ALICE at the LHC provides unique capabilities to study charmonium production at low transverse momenta ( p T ). At central rapidity, ( |y|<0.8 ), ALICE can reconstruct J/ ψ via their decay into two electrons down to zero p T . Results at mid-rapidity on the inclusive J/ ψ nuclear modification factor RAA as a function of centrality in Pb-Pb collisions at sNN=5.02 TeV and comparisons to lower energies and models are shown. In addition, the yield of the J/ ψ produced with very low p T in the most peripheral collisions and the J/ ψ elliptic flow ( v2 ) are also presented