curve #3017

y² = x³ − x² + 1072101215x + 159775535297761

a-invariants: [0, -1, 0, 1072101215, 159775535297761]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 77883686473803072
discriminant (Δ): -11107106649118160852288642777088
Faltings height: 4.6366
naive height: 78.9327
primes of bad reduction: 2, 3, 17, 47, 89, 257, 457, 2857
regulator: 35440.6385547988360079809244718875222981502188270457983
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:29 UTC
last updated: 2026-09-26 20:33:29 UTC

Witness: 8 independent points log in to add more points →

(28463, 14606472)
(93663, -32891728)
(169443, 72154508)
(7416111, 20196151544)
(21991465/256, -121906620501/4096)
(49425, -18261944)
(3813417/16, -7560165965/64)
(8597569, -25209642312)

Commentary

2-isogenous to curve#1352 via the rational 2-torsion point x=23857. 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 20:33:29 UTC · history