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On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields (CROSBI ID 233360)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Dujella, Andrej ; Jukić Bokun, Mirela ; Soldo, Ivan On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields // Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas, 111 (2017), 4; 1177-1185. doi: 10.1007/s13398-016-0356-5

Podaci o odgovornosti

Dujella, Andrej ; Jukić Bokun, Mirela ; Soldo, Ivan

engleski

On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields

The possible torsion groups of elliptic curves induced by Diophantine triples over quadratic fields, which do not appear over Q, are Z/2Z × Z/10Z, Z/2Z × Z/12Z and Z/4Z × Z/4Z. In this paper, we show that all these torsion groups indeed appear over some quadratic field. Moreover, we prove that there are infinitely many Diophantine triples over quadratic fields which induce elliptic curves with these torsion groups.

Elliptic curve ; quadratic field ; torsion group ; Diophantine triple

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Podaci o izdanju

111 (4)

2017.

1177-1185

objavljeno

1578-7303

1579-1505

10.1007/s13398-016-0356-5

Povezanost rada

Matematika

Poveznice
Indeksiranost