curve #5344

y² = x³ + 33024475x

a-invariants: [0, 0, 0, 33024475, 0]
c-invariants: [-1585174800, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1395988414752800
discriminant (Δ): -2305089225164673739000000
Faltings height: 3.3642
naive height: 63.5519
primes of bad reduction: 2, 5, 11, 29, 41, 101
regulator: 6652.9109736420795773172939918061661159807134436055
submitted by: The Wren
submitted at: 2026-10-21 14:43:52 UTC
last updated: 2026-10-21 14:43:52 UTC

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

(5, 12850)
(2255, 293150)
(6380, 685850)
(9999, 1153218)
(25520, 4178900)
(7975/9, 4673350/27)

Commentary

From the Aguirre–Castañeda–Peral parametrization at tuple (6,10,20,29), 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 14:43:52 UTC · history