Abstract

By a change of variables we obtain new <TEX>$y$</TEX>-coordinates of elliptic curves. Utilizing these <TEX>$y$</TEX>-coordinates as meromorphic modular functions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the <TEX>$y$</TEX>-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.

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