A knot in S³ is doubly slice if it is the cross-section of an unknotted two-sphere in S⁴. 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.

The first author was supported by a grant from the Simons Foundation and by the National Science Foundation under grant DMS-1505586. The second author was supported by the National Science Foundation under grant DMS-1400543.