curve #2706

y² = x³ − x² − 153949014520x − 22654301237274368

a-invariants: [0, -1, 0, -153949014520, -22654301237274368]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 922220880
discriminant (Δ): 11801905982734382614627969311360000
Faltings height: 5.3153
naive height: 88.8933
primes of bad reduction: 2, 3, 5, 7, 23, 29, 823
regulator: 109.43882875946963408820599383823040233452378
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:36 UTC
last updated: 2026-09-26 20:18:36 UTC

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

(-9690964/49, 2588648460/343)
(-24551423/121, 20140533756/1331)
(7782381/4, -21230258665/8)

Commentary

2-isogenous to curve#1571 via the rational 2-torsion point x=511025. 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 20:18:36 UTC · history