For an integer $N \ge 1$, the complex analytic compact modular curve $X_0(N)(\mathbb C)$ is obtained by compactifying $\Gamma_0(N)\backslash\mathfrak H$, and its non-cuspidal points classify pairs $(E,C)$ consisting of an elliptic curve $E$ over $\mathbb C$ and a cyclic subgroup $C \subset E[N]$ of order $N$.