Glasnik Matematicki, Vol. 42, No.1 (2007), 3-18.

ON MORDELL-WEIL GROUPS OF ELLIPTIC CURVES INDUCED BY DIOPHANTINE TRIPLES

Andrej Dujella

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail: duje@math.hr

Abstract.   We study the possible structure of the groups of rational points on elliptic curves of the form y2 = (ax+1)(bx+1)(cx+1), where a,b,c are non-zero rationals such that the product of any two of them is one less than a square.

2000 Mathematics Subject Classification.   11G05.

Key words and phrases.   Elliptic curves, rank, torsion group, Diophantine triple.

Full text (PDF) (free access)

DOI: 10.3336/gm.42.1.01

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