1) Function TransformationCurves( $C:y^{\text{2}}=f\left(x\right)$ ).

2) Computation of the roots of f.

3) Choose a root of f.

4) $a\leftarrow f\left(a\right)\mathrm{<mo>\; =\; </mo>0}$ .

5) Compute: $F=x^{2g+2}f\left(\frac{1+ax}{x}\right)$ .

6) $C^{\prime }$ = Hyperelliptic(F).

7) Return $C^{\prime }$ .