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Using data from the extended Kepler mission in K2 Campaign 10 we identify twoeclipsing binaries containing white dwarfs with cool companions that haveextremely short orbital periods of only 71.2 min (SDSS J1205-0242, a.k.a. EPIC201283111) and 72.5 min (SDSS J1231+0041, a.k.a. EPIC 248368963). Despite theirshort periods, both systems are detached with small, low-mass companions, inone case a brown dwarf, and the other case either a brown dwarf or a low-massstar. We present follow-up photometry and spectroscopy of both binaries, aswell as phase-resolved spectroscopy of the brighter system, and use these datato place preliminary estimates on the physical and binary parameters. SDSSJ1205-0242 is composed of a $0.39\pm0.02$M$_\odot$ helium-core white dwarfwhich is totally eclipsed by a $0.049\pm0.006$M$_\odot$ ($51\pm6$M$_J$) browndwarf companion, while SDSS J1231+0041 is composed of a $0.56\pm0.07$M$_\odot$white dwarf which is partially eclipsed by a companion of mass $\lesssim0.095$M$_\odot$. In the case of SDSS J1205-0242 we look at the combinedconstraints from common-envelope evolution and brown dwarf models; the systemis compatible with similar constraints from other post common-envelope binariesgiven the current parameter uncertainties, but has potential for futurerefinement.

Two white dwarfs in ultrashort binaries with detached, eclipsing, likely substellar companions detected by K2