curve #1144

y² + xy = x³ − 2274444314594204850x − 1114879880778907709634448725

a-invariants: [1, 0, 0, -2274444314594204850, -1114879880778907709634448725]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 965575150587952905
discriminant (Δ): 216061451167651643918817073979733942195905858470134471225
Faltings height: 9.5309
naive height: 138.4184
primes of bad reduction: 3, 5, 7, 11, 13, 19, 23, 29, 137, 173, 347, 617
regulator: 276991.02745939693646544486082098299243157800924115
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:30 UTC
last updated: 2026-09-23 21:37:30 UTC

Witness: 6 independent points log in to add more points →

(-11059644963/16, -721259523603501/64)
(-2304249597/4, -16347624543909/8)
(-27544064766/25, -915160944861333/125)
(-806505198, -13959520242129)
(-643604670, -9075177562365)
(705575639106, -592672303525047453)

Commentary

Obtained by computing a rational isogeny from curve#1112 and mapping all 6 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 21:37:30 UTC · history