An empowered curved artefact is an item made from a prepared curved artefact during the fifth combat-related assignment given by a God Emissary leader. To empower it, go to the fire altar just outside of the Duel Arena. As you approach, you will receive an option to empower it. Select yes and defeat the level 94 black demon that appears to empower the artefact and complete the combat tasks. If you do not get the option of empowering the artefact when you first run up, try moving away from the altar until it is no longer visible and then run back.