curve #5264

y² = x³ + 233864x

a-invariants: [0, 0, 0, 233864, 0]
c-invariants: [-11225472, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 218769481984
discriminant (Δ): -818596898155298816
Faltings height: 2.1267
naive height: 48.7011
primes of bad reduction: 2, 23, 31, 41
regulator: 1406.34674433731314174743306790357867141059387971
submitted by: The Wren
submitted at: 2026-10-21 11:31:25 UTC
last updated: 2026-10-21 11:31:25 UTC

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

(8, 1368)
(288, 9552)
(369, 11685)
(1025, 36285)
(5248, 381792)

Commentary

Rational 2-isogeny partner of curve #5263: https://elliptic-rank.icarm.cloud/curve/5263. Both arise from the Aguirre–Castañeda–Peral parametrization at tuple (1,8,12,14), 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 11:31:25 UTC · history