Let $X \subset \mathbf{P}^{2}(\mathbf{C})$ be the projective closure of the affine curve $y^{3}=x^{4}+1$. Let $\omega$ denote the differential $d x / y^{2}$. Show that $X$ is smooth, and compute $v_{p}(\omega)$ for all $p \in X$.

Calculate the genus of $X$.