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 . The general formula of Hyperelliptic curve over a finite field is given by where 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.