curve #2836

y² + xy + y = x³ − 23104526426914x + 43081948731506022632

a-invariants: [1, 0, 1, -23104526426914, 43081948731506022632]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 12059599736130
discriminant (Δ): -12462670641263425938977862888259236959940
Faltings height: 6.5162
naive height: 103.9424
primes of bad reduction: 2, 3, 5, 23, 41, 61, 107, 241, 271
regulator: 3846.13778673917998284144625375509405683742645022
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:37 UTC
last updated: 2026-09-26 20:24:37 UTC

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

(-20884313/4, 37018344097/8)
(520302982/169, -2340127574452/2197)
(276989040/121, 1967155391141/1331)
(4562261515/729, -235926356232601/19683)
(99583556725/2401, -31225686589128361/117649)

Commentary

2-isogenous to curve#1247 via the rational 2-torsion point x=2777581. 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 20:24:37 UTC · history