  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.
