The even parity Goldfeld conjecture: Congruent number elliptic curves

p-converse to a theorem of Gross–Zagier, Kolyvagin and Rubin

(2019) Ashay A. Burungale et al.   INVENTIONES MATHEMATICAE

Explicit Gross–Zagier and Waldspurger formulae

(2015) Li Cai et al.   Algebra & Number Theory

Quadratic twists of elliptic curves

(2014) John Coates et al.   PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY

On the ranks of the 2-Selmer groups of twists of a given elliptic curve

(2013) Daniel Kane   Algebra & Number Theory

Disparity in Selmer ranks of quadratic twists of elliptic curves

(2013) Zev Klagsbrun et al.   ANNALS OF MATHEMATICS

The Iwasawa Main Conjectures for GL2

(2013) Christopher Skinner et al.   INVENTIONES MATHEMATICAE

Random maximal isotropic subspaces and Selmer groups

(2011) Bjorn Poonen et al.   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

On the Birch-Swinnerton-Dyer quotients modulo squares

(2010) Tim Dokchitser et al.   ANNALS OF MATHEMATICS

Elliptic curves with all quadratic twists of positive rank

(2009) Tim Dokchitser et al.   ACTA ARITHMETICA

The effect of twisting on the 2-Selmer group

(2008) PETER SWINNERTON–DYER   MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY