Original scientific paper

https://doi.org/10.3336/gm.47.2.04

Elliptic curves over quadratic fields with fixed torsion subgroup and positive rank

Mirela Jukić Bokun orcid.org/0000-0003-3461-8506 ; Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, 31 000 Osijek, Croatia

Abstract

For each of the torsion groups Z/2Z Z/10Z, Z/2Z 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.

Keywords

Elliptic curve; torsion group; rank; quadratic field

Hrčak ID:

93941

URI

https://hrcak.srce.hr/93941

Publication date:

19.12.2012.

Visits: 1.273 *