curve #1183

y² + xy = x³ − 748692454000090200x + 559647059958559043288903232

a-invariants: [1, 0, 0, -748692454000090200, 559647059958559043288903232]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 931401536730
discriminant (Δ): -108445456250959127892349568038660212751593141499330560000
Faltings height: 9.4405
naive height: 136.7018
primes of bad reduction: 2, 3, 5, 7, 17, 29, 79, 263, 433
regulator: 3563.0723504771183700436091068939908207856682
submitted by: David Renshaw
submitted at: 2026-09-23 21:38:38 UTC
last updated: 2026-09-23 21:38:38 UTC

Witness: 3 independent points log in to add more points →

(40647122356/9, -8068498576416644/27)
(-2048621374634064/3073009, -148750093399880187578904/5386984777)
(2182664073396/2809, -3147802599391988124/148877)

Commentary

Obtained by computing a rational isogeny from curve#1087 and mapping all 3 independent witness points to the global minimal model. Isogenies preserve the Mordell-Weil rank; the image points are independently certified by the site verifier. Torsion computed exactly with PARI/GP elltors. Conductor is unchanged by the isogeny.

last edited by David Renshaw at 2026-09-23 21:38:38 UTC · history