890905
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:40:24 UTC
last updated: 2026-09-18 12:40:24 UTC

(22368, -195283)
(37005, 3610337)
(22163, -322793)
(-38025, -6568733)
(-44339, 4731359)
(-10527/4, 46692809/8)
(32331, 2148031)
(-36385, -6855077)
(30445, -1565503)
(26632, 141983)
(21097, -732547)
(49961, -7976509)

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

last edited by Michael Rubinstein at 2026-09-18 12:40:24 UTC · history