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math.NT2008★ 4 cited
A note on Larsen's conjecture and ranks of elliptic curves
Tim Dokchitser, Vladimir Dokchitser
Let E be an elliptic curve defined over a number field K. Michael Larsen conjectured that for any finitely generated subgroup G of Gal(\bar K/K), the Mordell-Weil rank of E is unbo…
math.NT2008★ 19 cited
Elliptic curves with all quadratic twists of positive rank
Tim Dokchitser, Vladimir Dokchitser
We observe that there are elliptic curves over number fields all of whose quadratic twists must have positive rank, assuming the Birch-Swinnerton-Dyer conjecture. We give a classif…