Torsion of rational elliptic curves over quadratic fields II

Abstract

Let E be an elliptic curve defined over Q and let G=E(Q)_tors be the associated torsion group. In a previous paper, the authors studied, for a given G, which possible groups G\leq H could appear such that H=E(K)_tors, for [K:Q]=2. In the present paper, we go further in this study and compute, under this assumption and for every such G, all the possible situations where G\neq H. The result is optimal, as we also display examples for every situation we state as possible. As a consequence, the maximum number of quadratic number fields K such that E(Q)_tors\neq E(K)_tors is easily obtained.

To appear in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemática RACSAM

References in corpus (2)

• Torsion of rational elliptic curves over quadratic fields
• Covering techniques and rational points on some genus 5 curves

Cited by in corpus (7)

• 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
• Torsion of rational elliptic curves over cubic fields
• On the minimal degree of definition of p-primary torsion subgroups of elliptic curves
• An algorithm for determining torsion growth of elliptic curves
• Squares in arithmetic progression over certain non-primitive quartic number fields