curve #5265

y² = x³ − 15805x

a-invariants: [0, 0, 0, -15805, 0]
c-invariants: [758640, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 7993536800
discriminant (Δ): 252675698248000
Faltings height: 1.4531
naive height: 40.6178
primes of bad reduction: 2, 5, 29, 109
regulator: 161.2704960207595304635120687844158365834192768
submitted by: The Wren
submitted at: 2026-10-21 11:32:42 UTC
last updated: 2026-10-21 11:32:42 UTC

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

(-125, 150)
(-116, 522)
(-109, 654)
(-981/25, 93522/125)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (4,7,8,11), 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 11:32:42 UTC · history