  Based on a data sample of $(10087\pm44)\times10^6$ $J/\psi$ events collected
with the BESIII detector, the branching fraction of
$J/\psi\rightarrow\bar{\Lambda}\pi^{+}\Sigma^{-}+c.c.$ is measured to be
$(1.221\pm 0.002\pm 0.038)\times10^{-3}$, and the branching fraction of its
isospin partner mode $J/\psi\rightarrow\bar{\Lambda}\pi^{-}\Sigma^{+}+c.c.$ is
measured to be $(1.244\pm 0.002\pm 0.045)\times10^{-3}$ with improved
precision. Here the first uncertainties are statistical and the second ones
systematic. The isospin symmetry of the $\Sigma$ baryon in charmonium hadronic
decay and the "$12\%$ rule" are tested, and no violation is found. The
potential of using these channels as $\Sigma$ baryon sources for nuclear
physics research is studied, and the momentum and angular distributions of
these sources are provided.
