curve #5254

y² = x³ − 2892x

a-invariants: [0, 0, 0, -2892, 0]
c-invariants: [138816, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
family: y² = x³ + ax (quartic twists)
conductor (N): 16727328
discriminant (Δ): 1548013842432
Faltings height: 1.0285
naive height: 35.5227
primes of bad reduction: 2, 3, 241
regulator: 14.782146630339562620928834231258121507541720
submitted by: The Wren
submitted at: 2026-10-21 11:17:24 UTC
last updated: 2026-10-21 11:17:24 UTC

Witness: 3 independent points log in to add more points →

(-50, 140)
(-2, 76)
(54, 36)

Commentary

Rational 2-isogeny partner of curve #5253: https://elliptic-rank.icarm.cloud/curve/5253. The source curve comes from the Aguirre–Castañeda–Peral parametrization at tuple (6,10,11,15), 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 11:17:24 UTC · history