curve #5287

y² = x³ + 181871613x

a-invariants: [0, 0, 0, 181871613, 0]
c-invariants: [-8729837424, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 235216239041577024
discriminant (Δ): -385012411184566686767577408
Faltings height: 3.7907
naive height: 68.6700
primes of bad reduction: 2, 3, 7, 11, 37, 41, 173
regulator: 16833.872927888583430312686052659579815318117819863
submitted by: The Wren
submitted at: 2026-10-21 12:13:18 UTC
last updated: 2026-10-21 12:13:18 UTC

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

(2772, 724878)
(13776, 2262708)
(200244, 89809434)
(1353/4, 1984851/8)
(31857/4, 11181807/8)
(33825/4, 11710215/8)

Commentary

Rational 2-isogenous endpoint of the Aguirre–Castañeda–Peral parametrization at tuple (6,8,12,17), 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 12:13:18 UTC · history