curve #2920

y² + xy = x³ − 8775528159168237987910x + 318804869575042340614036099040100

a-invariants: [1, 0, 0, -8775528159168237987910, 318804869575042340614036099040100]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 2258228975265200784470
discriminant (Δ): -655627543267378610060412595544576918156889807797205950381656000000
Faltings height: 11.4533
naive height: 163.2074
primes of bad reduction: 2, 5, 13, 29, 37, 43, 73, 97, 163, 211, 277, 5581
regulator: 508395.0135300124070219387019938532602770121622266179
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:28:25 UTC
last updated: 2026-09-26 20:28:25 UTC

Witness: 7 independent points log in to add more points →

(35287239459367480/66049, -6533016899715065403394530/16974593)
(-23093969804641034/491401, 8628490913898384567135942/344472101)
(-8917792479425504/119025, -968012976517033138859066/41063625)
(1463321465020, -1766608171934182710)
(35126328981723772, -6583383396938297894753718)
(-85538665784, -21061227650166678)
(3986889920, -16848775764582710)

Commentary

2-isogenous to curve#1266 via the rational 2-torsion point x=54130221868. 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 20:28:25 UTC · history