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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2511.07131 |
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| _version_ | 1866915609646727168 |
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| author | Amir, Beyza Mevlüde Sadek, Mohammad El-Sissi, Nermine |
| author_facet | Amir, Beyza Mevlüde Sadek, Mohammad El-Sissi, Nermine |
| contents | Let $f \in \mathbb Q[x]$ be a square-free polynomial of degree at least $3$, $m_i$, $i=1,2,3$, odd positive integers, and $a_i$, $i=1,2,3$, non-zero rational numbers. We show the existence of a rational function $D\in\mathbb{Q}(v_1,v_2,v_3,v_4)$ such that the Jacobian of the quadratic twist of $y^2=f(x)$ and the Jacobian of the $m_i$-twist, respectively $2m_i$-twist, of $y^2=x^{m_i}+a_i^2$, $i=1,2,3$, by $D$ are all of positive Mordell-Weil ranks. As an application, we present families of hyperelliptic curves with large Mordell-Weil rank. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07131 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Families of twists of tuples of hyperelliptic curves Amir, Beyza Mevlüde Sadek, Mohammad El-Sissi, Nermine Number Theory Let $f \in \mathbb Q[x]$ be a square-free polynomial of degree at least $3$, $m_i$, $i=1,2,3$, odd positive integers, and $a_i$, $i=1,2,3$, non-zero rational numbers. We show the existence of a rational function $D\in\mathbb{Q}(v_1,v_2,v_3,v_4)$ such that the Jacobian of the quadratic twist of $y^2=f(x)$ and the Jacobian of the $m_i$-twist, respectively $2m_i$-twist, of $y^2=x^{m_i}+a_i^2$, $i=1,2,3$, by $D$ are all of positive Mordell-Weil ranks. As an application, we present families of hyperelliptic curves with large Mordell-Weil rank. |
| title | Families of twists of tuples of hyperelliptic curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2511.07131 |