Database of Hilbert Polynomials

class sage.databases.db_class_polynomials.AtkinClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Atkin class polynomials.

model = 'Atk'

class sage.databases.db_class_polynomials.ClassPolynomialDatabase

Bases: object

class sage.databases.db_class_polynomials.DedekindEtaClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Dedekind eta class polynomials.

model = 'Eta'

class sage.databases.db_class_polynomials.HilbertClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Hilbert class polynomials.

EXAMPLES:

sage: db = HilbertClassPolynomialDatabase()
sage: db[-4]                     # optional - database_kohel
x - 1728
sage: db[-7]                     # optional - database_kohel
x + 3375
sage: f = db[-23]; f             # optional - database_kohel
x^3 + 3491750*x^2 - 5151296875*x + 12771880859375
sage: f.discriminant().factor()  # optional - database_kohel
-1 * 5^18 * 7^12 * 11^4 * 17^2 * 19^2 * 23
sage: db[-23]                    # optional - database_kohel
x^3 + 3491750*x^2 - 5151296875*x + 12771880859375

model = 'Cls'

class sage.databases.db_class_polynomials.WeberClassPolynomialDatabase

Bases: ClassPolynomialDatabase

The database of Weber class polynomials.