curve #5015

y² = x³ − 21025x

a-invariants: [0, 0, 0, -21025, 0]
c-invariants: [1009200, 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): 672800
discriminant (Δ): 594823321000000
Faltings height: 1.5244
naive height: 41.4740
primes of bad reduction: 2, 5, 29
regulator: 18.1334819031412355896087173160093069063430
submitted by: David Renshaw
submitted at: 2026-10-21 01:47:21 UTC
last updated: 2026-10-21 01:47:21 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 145. 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 01:47:21 UTC · history