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Kurma the tortoise is half-man, half-tortoise. He is often depicted with four arms. In his upper two hands he holds a disc and a conch shell. In his lower two hands he holds a club and a lotus. Sometimes these two hands are depicted in protection and boon-giving postures (mudras).
The demons were winning the battle against the gods. The gods came to Vishnu for help. He told the gods to churn the ocean to produce Amrita is the nectar for immortality.

The demons and demigods started to produce nectar from the sea by using the Mandara Mountain as the churning rod. The snake Vasoeki was used as a rope to churn. During churning the Madara Mountain started sinking in the ocean. Vishnu came as Kurma. Kurma’s shell served as the pivot for the Mandarachala Mountain.
Vishnu helped the gods to obtain the produced Amrita .The gods won the battle against the demons and the world was saved.
The first liquid that was produced during churning was a deadly poison. Shiva drank the poison. That is why he has a blue throat.