In this paper, we study the energy efficiency (EE) of a downlink multi-cell massive distributed antenna system (DAS) in the presence of pilot contamination (PC), where the antennas are clustered on the remote radio heads (RRHs). We employ a practical power consumption model by considering the transmit power, the circuit power, and the backhaul power, in contrast to most of the existing works which focus on co-located antenna systems (CAS) where the backhaul power is negligible. For a given average user rate, we consider the problem of maximizing the EE with respect to the number of each RRH antennas $n$, the number of RRHs $M$, the number of users $K$, and study the impact of system parameters on the optimal $n$, $M$ and $K$. Specifically, by applying random matrix theory, we derive the closed-form expressions of the optimal $n$, and find the solution of the optimal $M$ and $K$, under a simplified channel model with maximum ratio transmission. From the results, we find that to achieve the optimal EE, a large number of antennas is needed for a given user rate and PC. As the number of users increases, EE can be improved further by having more RRHs and antennas. Moreover, if the backhauling power is not large, massive DAS can be more energy efficient than massive CAS. These insights provide a useful guide to practical deployment of massive DAS.