Torsion of rational elliptic curves over quadratic 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 quadratic number field.

References in corpus (3)

• Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
• Torsion points on elliptic curves over number fields of small degree
• Galois Theory, discriminants and torsion subgroups of elliptic curves

Cited by in corpus (10)

• Complete classification of the torsion structures of rational elliptic curves over quintic number fields
• Torsion of rational elliptic curves over quartic Galois number fields
• On the torsion of rational elliptic curves over quartic fields
• Torsion of rational elliptic curves over quadratic fields II
• Torsion of rational elliptic curves over cubic fields
• An algorithm for determining torsion growth of elliptic curves
• On the torsion group of elliptic curves induced by Diophantine triples over quadratic fields
• Groups of generalized $G$-type and applications to torsion subgroups of rational elliptic curves over infinite extensions of $\mathbb{Q}$
• Growth of Odd Torsion Over Imaginary Quadratic Fields of Class Number 1
• Squares in arithmetic progression over certain non-primitive quartic number fields