curve #3803

y² + xy + y = x³ − 104090690933x + 12923707417896492

a-invariants: [1, 0, 1, -104090690933, 12923707417896492]
rank (lower bound): ≥ 13
torsion subgroup: trivial
conductor (N): 32385292333257670247550849142
discriminant (Δ): 26102545620605682219525984408452
Faltings height: 5.0245
naive height: 87.7192
primes of bad reduction: 2, 13, 31, 98110447, 409541131137302231
regulator: 89307876842798.75117822634301849541540204173634718293390619734043
submitted by: Michael Rubinstein
submitted at: 2026-10-02 09:36:41 UTC
last updated: 2026-10-02 09:36:41 UTC

(-86683, 145972336)
(2445, 112556408)
(180278, 4095230)
(4527621, 9607884048)
(12817210, 45866254826)
(-1354461126/3721, 11576899061607/226981)
(30811719/169, 5328692760/2197)
(275225111/2116, 3869136851755/97336)
(97838327/1369, 3872293210480/50653)
(1671129286/2209, 62868685895794/103823)
(6683485506/32041, 96597085537542/5735339)
(75042701287/21609, 20465902878760928/3176523)
(13286908255116/70274689, 791048241025223421/589112717887)

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

last edited by Michael Rubinstein at 2026-10-02 09:36:41 UTC · history