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On the φ-Selmer groups of the elliptic curves y 2 = x 3 − Dx


AbstractWe study the variation of the φ-Selmer groups of the elliptic curvesy2=x3−Dxunder quartic twists by square-free integers. We obtain a complete description of the distribution of the size of this group when the integerDis constrained to lie in a family for which the relative Tamagawa number of the isogeny φ is fixed.

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