curve #5010

y² = x³ − 900x

a-invariants: [0, 0, 0, -900, 0]
c-invariants: [43200, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 14400
discriminant (Δ): 46656000000
Faltings height: 0.7366
naive height: 32.0208
primes of bad reduction: 2, 3, 5
regulator: 1.348234701331308527208182096390747361896
submitted by: David Renshaw
submitted at: 2026-10-21 01:46:47 UTC
last updated: 2026-10-21 01:46:47 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 30. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 1.

last edited by David Renshaw at 2026-10-21 01:46:47 UTC · history