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 three-genus equal to half the degree of the Alexander polynomial. This is sufficient to identify all fibered knots of 11 crossings or fewer.
For 12 crossing knots, much of the original analysis was carried out by Stoimenow and Hirasawa.
12n_{57, 210, 214, 258, 279, 382, 394, 464, 483, 535, 650, 801, 815}: These are the thirteen 12 crossing knots for which the Alexander polynomial is monic and has degree twice the three-genus of the knot, but which are not fibered. Four of these were found by Mikami Hirasawa and the rest by Stefan Friedl and Taehee Kim.