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

Fisher, T. and Newton, R. ORCID: https://orcid.org/0000-0003-4925-635X (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 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
URI	https://reading-clone.eprints-hosting.org/id/eprint/58175
Identification Number/DOI	10.1142/S1793042114500602
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	World Scientific
Publisher Statement	This version may differ from the version published in International Journal of Number Theory.
Download/View statistics	View download statistics for this item