Cute Girl. 3 year relationship breakable?

There is this super cute girl in my class. We have the flirting vibe always, and whenever we do group projects we always sit next to each other.

The first day that we flirted I thought I really had her. We sent notes back and fourth to each-other. Right when i asked for her number she said her boyfriend wouldn't like that and he is the jealous type.

I think she is just scared of breaking up with him. A jealous guy? Haven't heard of that for a long time and doesn't sound too alpha, or fun to be around with.

At this point it seems like an easy take but I don't know what else to do?

Give her my number? What is that going to do?

thanks,
Alex