curve #2815

y² + xy + y = x³ − 1743549621383x + 10407875313868888556

a-invariants: [1, 0, 1, -1743549621383, 10407875313868888556]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 42652114744890
discriminant (Δ): -46456691379466975569936848910769041656250
Faltings height: 6.4829
naive height: 101.1013
primes of bad reduction: 2, 3, 5, 7, 17, 29, 31, 37, 43, 8353
regulator: 3261.47201084168621545801537945114298304527707562
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:40 UTC
last updated: 2026-09-26 20:23:40 UTC

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

(1042926, 3117790159)
(141987715/36, 1739486036797/216)
(-2439810, 373262767)
(12919114140/1681, 1463303900975432/68921)
(-1654910/9, -88408645891/27)

Commentary

2-isogenous to curve#1669 via the rational 2-torsion point x=1224183. 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 20:23:40 UTC · history