Naslov
Torsion of elliptic curves over cubic fields

Autori
Najman, Filip

Izvornik
Journal of number theory (0022-314X) 132 (2012), 1; 26-36

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
torsion group ; elliptic curves ; cubic fields

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA