Ja Kyung Koo, Dong Hwa Shin
Published 2010-07-14, updated 2013-03-06Version 3
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.
Comments: We changed its title and shortened its contents
Isogeny relations in products of families of elliptic curves
Rank statistics for a family of elliptic curves over a function field
Elliptic curves and analogies between number fields and function fields
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