 Cuspidal cubic

The projective algebraic curve $D=\{y^{2}z=x^3\}\subset {\mathbb{P}}^2$ is an irreducible cubic with a cusp at $[0:0:1]$. In the chart $z=1$, its equation is $y^2=x^3$, with parametrization $(x,y)=(t^2,t^3)$. Its affine version $y^2=z^3$, used below, differs only by renaming a coordinate. At the point $[0:1:0]$, the chart $y=1$ gives $z=x^3$, which is smooth and exhibits its unique smooth flex of a cuspidal cubic.