Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8)
In this research, we study the Diophantine equations of the form which constitute algebraically abelian variety in projective space and represent, in geometric form, family of elliptic curves over field , besides to building isomorphism between this elliptic curve and subset of ring of integrals...
| Main Authors: | , |
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| Format: | Article |
| Language: | Arabic |
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Tishreen University
2019-02-01
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| Series: | مجلة جامعة تشرين للبحوث والدراسات العلمية، سلسلة العلوم الأساسية |
| Online Access: | http://www.journal.tishreen.edu.sy/index.php/bassnc/article/view/3743 |
| Summary: |
In this research, we study the Diophantine equations of the form which constitute algebraically abelian variety in projective space and represent, in geometric form, family of elliptic curves over field , besides to building isomorphism between this elliptic curve and subset of ring of integrals, thus find the maximal finite extension for field and determine the number of points that are finite torsion and torsion to this family in which we can determine some value of such that the rank of elliptic curve above the field equal to one.
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| ISSN: | 2079-3057 2663-4252 |