Back pain with elliptical

Hi I'm new to this forum.....two years ago, I did the elliptical machine at the university's gym three times a week.  I loved it!  It was a great way to burn a lot of calories and get my heart rate up.  Problem is, I began to have really bad back pain.  My doctor told me to stop using the elliptical machine.  I started doing Pilates, which is great for strengthening my core, but not soo good for aerobic exercise.  So this is my question....now that I've spent two years strengthening my core, do you think maybe I can start doing the elliptical machine again?  I wonder if my ab muscles are now strong enough to keep my back from arching when I'm doing the elliptical.  Any t houghts about this?