curve #759

y² = x³ − 162487804927x + 24573741560967490

a-invariants: [0, 0, 0, -162487804927, 24573741560967490]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 25168869705838997533742636949448 ★ record for rank ≥ 14
discriminant (Δ): 13691865119976414658355994500499712
Faltings height: 5.3282
naive height: 89.0552
primes of bad reduction: 2, 17, 185065218425286746571637036393
regulator: 5793803353.82602785899794289548136225142373347080436717453318673789
submitted by: Michael Rubinstein
submitted at: 2026-09-18 10:55:12 UTC
last updated: 2026-09-18 10:55:12 UTC

(150959, 59032976)
(116891, -84720248)
(-236063, -223106062)
(-158407, -215262806)
(1211045, -1266470930)
(278357, 30198562)
(154801, -55946558)
(90201, 103204042)
(199853, 9079606)
(-338369, 202023512)
(-359447, 191149606)
(154597, 56111662)
(266918, -14813944)
(700209/4, -309224849/8)

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

last edited by Michael Rubinstein at 2026-09-18 10:55:13 UTC · history