curve #1161

y² = x³ − x² − 600214784x + 5660092102080

a-invariants: [0, -1, 0, -600214784, 5660092102080]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 1092624
discriminant (Δ): 28810309632
Faltings height: 3.1647
naive height: 72.2520
primes of bad reduction: 2, 3, 13, 17, 103
regulator: 395.39012815521442984002998113689013306162880
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:59 UTC
last updated: 2026-09-23 21:37:59 UTC

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

(24961, -2495896)
(168514/9, 26805338/27)
(378906/25, 26347254/125)

Commentary

Obtained by computing a rational isogeny from curve#1115 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 21:37:59 UTC · history