The classification of ship is beyond Battleship, which traditionally means "The" capital ship that leads fleets into battle.
They have colonies in them. Often used to set up planetary settlements.
Several different spinal mount high yield weaponry, Which remains classified. It is safe to assume by humans it is beyond Meson or even anti-proton yield.
Launching bays are large enough to hold Human sized battleships, and most of the fighter support is done by Drones that launch in rapid multi-'CHIP' fashion. (Some have commented it looks like a "Pringles" can emptying chips, but they are all Drones.... So thousands are able to be launched almost instantly.)
Typically there are 3 other class of ships found larger then this, one is the already mentioned BattleCON, the other is heavy mover Colony/Tera-forming ships. Then there are the Motherships.
Where as a BattleCON is the long term home for Alronians, with WORLD sized populations. Motherships are country or on small end city sized residents, usually near a BattleCON.
I have the USS Nuclear Nimitz class carrier for size comparison and the smallest nuke the US has ever made just to give idea of size.
Additionally there is a Destroyer and frigate of Altronian origin next to it.
EDMD, sometimes called EDMOND...
Extra Dimensional Mass Disruption
It converts matter to energy and back again. And in any form wanted. It will also 'record' what it scanned or took apart adding the data to their computer systems. (Backing up reality)
A Transporter weapon one might say.
And they have power system internal, but the ships are other dimensional internally. Also existing in a slight sink-well gravity field. (Dimensionally transcendental, not unlike the Tardis meets M.C. Escher..... )
Generally rumored to exist, but never really seen. And when seen most humans treat the those seeing them as lunatic fringe. (Doing drugs or really really drunk)
And the captains of these ships who 'let humans' occasionally see seem to have a weird sense of humor. They love looking for highly intelligent or loners and show up only to vanish... BUT those captains are rare. The really do not want anyone to realize how advanced they are or powerful. Especially since they have no interest in taking over anyone's world. (Guess they view the other races more like entertainment, but occasionally help secretly...)
More on that later.
How long can this ship go before it needs to refuel?
Well, they never need refueling. And they prefer to keep the matter in energy form. (Keep it cycling in a circle)
Power system is not unlike a Zero Point module, but they also have traditional energy systems as back up. Even a blackhole would be nothing to its energy capacity.
Generally their energy signature is zero. Because it is displaced, both the ship and the energy.
They also have multiple isolated energy modules, just in case.
They are not interested in overkill if they do not need to. So other then the visual, you often do not even get a gravity wave from its displacement.
So they don't play fair with conservation of energy at all then. The power systems just make unlimited energy with no input at all, do I have that right?
How big are their power systems in general? Could you put one of these systems in a cell phone sized device?
Does power output depend on system size?
Does the power system require a large startup energy to activate or do you just assemble it and energy flows out?
It is a complicated system.
The limits to its systems is capacity without burnout, and data storage for energy patterns. They tend to hold energy in a pattern that maximizes storage, like said, kinda of like a juggler.
The energy sources are held in a higher dimension, 4th or greater (Which is not time but hyper space).
They tend to hold a EDMD focal point to tap it.
I will likely have something about this later.
But a single Neutron star, even a Blazar, or even a blackhole, even a galactic, is not enough for their needs. At the same time the leave their energy systems at a 'hum' level.
There is always the danger of burning out the universe which they are NOT wanting to do. Lots of safe guards. Even the 'heat' added to the universe seems to accelerate the death of various universes they might visit.
They have the ability to travel any distance almost instantly (4D), time travel (5D, which they rarely do because of causality branches), and even parallel or divergent realities (6D).
Usually though they settle to having a water park on their ship and just relaxing as they do their science hobbies.