TITLE: Is there any genus one knot other than $5_2$ with Alexander polynomial $2t^2-3t+2$?
QUESTION [6 upvotes]: It is known that genus one fibred knots are two trefoils and the figure-eight knot. Is there any characterization of the knot $5_2$? Specifically, is there any other genus one knot that shares the same Alexander polynomial $2t^2-3t+2$ with $5_2$?

REPLY [3 votes]: Maybe a different approach but having the same flavor: Take a (untwisted) Whitehead double of any nontrivial knot $K$. Denote such a double knot $WD(K)$. Construct a satellite knot using $5_2$ knot as the pattern and $WD(K)$ as the companion. Then the Alexander polynomial of the satellite knot is the product of the Alexander polynomials of $5_2$ knot and $WD(K)$. The latter has the trivial Alexander polynomial.