TITLE: Infinite family of different prime knots with trivial Alexander polynomial
QUESTION [5 upvotes]: I am looking for infinite families of prime knots that have all Alexander polynomial equals to 1. I wrote "families" (and not "family") since perhaps there are different constructions out there.
Moreover, is there such a family for which all knots are of genus one (just as the Whitehead doubles)?

REPLY [2 votes]: Another family of examples is given by the "generalised Kinoshita-Terasaka" knots, here is a picture from Lickorish' "An introduction to Knot Theory".

Here $d$ is assumed to be even. Of course, this is not a family of genus 1 knots.