How do I prove that for an elliptic curve the only isomorphism is the following way?

Question

I habe an elliptic curve over a field $K$ given by:

$$E: y^2=x^3+Ax+B$$

Now I want to show that all changes of variables preserving this form are given by $x=u^2x$ and $y=u^3y$ with $u \in \bar{K}^*$... Any idea how to show it?