What important clue did Elrond find and what in particular knowledge did he use to find it?

Elrond found an important clue in the form of a piece of a broken sWord, which was identified as a remnant of Narsil, the sWord that had been used to cut the One Ring from Sauron's hand. His extensive knowledge of history and ancient artifacts, particularly the lore surrounding the Rings of Power, allowed him to recognize the significance of the sWord and its connection to the fate of Middle-earth. This clue ultimately helped in understanding the importance of the Ring and the need to destroy it.