Elliptic curves with torsion group Z/8Z or Z/2Z × Z/6Z (CROSBI ID 210192)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Dujella, Andrej ; Peral, Juan Carlos
engleski
Elliptic curves with torsion group Z/8Z or Z/2Z × Z/6Z
We show the existence of families of elliptic curves over Q whose generic rank is at least 2 for the torsion groups Z/8Z and Z/2Z × Z/6Z. Also in both cases we prove the existence of in nitely many elliptic curves, which are parameterized by the points of an elliptic curve with positive rank, with such torsion group and rank at least 3. These results represent an improvement of previous results by Campbell, Kulesz, Lecacheux, Dujella and Rabarison where families with rank at least 1 were constructed in both cases.
elliptic curves ; rank ; torsion group
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Podaci o izdanju
649
2015.
47-62
objavljeno
0271-4132
1098-3627
10.1090/conm/649/13019