The SL(2,C)-character variety of 818

Abstract

The knot 818 is the first non-arborescent hyperbolic knot. In 2020, Paoluzzi and Porti found its SL(2,C)-character variety with the aid of a computer, but many details were omitted. In this paper, we determine the character variety by a software-free procedure, which is easy to follow and enlightening. Along the way, we develop an efficient method for working with simultaneous conjugacy classes of four elements of SL(2,C).