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curve #2129

y² + xy = x³ − x² − 132x + 618

a-invariants: [1, -1, 0, -132, 618]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 702
discriminant (Δ): 702
Faltings height: -0.2207
naive height: 26.2663
primes of bad reduction: 2, 3, 13
regulator: 3.365198176839262188210969104763162797608
submitted by: hdeping
submitted at: 2026-09-26 10:38:40 UTC
last updated: 2026-09-26 10:38:40 UTC

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

(7/4, 151/8)

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 08:41:42 UTC · history

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