Adjoint twisted Alexander polynomials for parabolic representations of genus one two-bridge knots

In previous papers [19, 17], we computed the twisted Alexander polynomials and adjoint twisted Alexander polynomials for nonabelian $\mathrm{SL}_2(\mathbf{C})$-representations of genus one two-bridge knots. In this paper, we investigate their properties. When the $\mathrm{SL}_2(\mathbf{C})$-representation of a genus one two-bridge knot is parabolic, we show that (1) the coefficient of the highest degree term of the adjoint twisted Alexander polynomial is a rational multiple, independent of the representation, of the square of the twisted Alexander polynomial at $t=1$, and (2) the adjoint twisted Alexander polynomial is a monic polynomial if and only if the knot is fibered.