I told you of two kinds of serpent: the good one and the bad one. The former is what gives the nectar. The latter gives only poison. It is this latter one that is destroyed by the peacock of Lord SuBrahmanya and the Garuda-vehicle of Lord Vishnu. When the former (the good one, the nectar-showering serpent) is the form of SuBrahmanya, we say He is nAga-rAja, the King of snakes.
It is the same one that Lord Vishnu is having as his bed-rest. It is the same one that Lord Nataraja is having around his raised foot. And it is the same one who came as Patanjali and taught the yoga-shAstra, where, even if the kuNDalinI yoga is not particularly mentioned, the kuNDalinI that arises out of that yoga is of the serpent form.