Accessibility navigation


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

Fisher, T. and Newton, R. (2014) Computing the Cassels–Tate pairing on the 3-Selmer group of an elliptic curve. International Journal of Number Theory, 10 (7). pp. 1881-1907. ISSN 1793-7310

[img]
Preview
Text - Accepted Version
· Please see our End User Agreement before downloading.

426kB

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1142/S1793042114500602

Abstract/Summary

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.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:58175
Publisher:World Scientific
Publisher Statement:This version may differ from the version published in International Journal of Number Theory.

Downloads

Downloads per month over past year

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation