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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 by Harder and Zagier.

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Try Zagier's MPI preprint MPI/89-48 with the title The Brich Birch and Swinnerton-Dyer conjecture from a naive point of view.

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Try Zagier's MPI preprint MPI/89-48 with the title The Brich and Swinnerton-Dyer conjecture from a naive point of view.