Abstract
We show that the modular equation <TEX>${\phi}^{T_n}_m$</TEX> (X, Y) for the Thompson series <TEX>$T_n$</TEX> corresponding to <TEX>${\Gamma}_0$</TEX>(n) gives an affine model of the modular curve <TEX>$X_0$</TEX>(mn) which has better properties than the one derived from the modular j invariant. Here, m and n are relative prime. As an application, we construct a ring class field over an imaginary quadratic field K by singular values of <TEX>$T_n(z)\;and\;T_n$</TEX>(mz).
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