It's still "Fur Elise". The link I posted includes the full piece (3:38 long).
It's a beautiful piece, In my opinion, but some people actually wanted it banned from Beethoven.com at one time, due to "overplaying". I said then, and I still say now, that there is something inherently wrong with banning a piece by Beethoven from Beethoven Radio...
I believe Schroeder played that piece in one or more of the the "Peanuts" holiday cartoons.
Quod scripsi, scripsi.