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arXiv · 1007.2306

$y$-coordinates of elliptic curves

Ja Kyung Koo·Dong Hwa Shin
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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.

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Ja Kyung Koo, Dong Hwa Shin. 2010-07-14. $y$-coordinates of elliptic curves. https://arxiv.org/abs/1007.2306

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