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

Research in Number Theory20151:12

  • Received: 26 May 2015
  • Accepted: 29 June 2015
  • Published:


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.


  • Conjugacy Class
  • Elliptic Curve
  • Rational Point
  • Maximal Subgroup
  • Elliptic Curf