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curve #2130

y² + xy = x³ − x² − 141x + 681

a-invariants: [1, -1, 0, -141, 681]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 378
discriminant (Δ): -756
Faltings height: -0.2074
naive height: 26.4639
primes of bad reduction: 2, 3, 7
regulator: 1.302973442526375750235084318782954056302
submitted by: hdeping
submitted at: 2026-09-26 10:38:44 UTC
last updated: 2026-09-26 10:38:44 UTC

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

(4, 11)

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 = 45-9/1.

last edited by hdeping at 2026-09-27 08:41:58 UTC · history

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