  In this paper, we investigate the Noether symmetries of $F(T)$ cosmology
involving matter and dark energy. In this model, the dark energy is represented
by a canonical scalar field with a potential. Two special cases for dark energy
are considered including phantom energy and quintessence. We obtain $F(T)\sim
T^{3/4},$ and the scalar potential $V(\phi)\sim\phi^2$ for both models of dark
energy and discuss quantum picture of this model. Some astrophysical
implications are also discussed.
