Glasnik matematički, Vol. 51 No. 2, 2016.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.51.2.03
Elliptic curves with torsion group Z/6Z
Andrej Dujella
orcid.org/0000-0001-6867-5811
; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia
Juan Carlos Peral
; Departamento de Matemáticas, Universidad del País Vasco, 48080 Bilbao, Spain
Petra Tadić
; Department of Mathematics, Statistics and Information Science, Juraj Dobrila University of Pula, 52100 Pula, Croatia
Sažetak
We exhibit several families of elliptic curves with torsion group isomorphic to Z/6Z and generic rank at least 3. Families of this kind have been constructed previously by several authors: Lecacheux, Kihara, Eroshkin and Woo. We mention the details of some of them and we add other examples developed more recently by Dujella and Peral, and MacLeod. Then we apply an algorithm of Gusić and Tadić and we find the exact rank over Q(t) to be 3 and we also determine free generators of the Mordell-Weil group for each family. By suitable specializations, we obtain the known and new examples of curves over Q with torsion Z/6Z and rank 8, which is the current record.
Ključne riječi
Elliptic curves; torsion; rank
Hrčak ID:
170039
URI
Datum izdavanja:
3.12.2016.
Posjeta: 1.177 *