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- W4313598510 abstract "Consider the elliptic curve $E$ given by the Weierstrass equation $y^2 = x^3 - 11x - 14$, which has complex multiplication by the order of conductor $2$ inside $mathbb{Z}[i]$. It was recently observed in a paper of Daniels and Lozano-Robledo that, for each $n geq 2$, $mathbb{Q}(mu_{2^{n+1}}) subseteq mathbb{Q}(E[2^n])$. In this note, we prove that this (a priori surprising) ``tower of vertical entanglements'' is actually more a feature than a bug: it holds for any elliptic curve $E$ over $mathbb{Q}$ with complex multiplication by any order of even discriminant." @default.
- W4313598510 created "2023-01-06" @default.
- W4313598510 creator A5060681058 @default.
- W4313598510 date "2023-01-03" @default.
- W4313598510 modified "2023-09-23" @default.
- W4313598510 title "CM elliptic curves and vertically entangled 2-adic groups" @default.
- W4313598510 doi "https://doi.org/10.48550/arxiv.2301.01680" @default.
- W4313598510 hasPublicationYear "2023" @default.
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