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and they convey different things, so it's not really a question of picking the most "elegant," but rather recognizing which conveys the intended meaning. It all depends (has anyone ever said this before in this forum?) on the context.
"... after I finished reading it" might be exactly right, and not inelegant at all, for example if whoever "i" is had got a bad feeling from reading the first part of the book.
Edit: Wanted to point out that the question of whether it's better to say "it" or "the book" will depend entirely on the preceding text. So I might say, for example, "after I read the book" sounds fine, but if it was already referred to as "the book" in the beginning of that same sentence, then the ending I picked would sound quite inelegant. :-)