After the group kills the Trolls trying to eat them, they go to their cave where they find a collection of Elven swords. Gandalf gives Bilbo a sword that glows when Orcs are near.
The Elf City
Later in the film, after escaping from the Orcs, the group find themselves in Rivendel. They share a dinner with the Elves, where they hear the names and histories of the swords they found.
Bilbo pulls out his sword, but a Dwarf sitting beside him tells him to put it away, because it was to small to have a story.
What was the name of Bilbo's sword, and what was its story?