curve #5312

y² = x³ + 25254243x

a-invariants: [0, 0, 0, 25254243, 0]
c-invariants: [-1212203664, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 2267650807121952
discriminant (Δ): -1030820481399670315962048
Faltings height: 3.2972
naive height: 62.7471
primes of bad reduction: 2, 3, 7, 31, 67, 193
regulator: 9996.9880233676226972689261903952373018456480965614
submitted by: The Wren
submitted at: 2026-10-21 13:02:50 UTC
last updated: 2026-10-21 13:02:50 UTC

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

(193, 69866)
(1953, 238266)
(2412, 273762)
(5425, 544670)
(51724, 11818934)
(523404, 378682794)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (6,11,18,22), 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 13:02:50 UTC · history