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

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 $y$-co...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 50; no. 4; pp. 847 - 864
Main Authors Koo, Ja Kyung, Shin, Dong Hwa
Format Journal Article
LanguageKorean
Published 2013
Subjects
class field theory
complex multiplication
elliptic and modular units
modular functions
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO201319850774671
ISSN:0304-9914