We show that the modular equation ${phi}^{T_n}_m$ (X, Y) for the Thompson series $T_n$ corresponding to ${Gamma}_0$(n) gives an affine model of the modular curve $X_0$(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 $T_n(z);and;T_n$(mz).