curve #2780

y² + xy = x³ − 1984625901969663014x − 55730361981355753237538076

a-invariants: [1, 0, 0, -1984625901969663014, -55730361981355753237538076]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 187511281391406
discriminant (Δ): 498941486260560083314659917811614550899210327031683883264
Faltings height: 9.5689
naive height: 138.0095
primes of bad reduction: 2, 3, 7, 19, 23, 31, 37, 61, 151, 967
regulator: 804.8904237123832154511529539720868094197828387
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:05 UTC
last updated: 2026-09-26 20:22:05 UTC

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

(155013963856/25, -59428771274844094/125)
(17874660386680/1681, -74903697763298781682/68921)
(1700493580, -38558684923142)
(66966191764/25, -14709785802937222/125)

Commentary

2-isogenous to curve#1634 via the rational 2-torsion point x=224737695/4. 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 20:22:06 UTC · history