curve #5017

y² = x³ − 23716x

a-invariants: [0, 0, 0, -23716, 0]
c-invariants: [1138368, 0]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 379456
discriminant (Δ): 853698068844544
Faltings height: 1.5545
naive height: 41.8353
primes of bad reduction: 2, 7, 11
regulator: 6.91035241780150297009266080168233049674271
submitted by: David Renshaw
submitted at: 2026-10-21 01:47:25 UTC
last updated: 2026-10-21 01:47:25 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 154. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 2.

last edited by David Renshaw at 2026-10-21 01:47:25 UTC · history