curve #2781

y² + xy + y = x³ − 975519702164x + 370853133484300886

a-invariants: [1, 0, 1, -975519702164, 370853133484300886]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/6ℤ
conductor (N): 3637272210
discriminant (Δ): 36423277217282109926428927627500
Faltings height: 5.4104
naive height: 94.4323
primes of bad reduction: 2, 3, 5, 11, 13, 23, 191, 193
regulator: 64.77021721277704136819405362812158091096843604
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:22:09 UTC
last updated: 2026-09-26 20:22:09 UTC

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

(21900333/16, -80998835573/64)
(36584457/64, -1063184209/512)
(570609, -631547)
(683631, -153487523)

Commentary

2-isogenous to curve#1610 via the rational 2-torsion point x=-284991. 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 20:22:10 UTC · history