Determining whether an ideal is prime in $\Bbb Q[X,Y,Z,W]$ Is the ideal $(XZ^2-W^3, XW^2-Y^4, Y^4Z^2-W^5)$ prime in $\mathbb{Q}[X,Y,Z,W]$?
I tried writing the ideal as the kernel of a parametrization of the form $f(X) = T^a$, $f(Y) = T^b$, $f(Z) = T^c$ and $f(W)=T^d$ but it seems to be quite important how to choose $a,b,c,d$ in order to actually prove that the ideal is the kernel of such a homomorphism and most of the things I tried do not work.
I also got a hint that one of the generators can be written in terms of the other two, but I do not see how this helps. Thank you for your help!

Note that
$$Y^4Z^2-W^5=W^2(XZ^2-W^3)-W^2XZ^2+Y^4Z^2=W^2(XZ^2-W^3)+Z^2(Y^4-XW^2).$$
So the ideal $I=(XZ^2-W^3, Y^4-XW^2)$.
