Let C be an odd degree hyperelliptic curve over a number field K and J be its Jacobian. Let JX be the quadratic twist of J by a quadratic character 2 Hom(GK; f1g). For every non-negative integer r, we show the probability that dimF2(Sel2(J=K)) = r for a certain family of quadratic twists can be given explicitly conditional on some heuristic hypothesis.
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