$y$-coordinates of elliptic curves

Ja Kyung Koo; Dong Hwa Shin

$y$-coordinates of elliptic curves

Number Theory 2013-03-07 v3

Authors: Ja Kyung Koo , Dong Hwa Shin

Abstract

By a change of variables we obtain new $y$ -coordinates of elliptic curves. Utilizing these $y$ -coordinates as modular functions, together with the elliptic modular function, we generate the modular function fields of level $N\geq3$ . Furthermore, by means of the singular values of the $y$ -coordinates we construct the ray class fields modulo $N$ over imaginary quadratic fields as well as normal bases of these ray class fields.

Keywords

elliptic curves curves

Cite

@article{arxiv.1007.2306,
  title  = {$y$-coordinates of elliptic curves},
  author = {Ja Kyung Koo and Dong Hwa Shin},
  journal= {arXiv preprint arXiv:1007.2306},
  year   = {2013}
}

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