In mathematics, a superelliptic curve is an algebraic curve defined by an equation of the form y m = f, {\displaystyle y^{m}=f,} 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. Wikipedia