  The Noether gauge symmetry approach is revisited to study various quintom
scenarios (those that arise by the presence of two dynamical scalar fields) to
comprehend the role of dark energy in our universe. For such models, we obtain
smooth parameterizations of the equation of state of dark energy across the
boundary of cosmological constant $w_{\Lambda}=-1$. This study gives rise to
two new cases of the potential $V(\phi, \sigma)$, due to a quintom field in
which nonlinear coupling of the scalar fields arise. Besides we report that a
few cases of Noether gauge symmetries and their invariants in [Adnan Aslam, et.
al., Astrophys Space Sci (2013), 348:533-540] are incorrect. Consequently, the
given cosmological model in their paper is not a feasible quintom model.
