curve #5342

y² = x³ + 297690369198x

a-invariants: [0, 0, 0, 297690369198, 0]
c-invariants: [-14289137721504, 0]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 5671651578447459018445056
discriminant (Δ): -1688396052350443534845883412517785088
Faltings height: 5.6409
naive height: 90.8716
primes of bad reduction: 2, 3, 37, 101, 113, 293, 401
regulator: 59604803.7006291734599379247628813649583853840198666433
submitted by: The Wren
submitted at: 2026-10-21 14:30:00 UTC
last updated: 2026-10-21 14:30:00 UTC

Witness: 8 independent points log in to add more points →

(888, 16258836)
(273912, 319518348)
(45313/36, 4181166449/216)
(1062418/121, 68056827566/1331)
(1263106/9, 5698454138/27)
(11469778/81, 154632056194/729)
(214365778/3249, 26143411333886/185193)
(32930350575/259081, 26338557165070065/131872229)

Commentary

From the Aguirre–Castañeda–Peral parametrization at tuple (6,11,24,28), 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 14:30:00 UTC · history