Construction of class fields over imaginary quadratic fields using y-coordinates of elliptic curves
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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 fieldsof meromorphic modular functions. Furthermore, by means of the specialvalues 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.
Abstract
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 fieldsof meromorphic modular functions. Furthermore, by means of the specialvalues 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.
참고문헌 (14)
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