Ranks of elliptic curves in cyclic sextic extensions of $\mathbb{Q}$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909080937824256 |
|---|---|
| author | Kisilevsky, Hershy Kuwata, Masato |
| author_facet | Kisilevsky, Hershy Kuwata, Masato |
| contents | For an elliptic curve $E/\mathbb{Q}$ we show that there are infinitely many cyclic sextic extensions $K/\mathbb{Q}$ such that the Mordell-Weil group $E(K)$ has rank greater than the subgroup of $E(K)$ generated by all the $E(F)$ for the proper subfields $F \subset K$. For certain curves $E/\mathbb{Q}$ we show that the number of such fields $K$ of conductor less than $X$ is $\gg\sqrt X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01528 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ranks of elliptic curves in cyclic sextic extensions of $\mathbb{Q}$ Kisilevsky, Hershy Kuwata, Masato Number Theory 11G05, 14G05, 14G25, 11G40, 14J28 For an elliptic curve $E/\mathbb{Q}$ we show that there are infinitely many cyclic sextic extensions $K/\mathbb{Q}$ such that the Mordell-Weil group $E(K)$ has rank greater than the subgroup of $E(K)$ generated by all the $E(F)$ for the proper subfields $F \subset K$. For certain curves $E/\mathbb{Q}$ we show that the number of such fields $K$ of conductor less than $X$ is $\gg\sqrt X$. |
| title | Ranks of elliptic curves in cyclic sextic extensions of $\mathbb{Q}$ |
| topic | Number Theory 11G05, 14G05, 14G25, 11G40, 14J28 |
| url | https://arxiv.org/abs/2304.01528 |