Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields

Reichert, Markus A.

doi:10.1090/S0025-5718-1986-0829635-X

Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
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by Markus A. Reichert PDF

Math. Comp. 46 (1986), 637-658 Request permission

Abstract:

We determine equations of the modular curves ${X_1}(N)$ for $N = 11,13,14,15,16,17$ and 18. Except for $N = 17$, these are the only existing elliptic or hyperelliptic ${X_1}(N)$. Applying these ${X_1}(N)$, we calculate tables of elliptic curves E over quadratic fields K with torsion groups of one of the following isomorphism types: \[ {E_{{\operatorname {tor}}}}(K) \cong {\mathbf {Z}}/m{\mathbf {Z}},\quad m = 11,13,14,15,16\;{\text {and}}\;18.\]

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Explizite Bestimmung nichttrivialer Torsionsstrukturen elliptischer Kurven über quadratischen Zahlkörpern

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