Special value of an elliptic curve L-function (reviewed)

For elliptic curves over $\Q$, a natural normalization for its L-function is the one that yields a functional equation $s\leftrightarrow 2-s.$ This is known as the arithmetic normalization, because the Dirichlet coefficients are rational integers. We emphasize that the arithmetic normalization is being used by writing the L-function as $L(E,s)$. In this notation, the central point is at $s=1.$ The special value is the first non-zero value among $L(E,1), L'(E,1), L''(E,1), \ldots $