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curve #2133

y² + xy + y = x³ − 311x + 2080

a-invariants: [1, 0, 1, -311, 2080]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 1358
discriminant (Δ): -1358
Faltings height: -0.0533
naive height: 28.8284
primes of bad reduction: 2, 7, 97
regulator: 5.378365919528966679714283252311279390127
submitted by: hdeping
submitted at: 2026-09-26 10:40:23 UTC
last updated: 2026-09-26 10:40:23 UTC

Witness: 1 independent point log in to add more points →

(-11/16, 3055/64)

Commentary

Specialization of the torsion Z/3 family E: y^2+a*x*y+b^3*y=x^3, arising from x/y+y/z+z/x = k with k = -11/1.

last edited by hdeping at 2026-09-27 08:44:20 UTC · history

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