curve #5258

y² = x³ + 1443x

a-invariants: [0, 0, 0, 1443, 0]
c-invariants: [-69264, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 66631968
discriminant (Δ): -192299859648
Faltings height: 0.8547
naive height: 33.4370
primes of bad reduction: 2, 3, 13, 37
regulator: 23.704859684210369169724460482041654503093151
submitted by: The Wren
submitted at: 2026-10-21 11:23:30 UTC
last updated: 2026-10-21 11:23:30 UTC

Witness: 3 independent points log in to add more points →

(1, 38)
(3, 66)
(12, 138)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,2,8,9), 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 11:23:30 UTC · history