  We determine the minimal number of colors for non-trivial
$\mathbb{Z}$-colorings on the standard minimal diagrams of
$\mathbb{Z}$-colorable torus links. Also included are complete classifications
of such $\mathbb{Z}$-colorings and of such $\mathbb{Z}$-colorings by only four
colors, which are shown by using rack colorings on link diagrams.
