Dear SisterCM,
Fur Elise starts out with a trill between D# and E, using th 4th and 5th fingers. Since those fingers are naturally weaker many exercises have been designed to strengthen them.
I have two 'words' for you....
Hanon - in the big 3-book edition, published by Schirmer. Book 2 has scales, runs and trill exercises.
Czerny - lots of his books, easiest one I think is called "The Little Pianist".
Czerny was a concert pianist who was about to go on his grand European tour when war broke out. Never made it as a performer, but succeeded as a teacher - put out tons of books to torture his students. :-)
Having completed the Alfred course, you are ready for them...