In this question we work over an algebraically closed field of characteristic zero. Let $X^{o}=Z\left(x^{6}+x y^{5}+y^{6}-1\right) \subset \mathbb{A}^{2}$ and let $X \subset \mathbb{P}^{2}$ be the closure of $X^{o}$ in $\mathbb{P}^{2} .$

(a) Show that $X$ is a non-singular curve.

(b) Show that $\omega=d x /\left(5 x y^{4}+6 y^{5}\right)$ is a regular differential on $X$.

(c) Compute the divisor of $\omega$. What is the genus of $X$ ?