curve #5279

y² = x³ + 308655775428x

a-invariants: [0, 0, 0, 308655775428, 0]
c-invariants: [-14815477220544, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 527802701967091238688
discriminant (Δ): -1881928837176360061586174466636976128
Faltings height: 5.6499
naive height: 90.9801
primes of bad reduction: 2, 3, 7, 11, 13, 17, 19, 53, 79
regulator: 117253.9236533776357007954809963315560358765515951535
submitted by: The Wren
submitted at: 2026-10-21 11:56:45 UTC
last updated: 2026-10-21 11:56:45 UTC

Witness: 7 independent points log in to add more points →

(136458, 211327956)
(212212, 273965692)
(491946, 520478868)
(742938, 799613556)
(1890196, 2708650868)
(3645378, 7040440044)
(16416114, 66550926156)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (1,2,10,16), 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 11:56:46 UTC · history