  A knot in the three-sphere is doubly slice if it is the cross-section of an
unknotted two-sphere in the four-sphere. For low-crossing knots, the most
complete work to date gives a classification of doubly slice knots through 9
crossings. We extend that work through 12 crossings, resolving all but four
cases among the 2,977 prime knots in that range. The techniques involved in
this analysis include considerations of the Alexander module and signature
functions as well as calculations of the twisted Alexander polynomials for
higher-order branched covers. We give explicit illustrations of the double
slicing for each of the 20 knots shown to be smoothly doubly slice. We place
the study of doubly slice knots in a larger context by introducing the double
slice genus of a knot.
