According to Wuunferth the Unliving, the Necromancer Amulet is a legendary enchanted amulet of immense power and once belonged to Mannimarco, the King of Worms. At the end of Blood on the Ice...
Amulets and Necklaces are worn on the neck by various characters and the Dragonborn. Only one can be worn at a time. They can be found as random loot around Skyrim, taken by pickpocketing them from characters, or killing them and looting their body.
This quest begins when the Dragonborn strikes up a conversation with Torbjorn Shatter-Shield. The latter mentions that he and his wife are in mourning for their daughter, Friga, who was a victim of "the Butcher". He asks the Dragonborn for an Amulet of Arkay to help ease his wife's mourning.
The Amulet of the Elder Council is an unenchanted amulet. A variation called the jeweled amulet is a quest item received from Amaund Motierre during the quest "The Silence Has Been Broken.". It can only be found under its proper name in the Skyrim Testing Hall.