curve #2699

y² + xy + y = x³ + x² − 1793790311830x + 869792370000289427

a-invariants: [1, 1, 1, -1793790311830, 869792370000289427]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 990867570
discriminant (Δ): 42573079286403505742002551202160640000
Faltings height: 5.9695
naive height: 96.2597
primes of bad reduction: 2, 3, 5, 7, 11, 31, 101, 137
regulator: 26.612770981016028357684802045476606997964827
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:18 UTC
last updated: 2026-09-26 20:18:18 UTC

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

(71837369/25, -551339192013/125)
(352816097, -6627214437969)
(8068757, -22625072049)

Commentary

2-isogenous to curve#1572 via the rational 2-torsion point x=12289779/4. 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 20:18:18 UTC · history