Are these two curves birationally equivalent? I'm trying to work out if the following two curves are birationally equivalent:
$$Y^2 = 2X^4 + 17X^2 + 12$$
$$2Y^2 = X^4 - 17$$
(I'm considering the above as the affine shorthands for the projective curves they represent)
I saw elsewhere online that I could use the following code in magma:
K<x,y>:=AffineSpace(Rationals(),2);
C1A:=Curve(K,2*x^4+17*x^2+12-y^2);
C2A:=Curve(K,x^4-17-2*y^2);
C1:=ProjectiveClosure(C1A);
C2:=ProjectiveClosure(C2A);
IsIsomorphic(C1,C2);

However this gives me a runtime error.
Can anyone see an error with my code/approach above? Alternatively, if there's another way I can check if two curves like the above are birationally equivalent either by hand or by using Magma / Sage or something similar that would be really helpful.

In PARI/GP:
? ellinit(ellfromeqn(2*x^4+17*x^2+12-y^2)).j
%1 = 384200066/111747
? ellinit(ellfromeqn(x^4-17-2*y^2)).j
%2 = 1728

The curves are not birationally equivalent because they have different $j$-invariants.
