I will be the first one to offer an opinion for below. There are pros and cons to both.
Sure you can design by convention , but i feel you should only do that if there isnt any affordances to help a user. Here no matter where you put it they can see it and click it if they like.
Why put the login above?
For someone who likes using the keyboard and tab more, they can click once type their 1. username , 2. tab type password, 3. tab and click enter to log in.
if this is something where users would log in often and not want to save their password (stock account, bank account, something used at work or common computers), I would give this a plus to thus case.
If a user wants to stay logged in you can put a cookie there and keep it checked no matter where it is.
The only downside is that by putting it below someone may not notice it. But i think they are just as likely to not notice it in either location. some user testing could confirm it.