Thanks for the question 

With 13000 rank, i am enlisting few colleges where you can easily get CSE branch-

Mysore College of Engineering and Management, Mysore

NIE Institute of Technology, Mysore

Dayananda Sagar Academy of Technology and Management, Bangalore

SJB Institute of Technology, Bangalore

Acharya Institute of Technology, Bangalore

Mangalore Institute of Technology and Engineering, Mangalore

Reva University, Bangalore

Bangalore College of Engineering and Technology, Bangalore

Ms Ramaiah Institute of Technology 

KLS Vishwanathrao Deshpande Rural Institute of Technology, Haliyal

All the best