curve #2716

y² = x³ − x² − 119861866360x + 15940291844569600

a-invariants: [0, -1, 0, -119861866360, 15940291844569600]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 676608240
discriminant (Δ): 442943263104900399961486899840000
Faltings height: 5.1448
naive height: 88.1424
primes of bad reduction: 2, 3, 5, 7, 11, 19, 41, 47
regulator: 23.512514479752678090499761159735719648407312
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:19:02 UTC
last updated: 2026-09-26 20:19:02 UTC

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

(211132, -6718932)
(1919020/9, -236838140/27)
(3438601/16, -661028445/64)

Commentary

2-isogenous to curve#1569 via the rational 2-torsion point x=-385039. 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 20:19:02 UTC · history