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The effect of twisting on the 2-Selmer group

Published online by Cambridge University Press:  01 November 2008

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Let Γ be an elliptic curve defined over Q, all of whose 2-division points are rational, and let Γb be its quadratic twist by b. Subject to a mild additional condition on Γ, we find the limit of the probability distribution of the dimension of the 2-Selmer group of Γb as the number of prime factors of b increases; and we show that this distribution depends only on whether the 2-Selmer group of Γ has odd or even dimension.

Research Article
Copyright © Cambridge Philosophical Society 2008



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