  We study the relation between stellar rotation and magnetic activity for a
sample of 134 bright, nearby M dwarfs observed in the Kepler Two-Wheel (K2)
mission during campaigns C0 to C4. The K2 lightcurves yield photometrically
derived rotation periods for 97 stars (79 of which without previous period
measurement), as well as various measures for activity related to cool spots
and flares. We find a clear difference between fast and slow rotators with a
dividing line at a period of ~10d at which the activity level changes abruptly.
All photometric diagnostics of activity (spot cycle amplitude, flare peak
amplitude and residual variability after subtraction of spot and flare
variations) display the same dichotomy, pointing to a quick transition between
a high-activity mode for fast rotators and a low-activity mode for slow
rotators. This unexplained behavior is reminiscent of a dynamo mode-change seen
in numerical simulations that separates a dipolar from a multipolar regime. A
substantial number of the fast rotators are visual binaries. A tentative
explanation is accelerated disk evolution in binaries leading to higher initial
rotation rates on the main-sequence and associated longer spin-down and
activity lifetimes. We combine the K2 rotation periods with archival X-ray and
UV data. X-ray, FUV and NUV detections are found for 26, 41, and 11 stars from
our sample, respectively. Separating the fast from the slow rotators, we
determine for the first time the X-ray saturation level separately for early-
and for mid-M stars.
