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

  • Koo, Ja Kyung (Department of Mathematical Sciences, KAIST) ;
  • Shin, Dong Hwa (Department of Mathematics, Hankuk University of Foreign Studies)
  • Received : 2012.04.16
  • Published : 2013.07.01

Abstract

By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-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 $y$-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

Acknowledgement

Supported by : NRF of Korea

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