  In this paper we compute the degree of a curve which is the image of a
mapping $z\longmapsto (f(z): g(z): h(z))$ constructed out of three linearly
independent modular forms of the same even weight $\ge 4$ into $\mathbb P^2$.
We prove that in most cases this map is a birational equivalence and defined
over $\mathbb Z$. We use this to construct models of $X_0(N)$, $N\ge 2$, using
modular forms in $M_{12}(\Gamma_0(N))$ with integral $q$--expansion. The models
have degree equal to $\psi(N)$ (a classical Dedekind psi function). When genus
is at least one, we show the existence of models constructed using cuspidal
forms in $S_4(\Gamma_0(N))$ of degree $\le \psi(N)/3$ and in
$S_6(\Gamma_0(11))$ of degree 4. As an example of a different kind, we compute
the formula for the total degree i.e., the degree considered as a polynomial of
two (independent) variables of the classical modular polynomial (or the degree
of the canonical model of $X_0(N)$).
