curve #5039

y² = x³ − 277645740241x

a-invariants: [0, 0, 0, -277645740241, 0]
c-invariants: [13326995531568, 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): 8884663687712
discriminant (Δ): 1369786930488155560149026655284321344
Faltings height: 5.6234
naive height: 90.6624
primes of bad reduction: 2, 457, 1153
regulator: 31521.86776519268782895208347949383848195761704
submitted by: David Renshaw
submitted at: 2026-10-21 01:49:15 UTC
last updated: 2026-10-21 01:49:15 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 526921. 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 01:49:15 UTC · history