Naslov
Elliptic curves with torsion groups Z/8Z and Z/2Z × Z/6Z

Autori
Dujella, Andrej ; Kazalicki, Matija ; Peral, Juan Carlos

Izvornik
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A-Matematicas (1578-7303) 115 (2021); 169, 24

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

Ključne riječi
Elliptic curves, torsion group, rank

Sažetak
In this paper, we present details of seven elliptic curves over Q(u) with rank 2 and torsion group Z/8Z and five curves over Q(u) with rank 2 and torsion group Z/2Z × Z/6Z. We also exhibit some particular examples of curves with high rank over Q by specialization of the parameter. We present several sets of infinitely many elliptic curves in both torsion groups and rank at least 3 parametrized by elliptic curves having positive rank. In some of these sets we have performed calculations about the distribution of the root number. This has relation with recent heuristics concerning the rank bound for elliptic curves by Park, Poonen, Voight and Wood.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA