Past exam of the geometry course of the University of Oxford / 2011 / 5 / c / Solution

Compose the preceding transformations, applying ${\sigma }_{\lambda }$ first and then ${\tau }_{1/\lambda }$. With the square-root convention already specified,This invertible projective transformation fixes $[0:1:0]$ and carries $C_{\lambda }$ to $C_{1-1/\lambda }$. It is important to retain the sign of the chosen lift on the $y$ coordinate when computing its order later.