This is a beautiful valve. The 13E1 is a beam tetrode designed for DC control applications. The ratings are absolute maxima and based on its intended use as a series pass devices for generating stabilised HT rails.
Inside the anode can be seen two separate cathode and grid structures, both connected in parallel within the envelope.
The picture shows both the valves, and especially the golden control grid wire.
In this photograph of the bottom of the envelope, the insulated heater wires can clearly be seen. Also visible are the glass pips that the pins pass through.
The wide glass tube envelope is 60 mm in diameter and, excluding the B7A base pins, is 117 mm tall.
References: Datasheet & 1040. Type 13E1 was first introduced in 1955.