Glasnik Matematicki, Vol. 47, No. 2 (2012), 277-284.

ELLIPTIC CURVES OVER QUADRATIC FIELDS WITH FIXED TORSION SUBGROUP AND POSITIVE RANK

Mirela Jukić Bokun

Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia
e-mail: mirela@mathos.hr

Abstract.   For each of the torsion groups Z/2Z oplus Z/10Z, Z/2Z oplus Z/12Z, Z/15Z we find the quadratic field with the smallest absolute value of its discriminant such that there exists an elliptic curve with that torsion and positive rank. For the torsion groups Z/11Z, Z/14Z we solve the analogous problem after assuming the Parity conjecture.

2010 Mathematics Subject Classification.   11G05, 14H52, 11R11.

Key words and phrases.   Elliptic curve, torsion group, rank, quadratic field.

Full text (PDF) (free access)

DOI: 10.3336/gm.47.2.04

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