Thanks to a commenter who mentioned that a friend once told her carrot greens were poisonous, I did some research. It appears that there is a carrot top controversy about whether they are toxic or not. Alex and I ate them and lived to tell the tale, but I wanted to be a responsible blogger and at least share the information I found. Apparently all greens contain alkaloids so you should always rotate what types of greens you eat.
Here are some links for more reading: