The main subject of this paper is a generalization of previous results \textit{R. Schertz} [J. Number Theory 39, 285-326 (1991; Zbl 0739.11052)]. Let \(K\) be an imaginary quadratic number field and \({a}\), \( {b}\) integer ideals in \(K\). The author gives an explicit Galois generator for the ring of integers of the ray class field over \(K\), in relative extensions \(K( {qa})/K( {q})\) with some hypothesis on \( {q}\) and \( {a}\). Starting with new resolvent relations and an analytical interpretation for Galois extensions of fields of elliptic functions with respect to lattices \(\Gamma\subset\hat \Gamma\), he obtains the main result by using singular values of these functions in the complex multiplication context. Then the author applies his result to give explicit generators for Kummer orders considered in \textit{A. Srivastav} and \textit{M. J. Taylor} [Invent. Math. 99, 165-184 (1990; Zbl 0705.14031)].