curve #5255

y² = x³ + 1023x

a-invariants: [0, 0, 0, 1023, 0]
c-invariants: [-49104, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 33488928
discriminant (Δ): -68518346688
Faltings height: 0.7687
naive height: 32.4051
primes of bad reduction: 2, 3, 11, 31
regulator: 15.635159860139462234694386656082500311971436
submitted by: The Wren
submitted at: 2026-10-21 11:18:39 UTC
last updated: 2026-10-21 11:18:39 UTC

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

(1, 32)
(31, 248)
(124, 1426)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,3,4,6), 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 11:18:39 UTC · history