I have two curves, for example hyperelliptic:


\begin{align}
&y^2 = x^6 + 14x^4 + 5x^3 + 14x^2 + 18, \\\\
&y^2 = x^6 + 14x^4 + 5x^3 + 14x^2 + 5x + 1
\end{align}


Is it possible to check them on birational equivalence (is able one curve be birationally transformed to another?) via some computer algebra system (like GAP, Sage, Magma, Maple, Maxima or something)?


It would be great if such system be free, but it is almost OK if It isn't.



Is it possible to check two curves on birational equivalence by some computer algebra system?
I suppose Magma's `IsIsomorphic` will do the job.


From the [documentation](http://magma.maths.usyd.edu.au/magma/handbook/text/1238#13406)



> 
> IsIsomorphic(C, D) : Crv, Crv -> BoolElt,MapSch
>  Given irreducible curves C and D this function returns true is C and D are isomorphic over their common base field. If so, it also returns a scheme map giving an isomorphism between them. The curves C and D must be reduced. Currently the function requires that the curves are not both genus 0 nor both genus 1 unless the base field is finite. 
> 
> 
> 


Example code in the [web calculator](http://magma.maths.usyd.edu.au/calc/) 



```
K<x,y>:=AffineSpace(Rationals(),2);
C1A:=Curve(K,x^10-1-y^2);
C2A:=Curve(K,x^10-2^10-y^2);
C1:=ProjectiveClosure(C1A);
C2:=ProjectiveClosure(C2A);
IsIsomorphic(C1,C2);

true Mapping from: CrvPln: C1 to CrvPln: C2
with equations :
-2*$.1
    32*$.2
$.3

```

Wish this is implemented in sage.


