curve #2745

y² = x³ + x² − 53661141304x − 1396604752267264

a-invariants: [0, 1, 0, -53661141304, -1396604752267264]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 2428381032
discriminant (Δ): 9046570017216325919628185846498304
Faltings height: 5.2071
naive height: 85.7315
primes of bad reduction: 2, 3, 7, 11, 19, 23, 31, 97
regulator: 219.0215881641677935327224328992763001102466828
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:25 UTC
last updated: 2026-09-26 20:20:25 UTC

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

(-66793, 43469580)
(14476019/25, -50261391378/125)
(8278784/25, -16368800448/125)
(2595589/4, -3894717519/8)

Commentary

2-isogenous to curve#2122 via the rational 2-torsion point x=108668. 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 20:20:25 UTC · history