curve #5260

y² = x³ − 6525x

a-invariants: [0, 0, 0, -6525, 0]
c-invariants: [313200, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 6055200
discriminant (Δ): 17779581000000
Faltings height: 1.2319
naive height: 37.9638
primes of bad reduction: 2, 3, 5, 29
regulator: 9.8156370961162397281391004419767026788522723
submitted by: The Wren
submitted at: 2026-10-21 11:26:01 UTC
last updated: 2026-10-21 11:26:01 UTC

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

(-45, 450)
(-20, 350)
(225, 3150)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (2,3,9,14), 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 11:26:01 UTC · history