Certain CM class fields with smaller generators

We introduce an algorithm that computes explicit class fields of an imaginary quadratic field $K$ for a given modulus $\mathfrak{f}\subset\mathcal{O}_K$ more efficiently than the use of their classical counterparts. Therein, we prove the fact that certain values of a simple quotient of Siegel $\phi$-function are elements in the ray class field $K_{\mathfrak{f}}$ of $K$.