Real hyperelliptic curve

There are two types of hyperelliptic curves, a class of algebraic curves: real hyperelliptic curves and imaginary hyperelliptic curves which differ by the number of points at infinity. Hyperelliptic curves exist for every genus ${\displaystyle g\geq 1}$. The general formula of Hyperelliptic curve over a finite field ${\displaystyle K}$ is given by

where ${\displaystyle h(x),f(x)\in K}$ satisfy certain conditions. In this page, we describe more about real hyperelliptic curves, these are curves having two points at infinity while imaginary hyperelliptic curves have one point at infinity.