curve #3024

y² = x³ + x² − 2985887265x + 40053343216639

a-invariants: [0, 1, 0, -2985887265, 40053343216639]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 43121536946337856
discriminant (Δ): 1010648521564987157762875031552
Faltings height: 4.4592
naive height: 77.0651
primes of bad reduction: 2, 23, 41, 73, 359, 449, 1481
regulator: 33029.1048742026573009818023985947082977475069520810435
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:48 UTC
last updated: 2026-09-26 20:33:48 UTC

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

(-4711, 7349512)
(-57271, -4818128)
(270955, -138288408)
(-14611, 8975588)
(75017, -15434656)
(10490755/729, -5016526136/19683)
(54537, -6278816)
(467971/9, -136025864/27)

Commentary

2-isogenous to curve#1349 via the rational 2-torsion point x=30203. 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 20:33:48 UTC · history