The morphism $\phi: k \to V$ given by $\phi(t)= (t^2,t^3) $ is not an isomorphism

This statement is given as application of earlier results on the page $22 $ of the Daniel Perrin's Algebraic Geometry textbook from which I am self studying.

Here $k$ is a commutative field and $V$ is a affine algebraic set.

Application $6.9$ The morphism $\phi: k \to V=V(Y^2-X^3)$ given by $\phi(t)= (t^2,t^3) $ is not an isomorphism.

The author doesn't gives a detailed proof but just a couple of ideas using which I am not able to proof what is asked.

Can you please give a detailed proof of this?

I shall be grateful