curve #5300

y² = x³ + 14795x

a-invariants: [0, 0, 0, 14795, 0]
c-invariants: [-710160, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 7004544800
discriminant (Δ): -207264480632000
Faltings height: 1.4366
naive height: 40.4197
primes of bad reduction: 2, 5, 11, 269
regulator: 205.0368576177458225851772357600411366269125308
submitted by: The Wren
submitted at: 2026-10-21 12:40:56 UTC
last updated: 2026-10-21 12:40:56 UTC

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

(44, 858)
(55, 990)
(125, 1950)
(6336/25, 559416/125)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (5,7,8,20), 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 12:40:56 UTC · history