Spoiler:
That seems to imply that it is indeed an Aurora class ship, though Aurora were classed as a cruiser at one point i think, so a Battleship could be something entirely different. Also if you want my opinion on the name. Phoenix sounds like a name that would be used. The travellers are scavanger, from the flames of a war with the wraith a being(ship) emerges from the ashes. The symbolism of the pheonix works well in the context of how the ship is discovered/obtained.
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