Mod 4 Galois representations and elliptic curves
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- by Christopher Holden PDF
- Proc. Amer. Math. Soc. 136 (2008), 31-39 Request permission
Abstract:
Galois representations $\bar {\rho }: G_{\mathbb Q} \rightarrow GL_{2}(\mathbb Z/n)$ 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.References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 31-39
- MSC (2000): Primary 14H52
- DOI: https://doi.org/10.1090/S0002-9939-07-08899-5
- MathSciNet review: 2350385