curve #2870

y² = x³ − 22576467x − 20428465070

a-invariants: [0, 0, 0, -22576467, -20428465070]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 138417695568
discriminant (Δ): 556174696958373851615232
Faltings height: 3.2523
naive height: 62.4109
primes of bad reduction: 2, 3, 19, 43, 71, 73, 227
regulator: 244.70918997284217677420076965011915140599988490238
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:11 UTC
last updated: 2026-09-26 20:26:11 UTC

Witness: 6 independent points log in to add more points →

(-961, -19494)
(17849, -2294136)
(388919, -242524854)
(6194, -278154)
(-4191, -24016)
(-76999/25, -17628624/125)

Commentary

2-isogenous to curve#1297 via the rational 2-torsion point x=2105. 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 20:26:11 UTC · history