Elliptic Curves over Q and 2-adic Images of Galois

@inproceedings{ZureickBrown2015EllipticCO,
  title={Elliptic Curves over Q and 2-adic Images of Galois},
  author={David Zureick-Brown},
  year={2015}
}
We give a classification of all possible 2-adic images of Galois representations associated to elliptic curves over 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. 

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