curve #5263

y² = x³ − 58466x

a-invariants: [0, 0, 0, -58466, 0]
c-invariants: [2806368, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 218769481984
discriminant (Δ): 12790576533676544
Faltings height: 1.7801
naive height: 44.5422
primes of bad reduction: 2, 23, 31, 41
regulator: 703.173372168656570873716533951789335705296939851
submitted by: The Wren
submitted at: 2026-10-21 11:29:51 UTC
last updated: 2026-10-21 11:29:51 UTC

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

(-46, 1610)
(242, 154)
(248, 868)
(279, 2325)
(-713/9, 54901/27)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,12,14), 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 11:29:51 UTC · history