curve #5131

y² = x³ − 9x

a-invariants: [0, 0, 0, -9, 0]
c-invariants: [432, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 288
discriminant (Δ): 46656
Faltings height: -0.4147
naive height: 18.2053
primes of bad reduction: 2, 3
regulator: 1
submitted by: hdeping
submitted at: 2026-10-21 05:06:10 UTC
last updated: 2026-10-21 05:06:10 UTC

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