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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mod 4 Galois representations and elliptic curves


Author: Christopher Holden
Journal: Proc. Amer. Math. Soc. 136 (2008), 31-39
MSC (2000): Primary 14H52
Published electronically: September 25, 2007
MathSciNet review: 2350385
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Abstract: Galois representations $ \rhobar: G_{\mathbb{Q}} \rightarrow GL_{2}(\mathbb{Z}/n)$ with cyclotomic determinant all arise from the $ n$-torsion of elliptic curves for $ n=2,3,5$. For $ n=4$, we show the existence of more than a million such representations which are surjective and do not arise from any elliptic curve.


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Additional Information

Christopher Holden
Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706-1388
Email: holden@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08899-5
PII: S 0002-9939(07)08899-5
Received by editor(s): May 12, 2006
Received by editor(s) in revised form: September 1, 2006
Published electronically: September 25, 2007
Communicated by: Ken Ono
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.