curve #2753

y² + xy + y = x³ − x² − 2792338142x + 30161199794541

a-invariants: [1, -1, 1, -2792338142, 30161199794541]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1134044730
discriminant (Δ): 1000454955454348617459600000000
Faltings height: 4.4537
naive height: 76.8640
primes of bad reduction: 2, 3, 5, 7, 13, 131, 151
regulator: 23.88597145775194545960844304430979737622524752
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:47 UTC
last updated: 2026-09-26 20:20:47 UTC

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

(-57279, -1446261)
(62771, -10141311)
(-53679, -5010661)
(560571, -418153911)

Commentary

2-isogenous to curve#1600 via the rational 2-torsion point x=28793. 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 20:20:47 UTC · history