analytic rank
Analytic rank is a number theory term for the order to which an elliptic curve's L-function vanishes at s = 1.
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Last mentioned Analytic rank is the order to which the L-function attached to an elliptic curve over the rational numbers vanishes at s = 1. It is distinct from the algebraic rank, which is the rank of the group of rational points on the curve.
The Birch and Swinnerton-Dyer conjecture predicts that the two ranks are equal, and the analytic rank is used in the study of elliptic curves to estimate the algebraic rank.
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