  We propose a candidate for the hidden order in URu2Si2: a rank-5 E type spin
density wave between Uranium 5f crystal field doublets breaking time reversal
and lattice tetragonal symmetry in a manner consistent with recent torque
measurements [R. Okazaki et al, Science 331, 439 (2011)]. We argue that
coupling of this order parameter to magnetic probes can be hidden by crystal
field effects, while still having significant effects on transport,
thermodynamics and magnetic susceptibilities. In a simple tight-binding model
for the heavy quasiparticles, we show the connection between the hidden order
and antiferromagnetic phases arises since they form different components of
this single rank-5 pseudo-spin vector. Using a phenomenological theory, we show
the experimental pressure-temperature phase diagram can be qualitatively
reproduced by tuning terms which break pseudo-spin rotational symmetry. As a
test of our proposal, we predict the presence of small magnetic moments in the
basal plane oriented in the [110] direction ordered at the wave-vector (0,0,1).
