Do you need to enter your e-mail address to continue authorization on the site?

Question

User identification

Hello. I set up authorization through classmates on my site.

But when you click on the icon, a window appears with a form where you are asked to enter your email -

To continue authorization on the site, you need to enter your e-mail address

Is there a way for a person to log in without entering his email, too many actions.
After all, the very essence of authorization is to go to the site or register with one or two mouse clicks, Login and allow.