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3-Selmer groups for curves y 2 = x 3 + a

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Abstract

We explicitly perform some steps of a 3-descent algorithm for the curves y 2 = x 3 + a, a a nonzero integer. In general this will enable us to bound the order of the 3-Selmer group of such curves.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università della Calabria, Via P. Bucci-Cubo 30B, 87036, Arcavacata di Rende (CS), Italy

    Andrea Bandini

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  1. Andrea Bandini
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Correspondence to Andrea Bandini.

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Bandini, A. 3-Selmer groups for curves y 2 = x 3 + a . Czech Math J 58, 429–445 (2008). https://doi.org/10.1007/s10587-008-0025-8

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  • DOI: https://doi.org/10.1007/s10587-008-0025-8

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