Reichert, Markus A. Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields. (English) Zbl 0605.14028 Math. Comput. 46, 637-658 (Microfiche Suppl.) (1986). The author lists elliptic curves \(E\) defined over a quadratic field \(K\) (but not defined over \(\mathbb Q\) such that the torsion part of the group of \(K\)-rational points is cyclic of order \(N\), where \(N=11, 13, 14, 15, 16\) or 18. For each of these curves the \(j\)-invariant and its prime decomposition is also computed. The computations use explicit equations, which the author finds, for the modular curves \(X_ 1(N)\) for the above values of \(N\). Reviewer: B. Singh Cited in 4 ReviewsCited in 21 Documents MSC: 11G05 Elliptic curves over global fields 11Y16 Number-theoretic algorithms; complexity 14G25 Global ground fields in algebraic geometry 14H52 Elliptic curves Keywords:elliptic curves; torsion; j-invariant PDFBibTeX XMLCite \textit{M. A. Reichert}, Math. Comput. 46, 637--658 (1986; Zbl 0605.14028) Full Text: DOI Online Encyclopedia of Integer Sequences: Minimal degree of X_1(n).