curve #2811

y² = x³ − x² − 2135744x + 1106048064

a-invariants: [0, -1, 0, -2135744, 1106048064]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 62703888
discriminant (Δ): 95683738951223414784
Faltings height: 2.5740
naive height: 55.3366
primes of bad reduction: 2, 3, 13, 17, 23, 257
regulator: 27.52986278960443775503832395901323682199316358
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:29 UTC
last updated: 2026-09-26 20:23:29 UTC

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

(-40279/25, 2378844/125)
(-1416, 35904)
(11680/9, -614744/27)
(2954, -143406)

Commentary

2-isogenous to curve#1692 via the rational 2-torsion point x=3345. 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 20:23:29 UTC · history