curve #5040

y² = x³ − 292112144676x

a-invariants: [0, 0, 0, -292112144676, 0]
c-invariants: [14021382944448, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 4673794314816
discriminant (Δ): 1595250222676800677767931025059057664
Faltings height: 5.6361
naive height: 90.8148
primes of bad reduction: 2, 3, 11, 19, 431
regulator: 2071.027582917259560590755079172939948513829782
submitted by: David Renshaw
submitted at: 2026-10-21 01:49:19 UTC
last updated: 2026-10-21 01:49:19 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 540474. Found in an ellrank scan of squarefree n <= 6*10^5 with n = 1,2,3 mod 8.

last edited by David Renshaw at 2026-10-21 01:49:19 UTC · history