Papers › Elliptic curves over ℚ and 2-adic images of Galois
Elliptic curves over ℚ and 2-adic images of Galois
Jeremy Rouse, David Zureick-Brown
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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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