Real hyperelliptic curve

A hyperelliptic curve is a class of algebraic curves. 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. There are two types of hyperelliptic curves: real hyperelliptic curves and imaginary hyperelliptic curves which differ by the number of points at infinity. 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.

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