  While brown dwarfs show similarities with stars in their early life, their
spin evolution is much more akin to that of planets. We have used lightcurves
from the K2 mission to measure new rotation periods for 18 young brown dwarfs
in the Taurus star-forming region. Our sample spans masses from 0.02 to 0.08
Msol and has been characterised extensively in the past. To search for periods,
we utilize three different methods (autocorrelation, periodogram, Gaussian
Processes). The median period for brown dwarfs with disks is twice as long as
for those without (3.1 vs. 1.6 d), a signature of rotational braking by the
disk, albeit with small numbers. With an overall median period of 1.9 d, brown
dwarfs in Taurus rotate slower than their counterparts in somewhat older (3-10
Myr) star-forming regions, consistent with spin-up of the latter due to
contraction and angular momentum conservation, a clear sign that disk braking
overall is inefficient and/or temporary in this mass domain. We confirm the
presence of a linear increase of the typical rotation period as a function of
mass in the sub-stellar regime. The rotational velocities, when calculated
forward to the age of the solar system assuming angular momentum conservation,
fit the known spin-mass relation for solar system planets and extra-solar
planetary-mass objects. This spin-mass trend holds over six orders of magnitude
in mass, including objects from several different formation paths. Our result
implies that brown dwarfs by and large retain their primordial angular momentum
through the first few Myr of their evolution.
