curve #5274

y² = x³ + 1136987775x

a-invariants: [0, 0, 0, 1136987775, 0]
c-invariants: [-54575413200, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 183856526293255200
discriminant (Δ): -94069180237228752309831000000
Faltings height: 4.2490
naive height: 74.1685
primes of bad reduction: 2, 3, 5, 7, 11, 29, 31, 73
regulator: 10130.882539016821202309277985000407184414578294608
submitted by: The Wren
submitted at: 2026-10-21 11:46:29 UTC
last updated: 2026-10-21 11:46:29 UTC

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

(7975, 3094300)
(31465, 8180900)
(47740, 12770450)
(71775, 21245400)
(11935/9, 33179300/27)
(283185/16, 324246825/64)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (4,6,12,13), 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 11:46:29 UTC · history