Explicit Determination of Non-Trivial Torsion Structures of Elliptic Curves over Quadratic Number Fields

@inproceedings{Reichert1985ExplicitDO,
  title={Explicit Determination of Non-Trivial Torsion Structures of Elliptic Curves over Quadratic Number Fields},
  author={M. A. Reichert},
  booktitle={European Conference on Computer Algebra},
  year={1985}
}
We determine equations of the modular curves XX(N) for N = 11,13,14,15,16, 17 and 18. Except for N = 17, these are the only existing elliptic or hyperelliptic XX(N). Applying these X^N), we calculate tables of elliptic curves E over quadratic fields K with torsion groups of one of the following isomorphism types: Etor(K) s Z/mZ, m = 11,13, 14, 15, 16 and 18. 
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