SARS-CoV-2 contains four structural proteins in its genome. These proteins aid in the assembly and budding of new virions at the ER-Golgi intermediate compartment (ERGIC). Current fundamental research efforts largely focus on one of these proteins - the spike (S) protein. Since successful antiviral therapies are likely to target multiple viral components, there is considerable interest in understanding the biophysical role of its other structural proteins, in particular structural membrane proteins. Here, we have focused our efforts on the characterization of the full-length envelope (E) protein from SARS-CoV-2, combining experimental and computational approaches. Recombinant expression of the full-length E protein from SARS-CoV-2 reveals that this membrane protein is capable of independent multimerization, possibly as a tetrameric or smaller species. Fluorescence microscopy shows that the protein localizes intracellularly, and coarse-grained MD simulations indicate it causes bending of the surrounding lipid bilayer, corroborating a potential role for the E protein in viral budding. Although we did not find robust electrophysiological evidence of ion-channel activity, cells transfected with the E protein exhibited reduced intracellular Ca2+, which may further promote viral replication. However, our atomistic MD simulations revealed that previous NMR structures are relatively unstable, and result in models incapable of ion conduction. Our study highlights the importance of using high-resolution structural data obtained from a full-length protein to gain detailed molecular insights, and eventually permitting virtual drug screening.