A criterion to rule out torsion groups for elliptic curves over number fields

被引：15

作者：

Bruin P. ^{[1
]}

Najman F. ^{[2
,3
]}

机构：

[1] Mathematisch Instituut, Universiteit Leiden, Postbus 9512, Leiden, 2300, RA

[2] Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb

[3] Department of Mathematics, Massachusetts Institute of Technology, Cambridge, 02139, MA

来源：

Research in Number Theory | / 2卷 / 1期

关键词：

Elliptic Curve; Irreducible Component; Elliptic Curf; Abelian Variety; Number Field;

D O I：

10.1007/s40993-015-0031-5

中图分类号：

学科分类号：

摘要：

We present a criterion for proving that certain groups of the form Z/ mZ⊕ Z/ nZ do not occur as the torsion subgroup of any elliptic curve over suitable (families of) number fields. We apply this criterion to eliminate certain groups as torsion groups of elliptic curves over cubic and quartic fields. We also use this criterion to give the list of all torsion groups of elliptic curves occurring over a specific cubic field and over a specific quartic field. © 2016, The Author(s).

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