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 $5\_2$?



Is there any genus one knot other than $5_2$ with Alexander polynomial $2t^2-3t+2$?
Ian Agol, in the comments says:



> 
> Yes, there should be plenty. Think of the Seifert surface for the 5\_2
> knot as a disk with two strips (1-handles) attached. By tying knots
> into the strips (with zero framing so as not to change the linking
> form), you can obtain many knots with a genus 1 Sefert surface with
> the same Seifert form and hence same Alexander polynomial.
> 
> 
> 


