Torsion of rational elliptic curves over cubic fields

Abstract

Let E be an elliptic curve defined over Q. We study the relationship between the torsion subgroup E(Q)_tors and the torsion subgroup E(K)_tors, where K is a cubic number field. In particular, We study the number of cubic number fields K such that E(Q)_tors\neq E(K)_tors.

Rocky Mountain Journal of Mathematica, to appear

References in corpus (2)

• Torsion of rational elliptic curves over quadratic fields
• Torsion of rational elliptic curves over quadratic fields II

Cited by in corpus (6)

• Growth of torsion groups of elliptic curves upon base change
• Complete classification of the torsion structures of rational elliptic curves over quintic number fields
• On the torsion of rational elliptic curves over quartic fields
• An algorithm for determining torsion growth of elliptic curves
• Torsion of elliptic curves with rational $j$-invariant defined over number fields of prime degree
• Torsion of rational elliptic curves over different types of cubic fields