curve #3019

y² = x³ + x² − 1299173505x − 10662118981601

a-invariants: [0, 1, 0, -1299173505, -10662118981601]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 65155172589047744
discriminant (Δ): 91233881284152150745937641472
Faltings height: 4.2566
naive height: 74.5686
primes of bad reduction: 2, 7, 31, 41, 113, 127, 1721
regulator: 78412.4700522768236175637840453027344948731803573004399
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:33:33 UTC
last updated: 2026-09-26 20:33:33 UTC

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

(-18343, 2645216)
(39869, -957068)
(-9571, 946372)
(-12391, 1879792)
(-95654/9, -37658411/27)
(-21621, -2705672)
(356851/9, -10876024/27)
(-3733309/121, -302908984/1331)

Commentary

2-isogenous to curve#1350 via the rational 2-torsion point x=15443. 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 20:33:33 UTC · history