curve #587

y² + xy = x³ − x² − 6935133529x + 1323087002140129

a-invariants: [1, -1, 0, -6935133529, 1323087002140129]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 367446112571792983028151976807954
discriminant (Δ): -734892225143585966056303953615908
Faltings height: 4.9874
naive height: 83.1606
primes of bad reduction: 2, 183723056285896491514075988403977
regulator: 24662503991252.6481335621283437477343973844614278318276303317627336
submitted by: Michael Rubinstein
submitted at: 2026-09-05 21:55:34 UTC
last updated: 2026-09-05 21:55:34 UTC

(-1303, 36498888)
(-788, 36449693)
(2045, 36177883)
(50040, 33161593)
(69241, 34241480)
(1250116, 1394481029)
(2850180, 4808467013)
(5094983, 11496403665)
(16819449, 68969872328)
(-1709/9, 982596296/27)
(88063/9, 956813195/27)
(3017764/9, 5167680455/27)
(15815067/121, 68423558888/1331)
(7335727690/56169, 683757412791509/13312053)

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

last edited by Michael Rubinstein at 2026-09-05 21:55:34 UTC · history