Title: On a simple model of X_0(N),
Abstract: We find plane models for all $X_0(N)$, $N\geq 2$. We observe a map from the
modular curve $X_0(N)$ to the projective plane constructed using modular forms
of weight $12$ for the group $\Gamma_0(N)$; the Ramanujan function $\Delta$,
$\Delta(N\cdot)$ and the third power of Eisestein series of weight $4$,
$E_4^3$, and prove that this map is birational equivalence for every $N\geq 2$.
The equation of the model is the minimal polynomial of $\Delta(N\cdot)/\Delta$
over $\mathbb{C}(j)$.