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Torsion of elliptic curves over cubic fields (CROSBI ID 173311)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Najman, Filip Torsion of elliptic curves over cubic fields // Journal of number theory, 132 (2012), 1; 26-36. doi: 10.1016/j.jnt.2011.06.013

Podaci o odgovornosti

Najman, Filip

engleski

Torsion of elliptic curves over cubic fields

Although it is not known which groups can appear as torsion over cubic fields, it is known which groups can appear for infinitely many non-isomorphic curves. We denote the set of these groups as S. In this paper we deal with three problems concerning the torsion of elliptic curves over cubic fields. First, we study the possible torsion groups of elliptic curves that appear over the field with smallest absolute value of its discriminant and having Galois group S_3 and over the field with smallest absolute value of its discriminant and having Galois group Z/3Z. Secondly, for all except two groups G in S, we find the field K with smallest absolute value of its discriminant such that there exists an elliptic curve over K having G as torsion. Finally, for every G in S and every cubic field K we determine whether there exists infinitely many non-isomorphic elliptic curves with torsion G.

torsion group ; elliptic curves ; cubic fields

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Podaci o izdanju

132 (1)

2012.

26-36

objavljeno

0022-314X

1096-1658

10.1016/j.jnt.2011.06.013

Povezanost rada