curve #5032

y² = x³ − 60310756x

a-invariants: [0, 0, 0, -60310756, 0]
c-invariants: [2894916288, 0]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 964972096
discriminant (Δ): 14039908946045647395917824
Faltings height: 3.5148
naive height: 65.3587
primes of bad reduction: 2, 11, 353
regulator: 329.89626446750193393911104584365069372853837
submitted by: David Renshaw
submitted at: 2026-10-21 01:48:36 UTC
last updated: 2026-10-21 01:48:36 UTC

Witness: 3 independent points log in to add more points →

(-6875, 299475)
(11638, 935088)
(288684, 155051820)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x with n = 7766. Found in an exhaustive ellrank scan of squarefree n <= 20000; one of the smallest n of rank 3.

last edited by David Renshaw at 2026-10-21 01:48:36 UTC · history