  We consider reshaping of closed Janus filaments acquiring intrinsic curvature
upon actuation of an active component -- a nematic elastomer elongating upon
phase transition. Linear stability analysis establishes instability thresholds
of circles with no imposed twist, dependent on the ratio $q$ of the intrinsic
curvature to the inverse radius of the original circle. Twisted circles are
proven to be absolutely unstable but the linear analysis well predicts the
dependence of the looping number of the emerging configurations on the imposed
twist. Modeling stable configurations by relaxing numerically the overall
elastic energy detects multiple stable and metastable states with different
looping numbers. The bifurcation of untwisted circles turns out to be
subcritical, so that nonplanar shapes with a lower energy exist at $q$ below
the critical value. The looping number of stable shapes generally increases
with $q$.
