The character variety of some classes of rational knots

We propose a method to determine the character variety of a class J(m,n) of rational knots, which includes the twist knots. The defining polynomials depend only on the variables m and n. This answers for these classes of knots a question posed in [H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, On the character variety of group representations of a 2-bridge link p/3 into PSL(2,C), Bot. Soc. Mat. Mexicana 37(2) (1992) 241-262], and allows us to give an easy geometrical description of the considered character variety. Our results are obtained by using special presentations of the knot groups whose relators are palindromes.