curve #5028

y² = x³ − 23961025x

a-invariants: [0, 0, 0, -23961025, 0]
c-invariants: [1150129200, 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): 766752800
discriminant (Δ): 880432672796160121000000
Faltings height: 3.2840
naive height: 62.5894
primes of bad reduction: 2, 5, 11, 89
regulator: 171.32411051695053407095125618871559280312194
submitted by: David Renshaw
submitted at: 2026-10-21 01:48:21 UTC
last updated: 2026-10-21 01:48:21 UTC

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

(-4356, 147378)
(-55, 36300)
(-143055/49, 72817800/343)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x with n = 4895. 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 01:48:21 UTC · history