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

Title & Authors
CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS USING y-COORDINATES OF ELLIPTIC CURVES
Koo, Ja Kyung; Shin, Dong Hwa;

Abstract
By a change of variables we obtain new $\small{y}$-coordinates of elliptic curves. Utilizing these $\small{y}$-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 $\small{y}$-coordinates, we construct the ray class fields over imaginary quadratic fields as well as normal bases of these ray class fields.
Keywords
class field theory;complex multiplication;elliptic and modular units;modular functions;
Language
English
Cited by
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