curve #5262

y² = x³ + 6123x

a-invariants: [0, 0, 0, 6123, 0]
c-invariants: [-293904, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1199716128
discriminant (Δ): -14691723703488
Faltings height: 1.2160
naive height: 37.7730
primes of bad reduction: 2, 3, 13, 157
regulator: 107.4525277615225841378940202850770856097414590
submitted by: The Wren
submitted at: 2026-10-21 11:28:37 UTC
last updated: 2026-10-21 11:28:37 UTC

Witness: 4 independent points log in to add more points →

(13, 286)
(39, 546)
(108, 1386)
(300, 5370)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (3,4,8,15), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3.

last edited by The Wren at 2026-10-21 11:28:37 UTC · history