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- W2041071303 abstract "We consider an elliptic curve $E$ defined over ${bf Q}$ which has an isogeny of prime degree $p$ defined over ${bf Q}$. Assuming that $E$ does not have complex multiplication and that $p > 7$, we show that the image of the Galois representation defined by the action of $G_{{bf Q}}$ on the $p$-adic Tate module is as large as possible, given the existence of such an isogeny. Under a certain additional assumption, we also prove that result for $p = 7$. For $p = 5$, we show that the image is as large as allowed by the isogenies of $p$-power degree defined over ${bf Q}$." @default.
- W2041071303 created "2016-06-24" @default.
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- W2041071303 date "2012-01-01" @default.
- W2041071303 modified "2023-10-16" @default.
- W2041071303 title "The image of Galois representations attached to elliptic curves with an isogeny" @default.
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- W2041071303 doi "https://doi.org/10.1353/ajm.2012.0040" @default.
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