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

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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

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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: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.
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