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Results tagged with complex-multiplication
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user 5015
3
votes
Elliptic curve with CM and image of Galois representation in normalizer of nonsplit Cartan
By cm theory, $E[p]$ is isomorphic to $\mathcal{O}_K/(p)$ as an $\mathcal{O}_K$-module. Elements in $\operatorname{Gal}(\bar{\mathbb{Q}}/K)$ act $\mathcal{O}_K$-linearly on $E[p]$ since they commute w …
- 8,945
8
votes
Example of elliptic curve with CM (complex multiplication) by \sqrt{-7}
I am sure others (magma, etc) can do the same. With sage the following lines will produce the rational functions $\bigl(f(x,y), g(x,y)\bigr)$ representing the multiplication by $(1\pm\sqrt{-7})/2$ on …
- 8,945