curve #5288

y² = x³ − 4111371900x

a-invariants: [0, 0, 0, -4111371900, 0]
c-invariants: [197345851200, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 150252256889863200
discriminant (Δ): 4447748929597667678333376000000
Faltings height: 4.5703
naive height: 78.0247
primes of bad reduction: 2, 3, 5, 23, 31, 43, 149
regulator: 3920.7978762314648947569130366211351966759336115217
submitted by: The Wren
submitted at: 2026-10-21 12:14:45 UTC
last updated: 2026-10-21 12:14:45 UTC

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

(-53475, 8181675)
(-43806, 9800028)
(-22350, 8984700)
(-8556, 5877972)
(64170, 641700)
(138570, 45728100)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (2,11,17,19), 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 12:14:45 UTC · history