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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.00215 |
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| _version_ | 1866918223004303360 |
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| author | Sultanow, Eldar Jeschke, Anja Tfiha, Amir Darwish Tehrani, Madjid Buchanan, William J |
| author_facet | Sultanow, Eldar Jeschke, Anja Tfiha, Amir Darwish Tehrani, Madjid Buchanan, William J |
| contents | Let $p$ and $q$ be two distinct odd primes, $p<q$ and $E_{p,q}:y^2=x^3-pqx$ be an elliptic curve. Fix a line $L_{a.b}:y=\frac{a}{b}x$ where $a\in \mathbb{Z},b\in \mathbb{N}$ and $(a,b)=1$. We study sufficient conditions that $p$ and $q$ must satisfy so that there are infinitely many elliptic curves $E_{p,q}$ that intersect $L_{a,b}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00215 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On families of elliptic curves $E_{p,q}:y^2=x^3-pqx$ that intersect the same line $L_{a,b}:y=\frac{a}{b}x$ of rational slope Sultanow, Eldar Jeschke, Anja Tfiha, Amir Darwish Tehrani, Madjid Buchanan, William J Number Theory Algebraic Geometry 14H52 Let $p$ and $q$ be two distinct odd primes, $p<q$ and $E_{p,q}:y^2=x^3-pqx$ be an elliptic curve. Fix a line $L_{a.b}:y=\frac{a}{b}x$ where $a\in \mathbb{Z},b\in \mathbb{N}$ and $(a,b)=1$. We study sufficient conditions that $p$ and $q$ must satisfy so that there are infinitely many elliptic curves $E_{p,q}$ that intersect $L_{a,b}$. |
| title | On families of elliptic curves $E_{p,q}:y^2=x^3-pqx$ that intersect the same line $L_{a,b}:y=\frac{a}{b}x$ of rational slope |
| topic | Number Theory Algebraic Geometry 14H52 |
| url | https://arxiv.org/abs/2401.00215 |