curve #5069

y² = x³ − 371819452900x

a-invariants: [0, 0, 0, -371819452900, 0]
c-invariants: [17847333739200, 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): 5949111246400
discriminant (Δ): 3289851512511513307511135864896000000
Faltings height: 5.6965
naive height: 91.5386
primes of bad reduction: 2, 5, 7, 31, 281
regulator: 1753.000526694878701341731480291417686523611011
submitted by: David Renshaw
submitted at: 2026-10-21 02:01:27 UTC
last updated: 2026-10-21 02:01:27 UTC

Witness: 4 independent points log in to add more points →

(-125426, 211335432)
(3373405, 6093815175)
(-1244052754/5041, 99141938921256/357911)
(-8711/4, 227644563/8)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x with n = 609770. Found by a Mestre-Nagao sieve over n <= 10^7 (n = 1,2,3 mod 8), top candidates checked with ellrank.

last edited by David Renshaw at 2026-10-21 02:01:27 UTC · history