curve #5304

y² = x³ + 157339828x

a-invariants: [0, 0, 0, 157339828, 0]
c-invariants: [-7552311744, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 49511642950139168
discriminant (Δ): -249284908344713896613859328
Faltings height: 3.7545
naive height: 68.2354
primes of bad reduction: 2, 17, 53, 149, 293
regulator: 21165.341449033988405894256017221665341797508008557
submitted by: The Wren
submitted at: 2026-10-21 12:47:43 UTC
last updated: 2026-10-21 12:47:43 UTC

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

(293, 214769)
(2384, 623416)
(7301, 1240127)
(22797, 3928683)
(134249/16, 88470091/64)
(536996/121, 1179780212/1331)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,11,20), 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 12:47:43 UTC · history