Ekadasi as the name indicates is the 11th day from either the Newmoon day [Amavasya]or from the full moon day[pournami]Among the about 24 -25days in a calendar year the ekadasi which bears the namr Beema Ekadasi is the Ekadasi which falls on the waxing moon[Shukla paksha] period in the Tamil month of Aani.Yogini ekadasi is one which falls in the waning fortnight [krishna paksham]of Aadi month.Vaikunta Ekadasi falls on the waxing fortnight of Margazhi month.Bhishma Ekadasi is one which falls on the waxing  fortnight of Thai month.This day is also celebrated as the Birthday of Sri Vishnu Sahasranamam.Kaikasi Ekadasi is named after a raga which bears the same name.
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Gajendra Moksham story in the Bhagavatham is known to all of us.The Elephant bore the name  Indhra Dyumnan  its previous birth.It was a Pandyan King.Hu hu was a gandharvan who disturbed the rishi Devalar while he was taking bath in a big tank by playfully cutching the rishi's feet.The angered rishi because of forceful awakening from his solitude cursed him to be born as a crocodile.
This Hu Hu as a crocodile caught hold of the leg of Gajendra while he tried to get a lotus by his trunk for offering it to Sri Narayana.The crocodile will not let go the Gajendra .Finally Gajebndra cried aloud to Narayana calling Adhi Moolame.Sri Narayana came immediately mounted on His mount Garuda .He killed the crocodile using His chakra thus liberating the crocodile to attain his Gandharva form ,Hu Hu thus got rid of his curse and Gajendra offered the lotus flower to Sti manNarayana.
it is said the same lotus flower is held in His palms by the Lord of Guruvayur.