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- W3103232193 abstract "Let $mathcal{O}$ be an order in the imaginary quadratic field $K$. For positive integers $M mid N$, we determine the least degree of an $mathcal{O}$-CM point on the modular curve $X(M,N)_{/K(zeta_M)}$ and also on the modular curve $X(M,N)_{/mathbb{Q}(zeta_M)}$: that is, we treat both the case in which the complex multiplication is rationally defined and the case in which we do not assume that the complex multiplication is rationally defined. To prove these results we establish several new theorems on rational cyclic isogenies of CM elliptic curves. In particular, we extend a result of Kwon that determines the set of positive integers $N$ for which there is an $mathcal{O}$-CM elliptic curve $E$ admitting a cyclic, $mathbb{Q}(j(E))$-rational $N$-isogeny." @default.
- W3103232193 created "2020-11-23" @default.
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- W3103232193 date "2020-06-15" @default.
- W3103232193 modified "2023-09-27" @default.
- W3103232193 title "Torsion points and isogenies on CM elliptic curves" @default.
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- W3103232193 doi "https://doi.org/10.1112/jlms.12329" @default.
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