curve #2759

y² + xy = x³ − 4736527724431320668640x − 112022655984835399921841753072400

a-invariants: [1, 0, 0, -4736527724431320668640, -112022655984835399921841753072400]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 503432816707590
discriminant (Δ): 1379602879710024845473007630677446045448693180547445131448473610000
Faltings height: 11.4225
naive height: 161.3424
primes of bad reduction: 2, 3, 5, 7, 11, 31, 41, 181, 809, 1171
regulator: 76960.23911401689165461460292854485719922639549
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:08 UTC
last updated: 2026-09-26 20:21:08 UTC

Witness: 4 independent points log in to add more points →

(8203405437959679/6724, 741797766799220460490101/551368)
(229023867166948050/508369, -108248303259850912565476620/362467097)
(46609619854678922740470/139519431529, 9831356966986072083777434461736220/52113716623006667)
(601119286570511895/7431076, -118392522405643314481951365/20257113176)

Commentary

2-isogenous to curve#1639 via the rational 2-torsion point x=14289410880. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:21:08 UTC · history