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arXiv · 1104.5031

Surjectivity of mod 2^n representations of elliptic curves

Tim Dokchitser·Vladimir Dokchitser
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Abstract

For an elliptic curve E over Q, the Galois action on the l-power torsion points defines representations whose images are subgroups of GL_2(Z/l^n Z). There are three exceptional prime powers l^n=2,3,4 when surjectivity of the mod l^n representation does not imply that for l^(n+1). Elliptic curves with surjective mod 3 but not mod 9 representation have been classified by Elkies. The purpose of this note is to do this in the other two cases.

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BibTeXRIS

Tim Dokchitser, Vladimir Dokchitser. 2011-04-26. Surjectivity of mod 2^n representations of elliptic curves. https://doi.org/10.1007/s00209-011-0967-7

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