curve #1132

y² = x³ − x² + 1996x + 102894

a-invariants: [0, -1, 0, 1996, 102894]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
conductor (N): 13217088
discriminant (Δ): -5141671922496
Faltings height: 1.1210
naive height: 36.6189
primes of bad reduction: 2, 3, 23, 41, 73
regulator: 385.8376612454826152965149916102298049028788583
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:03 UTC
last updated: 2026-09-23 21:37:03 UTC

Witness: 4 independent points log in to add more points →

(4141/36, 293095/216)
(67, 730)
(124041/3136, 86420475/175616)
(22766151/290521, 134191836360/156590819)

Commentary

Obtained by computing a rational isogeny from curve#14 and mapping all 4 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 21:37:03 UTC · history