Torsion of elliptic curves over cyclic cubic fields

Abstract

We determine all the possible torsion groups of elliptic curves over cyclic cubic fields, over non-cyclic totally real cubic fields and over complex cubic fields.

14 pages

References in corpus (1)

• Sporadic Cubic Torsion

Cited by in corpus (7)

• Sporadic Cubic Torsion
• Groups of generalized $G$-type and applications to torsion subgroups of rational elliptic curves over infinite extensions of $\mathbb{Q}$
• Rank Jumps and Growth of Shafarevich--Tate Groups for Elliptic Curves in $\mathbb{Z}/p\mathbb{Z}$-Extensions
• Elliptic curves with a point of order 13 defined over cyclic cubic fields
• Torsion of rational elliptic curves over different types of cubic fields
• A single source theorem for primitive points on curves
• Cyclic Cubic Points on Higher Genus Curves