Special value of an elliptic curve L-function (awaiting review)

The special value of an elliptic curve $E$ defined over a number field $K$ is the first nonzero value of $L^{(r)}(E,1)/r!$ for $r\in \Z_{\ge 0}$, where $L(E/K,s)$ is the L-function of $E$ in its arithmetic normalization. It is also known as the leading coefficient of the L-function.

The special value appears in the Birch and Swinnerton-Dyer conjecture.