Rational points on a modular curve $X_H$ that correspond to elliptic curves with complex multiplication are called **CM points**.

Over $\Q$ these correspond to rational points in the fiber of the map $j\colon X_H\to X(1)$ above one of the $13$ $j$-invariants of CM elliptic curves over $\Q$ corresponding to one of the **CM discriminants**
\[
-3,-4,-7,-8,-11,-12,-16,-19,-27, -27, -43,-67,-163,
\] of imaginary quadratic orders of class number one. These $13$ orders lie in $9$ distinct imaginary quadratic fields.

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- Review status: beta
- Last edited by Bjorn Poonen on 2022-03-24 18:03:36

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- 2022-03-24 18:03:36 by Bjorn Poonen
- 2022-03-20 17:57:49 by Andrew Sutherland
- 2022-03-20 17:56:38 by Andrew Sutherland
- 2022-03-20 17:55:38 by Andrew Sutherland
- 2022-03-20 17:55:24 by Andrew Sutherland

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