In [8], Swinnerton-Dyer considered the proportion of twists of an elliptic curve with full 2-torsion that have 2-Selmer group of a particular dimension. Swinnerton-Dyer obtained asymptotic results on the number of such twists using an unusual notion of asymptotic density. We build on this work to obtain similar results on the density of twists with particular rank of 2-Selmer group using the na...

The genus Berthelotia DC. (presently a synonym of the accepted name Pluchea Cass.), Asteraceae, Inuleae has been regarded as comprising two species, B. lanceolata and sericea (Nutt.) Rydb. It honors French naturalist Sabin Berthelot (1794–1880) for his contribution to studies flora fauna Canary Islands. Under leadership Philip Webb (1793–1854), co-authored most important work pertinent natural ...