Database of Modular Polynomials¶
-
class
sage.databases.db_modular_polynomials.AtkinModularCorrespondenceDatabase¶ Bases:
sage.databases.db_modular_polynomials.ModularCorrespondenceDatabase
-
class
sage.databases.db_modular_polynomials.AtkinModularPolynomialDatabase¶ Bases:
sage.databases.db_modular_polynomials.ModularPolynomialDatabaseThe database of modular polynomials Phi(x,j) for \(X_0(p)\), where x is a function on invariant under the Atkin-Lehner invariant, with pole of minimal order at infinity.
-
class
sage.databases.db_modular_polynomials.ClassicalModularPolynomialDatabase¶ Bases:
sage.databases.db_modular_polynomials.ModularPolynomialDatabaseThe database of classical modular polynomials, i.e. the polynomials Phi_N(X,Y) relating the j-functions j(q) and j(q^N).
-
class
sage.databases.db_modular_polynomials.DedekindEtaModularCorrespondenceDatabase¶ Bases:
sage.databases.db_modular_polynomials.ModularCorrespondenceDatabaseThe database of modular correspondences in \(X_0(p) \times X_0(p)\), where the model of the curves \(X_0(p) = \Bold{P}^1\) are specified by quotients of Dedekind’s eta function.
-
class
sage.databases.db_modular_polynomials.DedekindEtaModularPolynomialDatabase¶ Bases:
sage.databases.db_modular_polynomials.ModularPolynomialDatabaseThe database of modular polynomials Phi_N(X,Y) relating a quotient of Dedekind eta functions, well-defined on X_0(N), relating x(q) and the j-function j(q).
-
class
sage.databases.db_modular_polynomials.ModularCorrespondenceDatabase¶ Bases:
sage.databases.db_modular_polynomials.ModularPolynomialDatabase
-
class
sage.databases.db_modular_polynomials.ModularPolynomialDatabase¶ Bases:
object