curve #2872

y² + xy + y = x³ + 4061607x + 880022662

a-invariants: [1, 0, 1, 4061607, 880022662]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 121340359518
discriminant (Δ): -4622488801102933909218
Faltings height: 2.8462
naive height: 57.2649
primes of bad reduction: 2, 3, 7, 43, 193, 337, 1033
regulator: 661.72064388366632428929385969753112102735312307552
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:26:14 UTC
last updated: 2026-09-26 20:26:14 UTC

Witness: 6 independent points log in to add more points →

(-172, 13365)
(338, 47700)
(656, 61533)
(1346, 93060)
(10904/25, -6563943/125)
(9980, -1022562)

Commentary

2-isogenous to curve#1235 via the rational 2-torsion point x=107. 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 20:26:14 UTC · history