  The conjectures of Deligne, Be\u\i linson, and Bloch-Kato assert that there
should be relations between the arithmetic of algebro-geometric objects and the
special values of their $L$-functions. We make a numerical study for symmetric
power $L$-functions of elliptic curves, obtaining data about the validity of
their functional equations, frequency of vanishing of central values, and
divisibility of Bloch-Kato quotients.
