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Explicit n-descent on elliptic curves, I. Algebra

John Cremona·Tom Fisher·Cathy O'Neil·Denis Simon·Michael Stoll
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Abstract

This is the first in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n. The methods we describe are practical in the case n=3 for elliptic curves over the rationals, and have been implemented in Magma.

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John Cremona, Tom Fisher, Cathy O'Neil, Denis Simon, Michael Stoll. 2006-06-23. Explicit n-descent on elliptic curves, I. Algebra. https://doi.org/10.1515/crelle.2008.012

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