curve #2657

y² = x³ + x² − 22636920x + 41433671268

a-invariants: [0, 1, 0, -22636920, 41433671268]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 895440
discriminant (Δ): 484042276123136640000
Faltings height: 2.9356
naive height: 62.4189
primes of bad reduction: 2, 3, 5, 7, 13, 41
regulator: 2.31815437609645692241288104254896899003638
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:16:01 UTC
last updated: 2026-09-26 20:16:01 UTC

Witness: 2 independent points log in to add more points →

(4551, -180810)
(19986, -2751840)

Commentary

2-isogenous to curve#1472 via the rational 2-torsion point x=-5413. 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 20:16:01 UTC · history