The **2-Selmer rank** of an abelian variety is the rank of its 2-Selmer group.

The difference between the 2-Selmer rank and the 2-rank of the torsion subgroup is an upper bound on the rank of the Mordell-Weil group. This bound is tight if and only if the 2-part of the Tate-Shafarevich group is trivial

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-10-09 17:11:27

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

- 2020-10-09 17:11:27 by Andrew Sutherland (Reviewed)
- 2020-10-09 15:36:12 by Andrew Sutherland
- 2020-10-09 15:35:00 by Andrew Sutherland
- 2018-05-24 17:13:28 by John Cremona (Reviewed)

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