 Hyperelliptic curve

A hyperelliptic curve of genus at least two admits a degree-two map to ${\mathbb{P}}^1$ and can be represented in characteristic other than two by an equation $y^2=f(x)$ with $f$ square-free.

A hyperelliptic curve is a type of algebraic curve that generalizes the properties of elliptic curves. Specifically, it is defined over a field (often the field of complex numbers, rational numbers, or finite fields) and can be described by a specific kind of equation.