curve #5036

y² = x³ − 107794679041x

a-invariants: [0, 0, 0, -107794679041, 0]
c-invariants: [5174144593968, 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): 3449429729312
discriminant (Δ): 80162627783461697484809702993018944
Faltings height: 5.3869
naive height: 87.8241
primes of bad reduction: 2, 7, 17, 31, 89
regulator: 2330.942761646422577475980810185663238971978036
submitted by: David Renshaw
submitted at: 2026-10-21 01:49:03 UTC
last updated: 2026-10-21 01:49:03 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 328321. 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 01:49:03 UTC · history