Elliptic curves over $\mathbb{Q}$ and 2-adic images of Galois

Jeremy Rouse; David Zureick-Brown

Elliptic curves over $\mathbb{Q}$ and 2-adic images of Galois

Number Theory 2018-01-22 v3

Authors: Jeremy Rouse , David Zureick-Brown

Abstract

We give a classification of all possible $2$ -adic images of Galois representations associated to elliptic curves over $\mathbb{Q}$ . To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves.

Keywords

elliptic curves Galois representations 2-adic images modular curves rational points arithmetic geometry

Cite

@article{arxiv.1402.5997,
  title  = {Elliptic curves over $\mathbb{Q}$ and 2-adic images of Galois},
  author = {Jeremy Rouse and David Zureick-Brown},
  journal= {arXiv preprint arXiv:1402.5997},
  year   = {2018}
}

Comments

34 pages, 1 figure. The transcript of computations is available in the ancillary file 2adic.rar. (Apologies for the unusual file format. If this archive is created with tar, gzip or bzip2, arXiv will automatically extract it, and would would give links to each of these files on the site you are looking at.)

Elliptic curves over $\mathbb{Q}$ and 2-adic images of Galois

Abstract

Keywords

Cite

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