I was wondering whether anyone knows of any good non-technical or even popular expositions of the Birch—Swinnerton-Dyer conjecture, for someone with minimal background in elliptic curves. I was thinking of something along the lines of du Sautoy's excellent book '*The Music of the Primes*' on the Riemann hypothesis, though perhaps catering slightly less to the layman and more geared to a mathematical audience.


(Note when I say minimal background, I just mean a senior undergraduate level 'awareness' of the group law on elliptic curves, working with curves over finite fields, and the Mordell-Weil theorem.)



A non-technical account of the Birch—Swinnerton-Dyer Conjecture
Try Zagier's MPI preprint MPI/89-48 with the title *The 
Birch and Swinnerton-Dyer conjecture from a naive point
of view*.


**Addendum** (2012/02/23). An even more elementary introduction is [this one](http://people.mpim-bonn.mpg.de/zagier/files/tex/BSDwHarder/fulltext.pdf) by Harder and Zagier.


