On degrees and birationality of the maps \(X_0(N)\to \mathbb P^2\) constructed via modular forms
In this paper, the author proves a nice formula relating the degree of a curve which is the image of a mapping constructed out of three linearly independent modular forms of the same integral or half-integral weight into the projective space and the degree of that map. Based on this formula, a criterion for the birationality of the map is obtained. As an application, the author gives a formula for the total degree, namely the degree considered as a polynomial of two (independent) variables of the classical modular polynomial. An interesting example is given on birationality which lead to a question on the existence of explicit models for modular curves.
scientific article; zbMATH DE number 6608241