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Ranks of elliptic curves in cyclic sextic extensions of $\mathbb{Q}$
- Publication Year :
- 2023
-
Abstract
- 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 $\gg\sqrt X$.<br />Comment: 20 pages, 2 figures. Accepted for publication in Indagationes Mathematicae
- Subjects :
- Mathematics - Number Theory
11G05, 14G05, 14G25, 11G40, 14J28
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2304.01528
- Document Type :
- Working Paper