Yes, there is a cookie, it should say session=<long random string> and you need it to stay logged in. There's no way around it. May I ask what changes you made to your browser to improve your anonymity? They may be harming your anonymity. For example, not accepting cookies reduces your anonymity set to those Tor Browser users (well, hopefully you are using Tor Browser and not a regular browser) that don't accept cookies. That may be less than 1% of users. So your anonymity set is quite small through that change alone. A certain combination of changes in browser behavior could make you uniquely identifiable.