We currently use the following method to perform an http to https rewrite.

rewrite ^ https://$server_name$request_uri permanent;

I am planning to change it to the preferred method of:

return 301 https://$server_name$request_uri;

However, we'd like to also make sure any requests for domain.com are sent to www.domain.com, whether someone tries to access domain.com via http or https.

How would I write the redirect statement to rewrite http:// to https:// but also rewrite domain.com to www.domain.com?