Construction of elliptic curves with noninteger torsion points and noncyclic torsion groups

Sumi Jeong and Hwasin Park

Vol. 244 (2010), No. 2, 297–308

DOI: 10.2140/pjm.2010.244.297

Abstract

We study elliptic curves in Weierstrass form (with integer coefficients) that have noninteger torsion points over ℚ. After putting the curves in certain normal forms, we find conditions on their coefficients characterizing when the torsion group is isomorphic to ℤ∕2ℤ × ℤ∕2Nℤ, for each N = 1,2,3,4.

Keywords

elliptic curve

Mathematical Subject Classification 2000

Primary: 11G05, 14G05

Milestones

Received: 26 October 2007

Revised: 2 September 2008

Accepted: 14 November 2008

Published: 14 December 2009