Ranks of elliptic curves

The Birch and Swinnerton-Dyer conjecture relates the rank of an elliptic curve (and other arithmetic information) to the order of vanishing (and the first nonzero coefficient) of the associated $L$-function at the critical point.

Thus, results and conjectures about the critical values of varios families of $L$-function will give information about the ranks of elliptic curves.

(more details and some good references are sought.)

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