This is Arwens sword Hadhafang.
Hadhafang was wielded by Elrond during the battle between the Last Alliance of Elves and Men and the forces of the Dark Lord Sauron on the slopes of Mount Doom.
The blade is inscribed with Cirth runes in Sindarin that say "Aen estar Hadhafang i chathol hen, thand arod dan i thang an i arwen.", which translates to "This blade is called Hadhafang, a noble defense against the enemy throng for a noble lady."
More from The Lord of the Rings: The Fellowship of the Ring (2001)