ScholarLens Back to search
2014•International Journal of Number TheoryOpen access

Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve

Tom Fisher, Rachel Newton

Open full text 3 citations

Abstract

We extend the method of Cassels for computing the Cassels–Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Open-access reader

About this research paper

What this paper is about

We extend the method of Cassels for computing the Cassels–Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Why it matters

OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We extend the method of Cassels for computing the Cassels–Tate pairing on the 2-Selmer group of an elliptic curve, to the case of 3-Selmer groups. This requires significant modifications to both the local and global parts of the calculation. Our method is practical in sufficiently small examples, and can be used to improve the upper bound for the rank of an elliptic curve obtained by 3-descent.

Key concepts: Pairing, Elliptic curve, Rank (graph theory), Group (periodic table), Mathematics, Pure mathematics, Upper and lower bounds, Combinatorics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve — Research Paper | ScholarLens