Homomorphisms and Isomorphisms · Hard problem

Let $\varphi: \mathbb Z_{30} \to \mathbb Z_{30}$ send $k$ to $12k \bmod 30$. The image of $\varphi$ is a cyclic subgroup of $\mathbb Z_{30}$. How many elements of $\mathbb Z_{30}$ generate this image subgroup (viewing the image as a standalone cyclic group)?