curve #5018

y² = x³ − 25921x

a-invariants: [0, 0, 0, -25921, 0]
c-invariants: [1244208, 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): 829472
discriminant (Δ): 1114641555517504
Faltings height: 1.5767
naive height: 42.1020
primes of bad reduction: 2, 7, 23
regulator: 15.0626285004700100769351514769163228071357
submitted by: David Renshaw
submitted at: 2026-10-21 01:47:29 UTC
last updated: 2026-10-21 01:47:29 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 161. 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 01:47:29 UTC · history