In mathematics, the Mestre bound is a bound on the analytic rank of an elliptic curve in terms of its conductor, introduced by Mestre (1986).
See also Brumer bound
References Mestre, Jean-François (1986), "Formules explicites et minorations de conducteurs de variétés algébriques", Compositio Mathematica, 58 (2): 209–232, ISSN 0010-437X, MR 0844410