The sword of Aragorn, was the sword Aragorn II Elessar, wielded. In Lothlórien, Galadriel and Celeborn gifted Aragorn a sheath for his sword. There was an enchantment upon the scabbard so that the blade that was drawn from it would not be stained or broken, even in defeat.
In Rohan, Aragorn used it as evidence of his heritage when he, Legolas, and Gimli first meet Éomer. He reluctantly sets it aside before meeting Théoden, telling Háma that death will come to any man except himself who drew it from its scabbard.
If Aragorn took the Paths of the Dead, with the power of his sword he would be able to call forth an army greater than any living army, and with that army he would have a chance to stop the Corsairs and save Arwen. It was this sword that manages to have effect on the leader of the residents of the Paths of the Dead, unlike Legolas's bow or Gimli's axe, as shown in the movie. Aragorn uses the sword as his primary weapon for the rest of the film. In a deleted scene, just before the battle before the Morannon, Aragorn confronts Sauron through Denethor II's Palantír, and goads him by showing him his sword.
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