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- W1873059969 abstract "For a given group $G$ and an elliptic curve $E$ defined over a number field $K$, I discuss the problem of finding $G$-extensions of $K$ over which $E$ gains rank. I prove the following theorem, extending a result of Fearnley, Kisilevsky, and Kuwata: Let $n = 3,4,$ or $6$. If $K$ contains its $n^{th}$-roots of unity then, for any elliptic curve $E$ over $K$, there are infinitely many $mathbb{Z}/nmathbb{Z}$-extensions of $K$ over which $E$ gains rank." @default.
- W1873059969 created "2016-06-24" @default.
- W1873059969 creator A5051264384 @default.
- W1873059969 date "2013-01-01" @default.
- W1873059969 modified "2023-09-27" @default.
- W1873059969 title "Ranks of elliptic curves over cyclic cubic, quartic, and sextic extensions" @default.
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- W1873059969 hasPublicationYear "2013" @default.
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