Elliptic curves induced by Diophantine triples (CROSBI ID 248805)
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Podaci o odgovornosti
Dujella, Andrej ; Peral, Juan Carlos
engleski
Elliptic curves induced by Diophantine triples
Given a Diophantine triple {; ; ; ; ; ; ; ; ; c1(t), c2(t), c3(t)}; ; ; ; ; ; ; ; ; , the elliptic curve over Q(t) induced by this triple, i.e. y^2 = (c1(t)x+1) (c2(t)x+1)(c3(t)x+1), can have as torsion group one of the non-cyclic groups in Mazur's theorem, i.e. Z/2Z x Z/2Z, Z/2Z x Z/4Z, Z/2Z x Z/6Z or Z/2Z x Z/8Z. In this paper we present results concerning the rank over Q(t) of these curves improving in some of the cases the previously known results.
Elliptic curves, Diophantine triples, rank, torsion group
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Podaci o izdanju
113 (2)
2019.
791-806
objavljeno
1578-7303
1579-1505
10.1007/s13398-018-0513-0