I have a few friends from Amrita University, so I can give you some information regarding the required cutoff for admission at the institute.
With this rank, you will get admission at Amrita University but for getting a CSE branch you will need a rank below 3000. If your rank is above 3000, then you may ask the management and you might get Bangalore or Amritapuri branch for the CSE.
If you are not in the Tamil Nadu state quota category you cannot get a seat with the counseling process, you will need to contact the college for more details. If you belong to the state quota then you might get preference and get the branch of your choice.