Measurements of $\mathrm{J/\psi \rightarrow e^{+}e^{-}}$ with ALICE at the LHC

The ALICE detector provides excellent capabilities to study quarkonium production at the Large Hadron Collider (LHC). Heavy quarkonia, bound states of charm or beauty quark anti-quark pairs such as the $\mathrm{J/\psi}$, are expected to be produced by initial hard processes. Thus they will provide insight into the earliest and hottest stages of AA collisions where the formation of a Quark-Gluon Plasma (QGP) is expected. Furthermore, high-precision data from pp collisions represent an essential baseline for the measurement of nuclear modifications in heavy-ions and serve also as a crucial test for several models of quarkonium hadroproduction. In addition, the study of pA collisions allows to investigate nuclear modifications due to Cold Nuclear Matter (CNM) effects. In ALICE, $\mathrm{J/\psi}$ were measured in pp and Pb--Pb collisions down to $p_{\mathrm T}$ = 0 via their di-electron decay channel in the central barrel ($|y| <$ 0.8). Results on the nuclear modification factor ($R_{\mathrm{AA}}$) at central rapidities in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 2.76$ TeV will be shown and their implications discussed. A separation of the prompt and non-prompt components is also possible down to $p_{\mathrm T}$ of the $\mathrm{J/\psi}$ of 2 GeV/$c$.