Constructors for certain modular abelian varieties¶
AUTHORS:
William Stein (2007-03)
- sage.modular.abvar.constructor.AbelianVariety(X)[source]¶
Create the abelian variety corresponding to the given defining data.
INPUT:
X
– integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups
OUTPUT: a modular abelian variety
EXAMPLES:
sage: AbelianVariety(Gamma0(37)) Abelian variety J0(37) of dimension 2 sage: AbelianVariety('37a') Newform abelian subvariety 37a of dimension 1 of J0(37) sage: AbelianVariety(Newform('37a')) Newform abelian subvariety 37a of dimension 1 of J0(37) sage: AbelianVariety(ModularSymbols(37).cuspidal_submodule()) Abelian variety J0(37) of dimension 2 sage: AbelianVariety((Gamma0(37), Gamma0(11))) Abelian variety J0(37) x J0(11) of dimension 3 sage: AbelianVariety(37) Abelian variety J0(37) of dimension 2 sage: AbelianVariety([1,2,3]) Traceback (most recent call last): ... TypeError: X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups
>>> from sage.all import * >>> AbelianVariety(Gamma0(Integer(37))) Abelian variety J0(37) of dimension 2 >>> AbelianVariety('37a') Newform abelian subvariety 37a of dimension 1 of J0(37) >>> AbelianVariety(Newform('37a')) Newform abelian subvariety 37a of dimension 1 of J0(37) >>> AbelianVariety(ModularSymbols(Integer(37)).cuspidal_submodule()) Abelian variety J0(37) of dimension 2 >>> AbelianVariety((Gamma0(Integer(37)), Gamma0(Integer(11)))) Abelian variety J0(37) x J0(11) of dimension 3 >>> AbelianVariety(Integer(37)) Abelian variety J0(37) of dimension 2 >>> AbelianVariety([Integer(1),Integer(2),Integer(3)]) Traceback (most recent call last): ... TypeError: X must be an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups
AbelianVariety(Gamma0(37)) AbelianVariety('37a') AbelianVariety(Newform('37a')) AbelianVariety(ModularSymbols(37).cuspidal_submodule()) AbelianVariety((Gamma0(37), Gamma0(11))) AbelianVariety(37) AbelianVariety([1,2,3])
- sage.modular.abvar.constructor.J0(N)[source]¶
Return the Jacobian \(J_0(N)\) of the modular curve \(X_0(N)\).
EXAMPLES:
sage: J0(389) Abelian variety J0(389) of dimension 32
>>> from sage.all import * >>> J0(Integer(389)) Abelian variety J0(389) of dimension 32
J0(389)
The result is cached:
sage: J0(33) is J0(33) True
>>> from sage.all import * >>> J0(Integer(33)) is J0(Integer(33)) True
J0(33) is J0(33)
- sage.modular.abvar.constructor.J1(N)[source]¶
Return the Jacobian \(J_1(N)\) of the modular curve \(X_1(N)\).
EXAMPLES:
sage: J1(389) Abelian variety J1(389) of dimension 6112
>>> from sage.all import * >>> J1(Integer(389)) Abelian variety J1(389) of dimension 6112
J1(389)
- sage.modular.abvar.constructor.JH(N, H)[source]¶
Return the Jacobian \(J_H(N)\) of the modular curve \(X_H(N)\).
EXAMPLES:
sage: JH(389,[16]) Abelian variety JH(389,[16]) of dimension 64
>>> from sage.all import * >>> JH(Integer(389),[Integer(16)]) Abelian variety JH(389,[16]) of dimension 64
JH(389,[16])