curve #2819

y² + xy + y = x³ − x² − 1270563755x + 16719847800122

a-invariants: [1, -1, 1, -1270563755, 16719847800122]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 41419028475
discriminant (Δ): 10508729718803655594969140625
Faltings height: 4.1382
naive height: 74.5018
primes of bad reduction: 3, 5, 11, 23, 47, 113, 137
regulator: 184.691071705541576210242597292172008389318646943
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:51 UTC
last updated: 2026-09-26 20:23:51 UTC

Witness: 5 independent points log in to add more points →

(28213, -1838835)
(457365/16, -124972553/64)
(4841349/16, -10591186355/64)
(47154, -7875515)
(37804, -4784790)

Commentary

2-isogenous to curve#1652 via the rational 2-torsion point x=-8541. 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 20:23:52 UTC · history