curve #5301

y² = x³ − 341202x

a-invariants: [0, 0, 0, -341202, 0]
c-invariants: [16377696, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 7450803507456
discriminant (Δ): 2542229058351002112
Faltings height: 2.2211
naive height: 49.8343
primes of bad reduction: 2, 3, 19, 41, 73
regulator: 931.277320420634396145631458143700899265775735519
submitted by: The Wren
submitted at: 2026-10-21 12:43:25 UTC
last updated: 2026-10-21 12:43:25 UTC

Witness: 5 independent points log in to add more points →

(-584, 292)
(-57, 4389)
(1026, 27018)
(8322, 757302)
(-4161/49, 1826679/343)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (8,9,14,20), 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 12:43:25 UTC · history