A jet engine includes an external cowling, a member such as an oil reservoir, and a monitoring system for the member that is able to determine information relating to the member. The external cowling includes a visualization screen that is able to communicate with the monitoring system or directly with the member, so as to display the information specific to the member. When installed in the nacelle of the jet engine, this cowling becomes a smart cowling. The system also includes a method for inspecting a member of an aircraft jet engine and a corresponding computer program.