curve #5030

y² = x³ − 44502241x

a-invariants: [0, 0, 0, -44502241, 0]
c-invariants: [2136107568, 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): 1424071712
discriminant (Δ): 5640604089037380350945344
Faltings height: 3.4388
naive height: 64.4468
primes of bad reduction: 2, 7, 953
regulator: 669.56984537858352343841568723719390634759801
submitted by: David Renshaw
submitted at: 2026-10-21 01:48:28 UTC
last updated: 2026-10-21 01:48:28 UTC

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

(-5103, 306936)
(271663, 141551592)
(-99225/169, 353752560/2197)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x with n = 6671. 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 01:48:28 UTC · history