The **analytic rank** of an abelian variety is the analytic rank of its L-function. For a curve, we define its **analytic rank** to be the analytic rank of its Jacobian. Under the BSD conjecture, the analytic rank is expected to be equal the rank of the Mordell-Weil group of the abelian variety.

In general, unless otherwise specified, analytic ranks stored in the LMFDB are only known to be upper bounds on the true analytic rank--but they are all believed to be correct.

**Knowl status:**

- Review status: reviewed
- Last edited by John Voight on 2020-01-07 12:19:06

**Referred to by:**

- g2c.587.a.587.1.top
- g2c.analytic_sha
- g2c.bsd_invariants
- g2c.conditional_mw_group
- rcs.rigor.g2c
- lmfdb/genus2_curves/main.py (line 361)
- lmfdb/genus2_curves/templates/g2c_browse.html (line 139)
- lmfdb/genus2_curves/templates/g2c_curve.html (line 187)
- lmfdb/genus2_curves/templates/g2c_isogeny_class.html (lines 33-35)
- lmfdb/genus2_curves/templates/g2c_search_results.html (line 30)
- lmfdb/genus2_curves/templates/g2c_search_results.html (line 152)

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

- 2020-01-17 12:13:11 by Andrew Sutherland
- 2020-01-17 12:07:56 by Andrew Sutherland
- 2020-01-17 11:56:28 by Andrew Sutherland
- 2020-01-07 12:19:06 by John Voight (Reviewed)
- 2020-01-07 12:18:31 by John Voight
- 2020-01-07 12:16:58 by John Voight
- 2020-01-07 12:16:35 by John Voight
- 2020-01-07 06:11:54 by Andrew Sutherland
- 2019-09-05 19:41:12 by Kiran S. Kedlaya
- 2019-05-18 09:02:54 by Andrew Sutherland (Reviewed)
- 2019-05-18 08:51:16 by Andrew Sutherland
- 2018-05-23 16:28:30 by John Cremona (Reviewed)

**Differences**(show/hide)