Even-degree hyperelliptic model
= Even-degree hyperelliptic model
If $y^2=f(x)$ with $\deg f=2n$, the coordinates
$$
u=x^{-1},\qquad v=yx^{-n}
$$
give the second chart
$$
v^2=u^{2n}f(u^{-1}).
$$
There are two points $P_+,P_-$ above infinity.
= Even-degree hyperelliptic model
If $y^2=f(x)$ with $\deg f=2n$, the coordinates
$$
u=x^{-1},\qquad v=yx^{-n}
$$
give the second chart
$$
v^2=u^{2n}f(u^{-1}).
$$
There are two points $P_+,P_-$ above infinity.