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- W4313304738 abstract "For positive integers $M mid N$ and an order of discriminant $Delta$ in an imaginary quadratic field $K$ with discriminant $Delta_K < -4$, we determine the fiber of the morphism $X_0(M,N) rightarrow X(1)$ over the closed point $J_{Delta}$ corresponding to $Delta$. We also show that the fiber of the natural map $X_1(M,N) rightarrow X_0(M,N)$ over $J_{Delta}$ is connected. Putting this together we deduce the number of points in the fiber of $X_1(M,N) rightarrow X(1)$ over $J_{Delta}$ and their residual degrees. In the continuation of this work with F. Saia, these results will be extended to $Delta_K in {-4,3}$. These works provide all the information needed to compute, for each positive integer $d$, all subgroups of $E(F)[operatorname{tors}]$, where $F$ is a number field of degree $d$ and $E_{/F}$ is an elliptic curve with complex multiplication (CM)." @default.
- W4313304738 created "2023-01-06" @default.
- W4313304738 creator A5049455406 @default.
- W4313304738 date "2022-12-26" @default.
- W4313304738 modified "2023-09-23" @default.
- W4313304738 title "CM Elliptic Curves: Volcanoes, Reality and Applications" @default.
- W4313304738 doi "https://doi.org/10.48550/arxiv.2212.13316" @default.
- W4313304738 hasPublicationYear "2022" @default.
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