The Songbird Alchemist (Fullmetal fanfic)

Edward and Alphonse Elric believed in the alchemist's law of equivalent exchange when they lost their bodies in an etempt to transmutate their mother back to life and lost Al's body and Ed's right arm and left leg in exchange

Years later when they become state alchemists they learn that a very powerful girl only known as the songbird alchemist can peform alchemy without the law of equivalent exchange. They decide to head to a place known as Cristo ruins to find if the rumors are true and are surprised with what they find.