The analytic rank of a modular curve is the order of vanishing of its L-function at its central point, which is equal to the sums of the analytic ranks of the L-functions of the simple modular abelian varieties corresponding to Galois orbits of modular forms that are the isogeny factors of its Jacobian.
The Birch and Swinnerton-Dyer conjecture for modular abelian varieties implies that the analytic rank is equal to the Mordell-Weil rank of the Jacobian.
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- Last edited by Andrew Sutherland on 2022-03-20 15:14:17
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- columns.gps_gl2zhat_fine.coarse_class
- columns.gps_gl2zhat_fine.genus_minus_rank
- columns.gps_gl2zhat_fine.rank
- columns.gps_gl2zhat_test.rank
- columns.gps_shimura_test.genus_minus_rank
- modcurve.genus_minus_rank
- rcs.cande.modcurve
- lmfdb/modular_curves/main.py (line 335)
- lmfdb/modular_curves/main.py (line 787)
- lmfdb/modular_curves/main.py (line 1184)
- lmfdb/modular_curves/templates/modcurve.html (line 41)
- lmfdb/modular_curves/templates/modcurve.html (line 424)
- lmfdb/modular_curves/templates/modcurve.html (line 462)
- lmfdb/modular_curves/templates/modcurve.html (line 501)
- lmfdb/modular_curves/templates/modcurve_browse.html (line 33)
- lmfdb/modular_curves/templates/modcurve_isoclass.html (line 110)