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On binary quartics and the Cassels-Tate pairing

We use the invariant theory of binary quartics to give a new formula for the Cassels-Tate pairing on the 2-Selmer group of an elliptic curve. Unlike earlier methods, our formula does not require us to solve any conics. An important role in our construction is played by certain (2,2,2)-forms.


On binary quartics and the Cassels-Tate pairing   (14 pages)     dvi   ps   ps.gz   pdf