Vrangr was Galbatorix's name for Vrael's sword. Originally called Islingr, 'Light bringer', Vrangr translates in the Ancient Language as 'Awry', though in Du Vrangr Gata it can be translated as 'wandering'. It was taken from Vrael by Galbatorix after Vrael's defeat and death at Ristvak'baen. Vrangr was described as having a stark white blade, hilt and crossguard, and the gem within the pommel was clear "as a mountain spring". After it was taken by Galbatorix, however, Eragon noted that the sword "reminded him of a sun-bleached bone. It was the color of death, not life, and seemed far more dangerous than any shade of black, be it ever so dark." It seemed as if the sword had been "infected" with Galbatorix's darkness and became pale and colorless.
Vrangr's origins go further back than Vrael. In a reddit Q&A session, Christopher confirmed that indeed the sword was once Eragon I's (The first Dragon Rider). This makes it the first sword of the riders'.