curve #761

y² + y = x³ − 2558717707x + 49801921968156

a-invariants: [0, 0, 1, -2558717707, 49801921968156]
rank (lower bound): ≥ 12
torsion subgroup: trivial
conductor (N): 21585663145423055401656667
discriminant (Δ): 669155557508114717451356677
Faltings height: 4.1161
naive height: 76.6019
primes of bad reduction: 31, 22189, 89603, 350221997637971
regulator: 54892198.915186246329205835386852432770511273522687001023143683
submitted by: Michael Rubinstein
submitted at: 2026-09-18 11:17:12 UTC
last updated: 2026-09-18 11:17:12 UTC

(29633, 24753)
(33694, 1356761)
(-1212, 7273328)
(29776, -115101)
(22286, 1961385)
(30997, 521249)
(42281, -4147506)
(28776, 21524)
(5050, 6083517)
(66616, 13227684)
(-19099, 9576225)
(48822, 6422750)

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

last edited by Michael Rubinstein at 2026-09-18 11:17:12 UTC · history