Homological monodromy of a genus-one fibered knot
= Homological monodromy of a genus-one fibered knot
For a genus-one fibered knot, the fiber is a once-punctured torus and its monodromy acts on first homology by a matrix $M\in SL_2(\mathbb Z)$. Up to a Laurent unit, the one-variable Alexander polynomial is
$$
\det(tI-M)=t^2-\operatorname{tr}(M)t+1.
$$