## A bound for the torsion conductor of a non-CM elliptic curve

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- by Nathan Jones
- Proc. Amer. Math. Soc.
**137**(2009), 37-43 - DOI: https://doi.org/10.1090/S0002-9939-08-09436-7
- Published electronically: July 25, 2008
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## Abstract:

Given a non-CM elliptic curve $E$ over $\mathbb {Q}$ of discriminant $\Delta _E$, define the “torsion conductor” $m_E$ to be the smallest positive integer so that the Galois representation on the torsion of $E$ has image $\pi ^{-1}(\operatorname {Gal}(\mathbb {Q}(E[m_E])/\mathbb {Q}))$, where $\pi$ denotes the natural projection $GL_2(\hat {\mathbb {Z}}) \rightarrow GL_2(\mathbb {Z}/m_E\mathbb {Z})$. We show that, uniformly for semi-stable non-CM elliptic curves $E$ over $\mathbb {Q}$, one has ${m_E \ll \left ( \prod _{p \mid \Delta _E} p\right )^5}$.## References

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## Bibliographic Information

**Nathan Jones**- Affiliation: Centre de Recherches Mathématiques, Université de Montréal, P.O. Box 6128, Centre-ville Station, Montréal, Québec H3C 3J7, Canada
- MR Author ID: 842244
- Email: jones@dms.umontreal.ca
- Received by editor(s): September 6, 2007
- Received by editor(s) in revised form: November 25, 2007
- Published electronically: July 25, 2008
- Communicated by: Ken Ono
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 37-43 - MSC (2000): Primary 11G05, 11F80
- DOI: https://doi.org/10.1090/S0002-9939-08-09436-7
- MathSciNet review: 2439422