curve #2800

y² + xy + y = x³ − x² − 29026796x + 59863221006

a-invariants: [1, -1, 1, -29026796, 59863221006]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 86935797
discriminant (Δ): 17484600270723119534169
Faltings height: 3.1043
naive height: 63.1648
primes of bad reduction: 3, 13, 61, 937
regulator: 140.4511236362066789140343967981214125094816902
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:00 UTC
last updated: 2026-09-26 20:23:00 UTC

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

(433911, -286020292)
(4092, -99982)
(9399, -790380)
(5027, -204906)

Commentary

2-isogenous to curve#849 via the rational 2-torsion point x=-1459. 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 20:23:00 UTC · history