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The effect of twisting on the 2-Selmer group

Published online by Cambridge University Press:  01 November 2008

PETER SWINNERTON–DYER*
Affiliation:
DPMMS, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK. e-mail: hpfs100@dpmms.cam.ac.uk
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2008

References

REFERENCES

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