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https://doi.org/10.3336/gm.51.2.03

Elliptic curves with torsion group Z/6Z

Andrej Dujella   ORCID icon 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

Puni tekst: engleski, pdf (134 KB) str. 321-333 preuzimanja: 246* citiraj
APA 6th Edition
Dujella, A., Peral, J.C. i Tadić, P. (2016). Elliptic curves with torsion group Z/6Z. Glasnik matematički, 51 (2), 321-333. https://doi.org/10.3336/gm.51.2.03
MLA 8th Edition
Dujella, Andrej, et al. "Elliptic curves with torsion group Z/6Z." Glasnik matematički, vol. 51, br. 2, 2016, str. 321-333. https://doi.org/10.3336/gm.51.2.03. Citirano 22.02.2020.
Chicago 17th Edition
Dujella, Andrej, Juan Carlos Peral i Petra Tadić. "Elliptic curves with torsion group Z/6Z." Glasnik matematički 51, br. 2 (2016): 321-333. https://doi.org/10.3336/gm.51.2.03
Harvard
Dujella, A., Peral, J.C., i Tadić, P. (2016). 'Elliptic curves with torsion group Z/6Z', Glasnik matematički, 51(2), str. 321-333. https://doi.org/10.3336/gm.51.2.03
Vancouver
Dujella A, Peral JC, Tadić P. Elliptic curves with torsion group Z/6Z. Glasnik matematički [Internet]. 2016 [pristupljeno 22.02.2020.];51(2):321-333. https://doi.org/10.3336/gm.51.2.03
IEEE
A. Dujella, J.C. Peral i P. Tadić, "Elliptic curves with torsion group Z/6Z", Glasnik matematički, vol.51, br. 2, str. 321-333, 2016. [Online]. https://doi.org/10.3336/gm.51.2.03

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
https://hrcak.srce.hr/170039

Posjeta: 354 *