Traffic congestion is one of the major issues for urban traffic networks. The connected and autonomous vehicles (CAV) is an emerging technology that has the potential to address this issue by improving safety, efficiency, and capacity of the transportation system. In this paper, the problem of optimal trajectory planning of battery-electric CAVs in the context of cooperative crossing of an unsignalized intersection is addressed. An optimization-based centralized intersection controller is proposed to find the optimal velocity trajectory of each vehicle so as to minimize electric energy consumption and traffic throughput. Solving the underlying optimization problem for a group of CAVs is not straightforward because of the nonlinear and nonconvex dynamics, especially when the powertrain model is explicitly modelled. In order to ensure a rapid solution search and a unique global optimum, the optimal control problem (OCP) is reformulated via convex modeling techniques. Several simulation case studies show the effectiveness of the proposed approach and the trade-off between energy consumption and traffic throughput is illustrated.