I just got my first class artifact for my Siren. On the skills/powers page, I notice it says it is level 1 in the description and the number 1 appears beside its icon. Does that simply denote the level of the item, like owning a level X required weapon, or is it something that can improve somehow?
You will find higher level artifacts (up to a level of, I believe, 6) through gameplay as rare drops from enemies/chests. You will only keep the highest level drop of a given element (explosive, fire, corrosive, shock) per character. I'm not sure if there's any trick to finding artifacts as drops, they seem to occur like any other uncommon drop.