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Your search keyword '"Xiong, Maosheng"' showing total 1 results
Start Over Author "Xiong, Maosheng" Topic analytic geometry Journal journal of number theory Publisher academic press inc.
1 results on '"Xiong, Maosheng"'

1. On elliptic curves <f>y2=x3-n2x</f> with rank zero

Author

Feng, Keqin and Xiong, Maosheng

Subjects
*ALGEBRAIC curves, *ALGEBRAIC varieties, *CALCULUS, *ANALYTIC geometry
Abstract

In this paper we determine all elliptic curves En:y2=x3-n2x with the smallest 2-Selmer groups Sn=Sel2(En(Q))={1} and Sn′=Sel2(En′(Q))={±1,±n}(En′:y2=x3+4n2x) based on the 2-descent method. The values of n for such curves En are described in terms of graph-theory language. It is well known that the rank of the group En(Q) for such curves En is zero, the order of its Tate-Shafarevich group is odd, and such integers n are non-congruent numbers. [Copyright &y& Elsevier]

Published
2004
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