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By a change of variables we obtain new y-coordinates of el- liptic curves. Utilizing these y-coordinates as meromorphic modular func- tions, together with the elliptic modular function, we generate the fields of meromorphic modular functions. Furthermore, by means of the special values of the y-coordinates, we construct the ray class fields over imagi- nary quadratic fields as well as normal bases of these ray class fields.

CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS USING y-COORDINATES OF ELLIPTIC CURVES