On primitive elements of algebraic function fields and models of \(X_0(N)\) (Q2038987)

In the present paper, the authors study maps from the modular curves \(X_0(N)\) (\(N\geq 1\)) into the projective plane \(\mathbb{P}^2\) constructed via modular forms of the same weight based on the theory of primitive elements in finite separable field extensions. They prove that in most of the cases the constructed maps are birational.