10 research outputs found

    On several families of elliptic curves with arbitrary large Selmer groups

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    In this paper, we calculate the ϕ(ϕ^) \phi (\hat{\phi})-Selmer groups S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic curves y2=x(x+ϵpD)(x+ϵqD) y^{2} = x (x + \epsilon p D) (x + \epsilon q D) via descent theory (see [S, Chapter X]), in particular, we obtain that the Selmer groups of several families of such elliptic curves can be arbitrary large.Comment: 22 page

    Reactions of Solid-Supported Reagents and Solid Supports with Alcohols and Phenols through Their Hydroxyl Functional Group

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