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curve #2135

y² + xy + y = x³ − 145x + 692

a-invariants: [1, 0, 1, -145, 692]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 402
discriminant (Δ): -21100176
Faltings height: 0.1591
naive height: 26.6375
primes of bad reduction: 2, 3, 67
regulator: 0.3333883005018298838873982368063812134813
submitted by: hdeping
submitted at: 2026-09-26 10:44:31 UTC
last updated: 2026-09-26 10:44:31 UTC

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

(-5, 38)

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 = -7/3.

last edited by hdeping at 2026-09-27 08:42:29 UTC · history

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