curve #2710

y² + xy = x³ − 3971207861040x + 2785845565252608975

a-invariants: [1, 0, 0, -3971207861040, 2785845565252608975]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 880838805
discriminant (Δ): 655460745409415551307230784688150650625
Faltings height: 6.1863
naive height: 98.6439
primes of bad reduction: 3, 5, 7, 11, 31, 73, 337
regulator: 52.630404042721543665703172092498421407385587
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:46 UTC
last updated: 2026-09-26 20:18:46 UTC

Witness: 3 independent points log in to add more points →

(51721719495/61009, 2536493818599330/15069223)
(46529430, -317125234515)
(6248998905/256, -492435738133365/4096)

Commentary

2-isogenous to curve#1570 via the rational 2-torsion point x=18231631/4. 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 20:18:47 UTC · history