curve #5038

y² = x³ − 142221002884x

a-invariants: [0, 0, 0, -142221002884, 0]
c-invariants: [6826608138432, 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): 2275536046144
discriminant (Δ): 184107374339983951941296212194758656
Faltings height: 5.4562
naive height: 88.6555
primes of bad reduction: 2, 193, 977
regulator: 25766.68841547452725659192041731683443778576890
submitted by: David Renshaw
submitted at: 2026-10-21 01:49:11 UTC
last updated: 2026-10-21 01:49:11 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 377122. 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 01:49:11 UTC · history