curve #5267

y² = x³ + 872275x

a-invariants: [0, 0, 0, 872275, 0]
c-invariants: [-41869200, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 973905504800
discriminant (Δ): -42475671209971000000
Faltings height: 2.4558
naive height: 52.6502
primes of bad reduction: 2, 5, 23, 37, 41
regulator: 760.582338392711010933925157997813822277523570201
submitted by: The Wren
submitted at: 2026-10-21 11:35:43 UTC
last updated: 2026-10-21 11:35:43 UTC

Witness: 5 independent points log in to add more points →

(41, 5986)
(185, 12950)
(1035, 44850)
(18860, 2593250)
(4715/49, 3159050/343)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,2,13,14), 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 11:35:43 UTC · history