Hi, it's really a good rank that you have got. One can easily get Government college if he/she lies under rank range from 1-15000 from AP EAMCET. And as you can see that your rank is 12860 so I'm 100% sure that you can get a good government college with due respect of your desired branch.

You can also take help of Careers360 AP EAMCET College Predictor to predict your college on behalf of your rank you have got(link mentioned below);

Good Luck.