Coronaviruses, especially SARS-CoV-2, present an ongoing threat for human wellbeing. Consequently, elucidation of molecular determinants of their function and interaction with host is an important task. Whereas some of the coronaviral proteins are extensively characterized, others remain understudied. Here, we use molecular dynamics simulations to analyze the structure and dynamics of the SARS-CoV-2 envelope protein (E protein, a viroporin) in the monomeric form. The protein consists of three parts: hydrophobic α-helical transmembrane domain (TMD) and amphiphilic α-helices H2 and H3, which are connected by flexible linkers. We show that TMD is tilted in the membrane, with phenylalanines Phe20, Phe23 and Phe26 facing the lumen. H2 and H3 reside at the membrane surface. Orientation of H2 is not affected by glycosylation, but strongly influenced by palmitoylation pattern of cysteines Cys40, Cys43 and Cys44. On the other hand, glycosylation affects the orientation of H3 and prevents its stacking with H2. We also find that the E protein both generates and senses the membrane curvature, preferably localizing with the cytoplasmic part at the convex regions of the membrane. Curvature sensing may be favorable for assembly of the E protein oligomers, whereas induction of curvature may facilitate budding of the viral particles. The presented results may be helpful for better understanding of the function of coronaviral E protein and viroporins in general, and for overcoming the ongoing SARS-CoV-2 pandemic.