Rational singular moduli

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Numbers

Δ

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:

Definition

Let

H

be the upper half plane and

j

the

j

-invariant. A singular modulus is a number of the form

j (τ)

for an imaginary quadratic

τ \in H

. This list contains all rational singula moduli.

Parameters

Δ

— Discriminant

Comments

(1)

Δ

is the associated discriminant of the complex multiplication order

O = End ⟨ τ, 1 ⟩

Programs

(P1)

Sage

numbers = {d*f^2: j for d, f, j in cm_j_invariants_and_orders(QQ)}

Links

[1]

Data properties

Entries are of type: integer

Table is complete: yes