
joint with Rachel Newton
We extend the method of Cassels for computing the CasselsTate pairing on the 2Selmer group of an elliptic curve, to the case of 3Selmer 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 3descent.