Hyperelliptic curve

In algebraic geometry, a hyperelliptic curve is an algebraic curve given by an equation of the form

where f(x) is a polynomial of degree n > 4 with n distinct roots. A hyperelliptic function is an element of the function field of such a curve or possibly of the Jacobian variety on the curve, these two concepts being the same in the elliptic function case, but different in the present case. Fig. 1 is the graph of where