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.