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...
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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 |
| _version_ | 1797421976176820224 |
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| author | Hasan Sankari Mustafa bojakli |
| author_facet | Hasan Sankari Mustafa bojakli |
| author_sort | Hasan Sankari |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-03-09T07:26:29Z |
| format | Article |
| id | doaj.art-b2a340a3f85346669138451d0d5e96e9 |
| institution | Directory Open Access Journal |
| issn | 2079-3057 2663-4252 |
| language | Arabic |
| last_indexed | 2024-03-09T07:26:29Z |
| publishDate | 2019-02-01 |
| publisher | Tishreen University |
| record_format | Article |
| series | مجلة جامعة تشرين للبحوث والدراسات العلمية، سلسلة العلوم الأساسية |
| spelling | doaj.art-b2a340a3f85346669138451d0d5e96e92023-12-03T07:05:53ZaraTishreen Universityمجلة جامعة تشرين للبحوث والدراسات العلمية، سلسلة العلوم الأساسية2079-30572663-42522019-02-01393Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8)Hasan SankariMustafa bojakli 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. http://www.journal.tishreen.edu.sy/index.php/bassnc/article/view/3743 |
| spellingShingle | Hasan Sankari Mustafa bojakli Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8) مجلة جامعة تشرين للبحوث والدراسات العلمية، سلسلة العلوم الأساسية |
| title | Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8) |
| title_full | Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8) |
| title_fullStr | Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8) |
| title_full_unstemmed | Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8) |
| title_short | Solving the Diophantine equations y^2=x^3+Dx where D≡5(mod 8) |
| title_sort | solving the diophantine equations y 2 x 3 dx where d≡5 mod 8 |
| url | http://www.journal.tishreen.edu.sy/index.php/bassnc/article/view/3743 |
| work_keys_str_mv | AT hasansankari solvingthediophantineequationsy2x3dxwhered5mod8 AT mustafabojakli solvingthediophantineequationsy2x3dxwhered5mod8 |