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Computing the Cassels–Tate pairing on 3-isogeny Selmer groups via cubic norm equations
We explain a method for computing the Cassels–Tate pairing on the $3$-isogeny Selmer groups of an elliptic curve. This improves the upper bound on the rank of the elliptic curve coming from a descent by $3$-isogeny, to that coming from a full $3$-descent.