curve #5035

y² = x³ − 3331021225x

a-invariants: [0, 0, 0, -3331021225, 0]
c-invariants: [159889018800, 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): 106592679200
discriminant (Δ): 2365441293142306387680049000000
Faltings height: 4.5177
naive height: 77.3932
primes of bad reduction: 2, 5, 7, 17, 97
regulator: 699.3332796431145743278860588437772573972373787
submitted by: David Renshaw
submitted at: 2026-10-21 01:48:59 UTC
last updated: 2026-10-21 01:48:59 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 57715. 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 01:48:59 UTC · history