curve #5329

y² = x³ + 6953x

a-invariants: [0, 0, 0, 6953, 0]
c-invariants: [-333744, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 3094029376
discriminant (Δ): -21512786251328
Faltings height: 1.2478
naive height: 38.1544
primes of bad reduction: 2, 17, 409
regulator: 492.6757995507565125085453108434213835246015995
submitted by: The Wren
submitted at: 2026-10-21 13:19:31 UTC
last updated: 2026-10-21 13:19:31 UTC

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

(272, 4692)
(1636, 66258)
(153/4, 4539/8)
(409/1600, 2698173/64000)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (3,8,13,24), 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 13:19:31 UTC · history