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

Nathan Jones

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arXiv · 0711.1546

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

Nathan Jones

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Abstract

Given a non-CM elliptic curve E over Q, 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}(Gal(Q(E[m_E])/Q), where Pi denotes the natural projection GL_2(\hat{Z}) onto GL_2(Z/m_E Z). We show that, uniformly for semi-stable non-CM elliptic curves E over Q, m_E is less than a constant times the 5th power of the conductor of E.

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Nathan Jones. 2007-11-09. A bound for the "torsion conductor" of a non-CM elliptic curve. https://arxiv.org/abs/0711.1546

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