def METHOD_NAME(key, J):
    """
    Returns the cached abelian variety with given key. This is used
    internally by the abelian varieties constructor.
    INPUT:
    -  ``key`` - hashable
    -  ``J`` - modular abelian variety
    OUTPUT:
    -  ``J`` - returns the modabvar, to make code that uses
       this simpler
    EXAMPLES::
        sage: sage.modular.abvar.constructor._saved('37', J0(37))
        Abelian variety J0(37) of dimension 2
    """
    _cache[key] = weakref.ref(J)
    return J