curve #5034

y² = x³ − 2185936516x

a-invariants: [0, 0, 0, -2185936516, 0]
c-invariants: [104924952768, 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): 34974984256
discriminant (Δ): 668486450512929501982223110144
Faltings height: 4.4124
naive height: 76.1295
primes of bad reduction: 2, 97, 241
regulator: 3620.307540504331425198620923419834951477043726
submitted by: David Renshaw
submitted at: 2026-10-21 01:48:55 UTC
last updated: 2026-10-21 01:48:55 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 46754. 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 01:48:55 UTC · history