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.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-10-13 18:03:28

**Referred to by:**

**History:**(expand/hide all)

- 2023-06-08 14:29:22 by David Roe
- 2020-10-13 18:03:28 by Andrew Sutherland (Reviewed)
- 2019-02-08 10:59:20 by John Cremona (Reviewed)

**Differences**(show/hide)