45.1 Constructors for certain modular abelian varieties

Module: sage.modular.abvar.constructor

Constructors for certain modular abelian varieties.

Author: William Stein (2007-03)

Module-level Functions

AbelianVariety( X)

Create the abelian variety corresponding to the given definining data.

Input:

X: - an integer, string, newform, modsym space, congruence subgroup or tuple of congruence subgroups

Output: a modular abelian variety

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

J0( N)

Return the Jacobian of the modular curve .

sage: J0(389)
Abelian variety J0(389) of dimension 32

The result is cached:

sage: J0(33) is J0(33)
True

J1( N)

Return the Jacobian of the modular curve .

sage: J1(389)
Abelian variety J1(389) of dimension 6112

JH( N, H)

Return the Jacobian of the modular curve .

sage: JH(389,[2])
Abelian variety JH(389,[2]) of dimension 32

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