  Characterizing the distribution of flare properties and occurrence rates is
important for understanding habitability of M dwarf exoplanets. The GALEX space
telescope observed the GJ 65 system, composed of the active, flaring M stars BL
Cet and UV Cet, for 15900 seconds (~4.4 hours) in two ultraviolet bands. The
contrast in flux between flares and the photospheres of cool stars is maximized
at ultraviolet wavelengths, and GJ 65 is the brightest and nearest flaring M
dwarf system with significant GALEX coverage. It therefore represents the best
opportunity to measure low energy flares with GALEX. We construct high cadence
light curves from calibrated photon events and find 13 new flare events with
NUV energies ranging from 10^28.5 - 10^29.5 ergs and recover one previously
reported flare with an energy of 10^31 ergs. The newly reported flares are
among the smallest M dwarf flares observed in the ultraviolet with sufficient
time resolution to discern light curve morphology. The estimated flare
frequency at these low energies is consistent with extrapolation from the
distributions of higher-energy flares on active M dwarfs measured by other
surveys. The largest flare in our sample is bright enough to exceed the local
non-linearity threshold of the GALEX detectors, which precludes color analysis.
However, we detect quasi-periodic pulsations (QPP) during this flare in both
the FUV and NUV bands at a period of ~50 seconds, which we interpret as a
modulation of the flare's chromospheric thermal emission through periodic
triggering of reconnection by external MHD oscillations in the corona.
