Superelliptic curve
In mathematics, a superelliptic curve is an algebraic curve defined by an equation of the form y m = f ( x ) , {\displaystyle y^{m}=f(x),} where m ≥ 2 {\displaystyle m\geq 2} is an integer and f is a polynomial of degree d ≥ 3 {\displaystyle d\geq 3} with coefficients in a field k {\displaystyle k} ; more precisely, it is the smooth projective curve whose function field defined by this equation. The case m = 2 {\displaystyle m=2} and d = 3 , 4 {\displaystyle d=3,4} is an elliptic curve, the case m = 2 {\displaystyle m=2} and d ≥ 5 {\displaystyle d\geq 5} is a hyperelliptic curve, and the case m = 3 {\displaystyle m=3} and d ≥ 4 {\displaystyle d\geq 4} is an example of a trigonal curve.