Birch and Swinnerton-Dyer conjecture in the complex multiplication case and the congruent number problem

Kazuma Morita

For an elliptic curve $E$ over $K$, the Birch and Swinnerton-Dyer conjecture predicts that the rank of Mordell-Weil group $E(K)$ is equal to the order of the zero of $L(E_{/K},s)$…