Editing Hyperelliptic curve (section)

==Genus==

The degree of the polynomial determines the genus of the curve: a polynomial of degree 2''g'' + 1 or 2''g'' + 2 gives a curve of genus ''g''. When the degree is equal to 2''g'' + 1, the curve is called an [[imaginary hyperelliptic curve]]. Meanwhile, a curve of degree 2''g'' + 2 is termed a [[real hyperelliptic curve]]. This statement about genus remains true for ''g'' = 0 or 1, but those special cases are not called "hyperelliptic". In the case ''g'' = 1 (if one chooses a distinguished point), such a curve is called an [[elliptic curve]].