Singularity of $V(Y^2-X^3-X)\to\mathbb{P}^1$

Question

In "The Arithmetic of Elliptic Curves, in example I.3.7, Silverman define $\Phi:V(Y^2Z-X^3-X^2Z)\to\mathbb{P}^1$ with $\Phi(X,Y,Z)=[Y,X]$. He says that $\Phi$ is not regular at $[0,0,1]$. How to prove it?