is there any way for me to log in to minecraft with no email?

I have forgotten the email I signed up with but am still logged in to my account, however this is an old pc and I just got a new one but I just cant log in, is there any way for me to get back in to this account?

There is no legal way to log in without the account info, and sorry, Arquade doesn't give advice on how to violate EULAs.

Instead, find the file launcher_accounts.json in the .minecraft folder (on Windows it's %AppData%\Roaming\.minecraft ) on your old computer, and among other info you'll find your old email address in there. You may even try copying the file to your new computer.

If besides forgetting the email address you forgot the password, you'll need to contact Mojang support. (also, the purchase ID from the email you have received when buying the game would be an alternative credentials for the support contact).