A knot is called fibered if its complement is the total space of a fiber
bundle over S1. A fibered knot has monic Alexander polynomial and has
genus equal to half the degree of the Alexander polynomial.
This is sufficient to identify all fibered knots of 11 crossings or less.
For 12 crossing knots, much of the original analysis was carried out by
and Hirasawa. For 12 crossing knots there are 13 which are not fibered
satisfy these conditions.
Four of these 13 were identified by Mikami Hirasawa, and the rest by
Stefan Friedl and Taehee Kim.
Further information on particular knots.