Analytic order of Sha (numerical value) (reviewed)

For an elliptic curve defined over $\Q$ of rank $0$ or $1$, the analytic order of Ш is known to be rational and can been computed exactly. For curves of rank at least $2$ it is not known to be rational, but in all the cases where it has been computed is is close to a square integer, as predicted by the Birch and Swinnerton-Dyer conjecture; in these cases we display the rounded value.