curve #5271

y² = x³ − 22008042x

a-invariants: [0, 0, 0, -22008042, 0]
c-invariants: [1056386016, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 3444294490124544
discriminant (Δ): 682219600191265946245632
Faltings height: 3.2628
naive height: 62.3344
primes of bad reduction: 2, 3, 7, 19, 29, 317
regulator: 6963.5217077078636442703882662254855369380350009688
submitted by: The Wren
submitted at: 2026-10-21 11:41:48 UTC
last updated: 2026-10-21 11:41:48 UTC

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

(-4598, 63118)
(-4256, 128744)
(-3857, 165851)
(-342, 86526)
(4698, 17226)
(14616, 1673532)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (3,8,10,12), 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 11:41:48 UTC · history