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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
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