After the group kills the Troll's trying to eat them, they go to their cave where they find a collection of Elf swords. Gandalf gives Bilbo a magic Elf sword that glows when Orcs/Trolls are near.
The Elf City
Later in the film after escaping from the Orcs the group finds themselves in the Elf city. They share a dinner with the Elfs, where they hear stories and names about 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 it's story?