curve #5273

y² = x³ − 246030477x

a-invariants: [0, 0, 0, -246030477, 0]
c-invariants: [11809462896, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 1936991859611120928
discriminant (Δ): 953118062330482232841045312
Faltings height: 3.8663
naive height: 69.5765
primes of bad reduction: 2, 3, 7, 11, 17, 31, 43, 47
regulator: 6867.8593335049160478979166973384187798997337613940
submitted by: The Wren
submitted at: 2026-10-21 11:45:05 UTC
last updated: 2026-10-21 11:45:05 UTC

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

(-15351, 399126)
(-14663, 674498)
(-14229, 787338)
(-2021, 699266)
(24123, 2846514)
(64108, 15738514)

Commentary

Obtained from the Aguirre–Castañeda–Peral parametrization at tuple (8,11,13,14), 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 11:45:05 UTC · history