In mathematics, the Brumer bound is a bound for the rank of an elliptic curve, proved by Brumer (1992).
See also Mestre bound
References Brumer, Armand (1992), "The average rank of elliptic curves. I", Inventiones Mathematicae, 109 (3): 445–472, doi:10.1007/BF01232033, ISSN 0020-9910, MR 1176198