  Let $K$ be a tamely ramified abelian cubic number field with discriminant
$D_K$. We prove that the number of trace-one monic integral polynomials with
root field $K$ and height $H$ is equal to the number of ideals in the quadratic
field $\mathbb Q(\sqrt{-3})$ with norm $H^2 D_K^{-1/2}$.
