curve #2775

y² = x³ + x² − 23695884x − 43444000404

a-invariants: [0, 1, 0, -23695884, -43444000404]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 125565648
discriminant (Δ): 36475404146860685969664
Faltings height: 3.1128
naive height: 62.5560
primes of bad reduction: 2, 3, 13, 23, 673
regulator: 158.3180606290961287164439109117942625871420512
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:52 UTC
last updated: 2026-09-26 20:21:52 UTC

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

(17307, 2175030)
(-46047/16, 1944345/64)
(-377478/121, 15027480/1331)
(5646, -52728)

Commentary

2-isogenous to curve#1720 via the rational 2-torsion point x=6283. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:21:53 UTC · history