i dont know if theyre actually "core" but i do these, dont know names:
1. lay on my back on the floor and raise my legs, knees locked, above my head, past 90 degrees. once at the highest point i lift my ass and lower back as high off the floor as i can and repeat from floor to the last step.
2. lay on my back, and spin 360 kicking my feet as if someone is standing above me (bjj open guard style) rocking and kicking my legs. using my stomach back and leg muscles to rotate me