curve #2765

y² + xy = x³ − 88404229901x + 10116134337740305

a-invariants: [1, 0, 0, -88404229901, 10116134337740305]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 3913593970
discriminant (Δ): 8709952210706687914927679897600
Faltings height: 4.9643
naive height: 87.2292
primes of bad reduction: 2, 5, 11, 13, 17, 19, 37, 229
regulator: 34.69979523882825681242709603816565344810298874
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:21:27 UTC
last updated: 2026-09-26 20:21:27 UTC

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

(559314, -368575585)
(827998, -710749989)
(-307772, 90548751)
(-343302, 2456791)

Commentary

2-isogenous to curve#1611 via the rational 2-torsion point x=-86526. 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 20:21:27 UTC · history