curve #1643

y² = x³ + 30457819633596695100179965225

a-invariants: [0, 0, 0, 0, 30457819633596695100179965225]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 1096481506809481023606478748100
discriminant (Δ): -400757231591729993446722088575452627149103694832314417870000
Faltings height: 10.1156
naive height: 144.6954
primes of bad reduction: 2, 3, 5, 37, 41, 53, 73, 1231, 4831
regulator: 135878067.27641203761587464960686862946108288332719301438
submitted by: NDElkies
submitted at: 2026-09-25 02:15:22 UTC
last updated: 2026-09-25 02:15:22 UTC

(5130038900, 406775844709485)
(255881692910, 129437232221555535)
(224878383254, 106640493699154017)
(291207945620, 157146639625792365)
(25120488440, 3985280944128435)
(-2676929565, -106184137901590)
(-1628027676, 161687273530643)
(2918890200, 235215923409485)
(-872639080, 172607374924365)

3-isogenous to a twisted Fermat cubic from Nick Rogers' thesis (~2004).

last edited by NDElkies at 2026-09-25 02:15:22 UTC · history