Nowadays they don't send any information besides what you enter in the form (and ip and user-agent). Before they used to send something called qs_stamp, which was to prevent automating signup process.
We don't really know but Facebook owns IG so you can assume they record everything possible and then some, as both of them are in the same business of targetting ads at you (and conspiracy theorists say they're sharing some data with the government too, but I don't believe them).
If you use your smartphone they have even more data about you and if you ever logged into your personal Facebook from the same browser and PC as IG, then they know exactly where you live and what meds you take.
I see. I assume if I signed up using a mobile device then it would send more information?