show · ec.q.analytic_sha_value all knowls · up · search:

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.

Knowl status:
  • Review status: reviewed
  • Last edited by Andrew Sutherland on 2020-10-13 18:03:28
Referred to by:
History: (expand/hide all) Differences (show/hide)