Abstract. 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: m = 11,13, 14, 15, 16 and 18.
Abstract. 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: m = 11,13, 14, 15, 16 and 18.
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