I've seen two notations for the note progression of Für Elise that goes "E.-C-B-A" at the end. One is "E.-C-B-A", which was the one I heard first, and the other is "D.-C-B-A", which appeared in an RCM book and which my piano teacher insisted was the "correct" version.
Which one is correct if any? The most commonly known one seems to be "E.-C-B-A".
Is that book Urtext? If it is, it probably has some commentary which may or may not reveal something. The first edition of the piece is available on IMSLP, and has D in almost every case. The other versions seem to have E in every case, except one has D the very last time the figure appears.
Even if your book is urtext, it's not the-absolutely-correct-version. I've seen quite differing urtext editions of the same piece (some Chopin's valses come to mind; it's quite funny actually...). I would say usually urtext editions change when new data has come available, so your best bet is to try and find the most recent urtext possible and see what it tells you.
What you'll probably find in the commentary of an urtext version, if you find anything, is that it just lists which editions (including manuscripts, if available) contain which note, and maybe some argumentation why they picked the note they did. Just keep in mind that sometimes the composer wrote many different versions himself, and in any case he probably improvised a bit when he was playing, so I think one shouldn't think too much about it (like I often do).
