Rational singular moduli
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Numbers
$\Delta$
$j$
-163:
-262537412640768000
-67:
-147197952000
-43:
-884736000
-28:
16581375
-27:
-12288000
-19:
-884736
-16:
287496
-12:
54000
-11:
-32768
-8:
8000
-7:
-3375
-4:
1728
-3:
0
Definition
Let $H$ be the upper half plane and $j$ the $j$-invariant. A singular modulus is a number of the form $j(\tau)$ for an imaginary quadratic $\tau \in H$. This list contains all rational singula moduli.
Parameters
$\Delta$
—   Discriminant
$\Delta$ is the associated discriminant of the complex multiplication order $\mathcal{O} = \text{End}\langle\tau,1\rangle$.
numbers = {d*f^2: j for d, f, j in cm_j_invariants_and_orders(QQ)}