In this paper we consider the optimal operation of an energy community receiving incentives for energy virtually shared among the community members. A similar incentive scheme for renewable energy communities is adopted in Italy since 2020. The operational problem is formulated as the maxi-mization of the profit of the community over a given time horizon. The profit includes the incentive for the virtual self-consumption. The optimization exploits all available sources of flexibility, such as controllable loads and generators, and battery energy storage systems. Compared to previous work of the authors, the mixed-integer formulation proposed in this paper requires a smaller number of continuous variables. Still, the number of binary variables may be prohibitive when the size of the community grows. For this reason, an equivalent formulation in the form of convex maximization is derived, involving only continuous variables. We show examples where the latter problem can be solved in reasonable time, while the solution process of the mixed integer problem gets stuck. Moreover, a simple strategy to fairly redistribute the community benefits among its members is discussed.