def METHOD_NAME(self, x, sections, pad=False):
    r"""Finds the connected elements of the Operator. Starting
    from a given quantum number x, it finds all other quantum numbers x' such
    that the matrix element :math:`O(x,x')` is different from zero. In general there
    will be several different connected states x' satisfying this
    condition, and they are denoted here :math:`x'(k)`, for
    :math:`k=0,1...N_{\mathrm{connected}}`.
    This is a batched version, where x is a matrix of shape (batch_size,hilbert.size).
    Args:
        x (matrix): A matrix of shape (batch_size,hilbert.size) containing
                    the batch of quantum numbers x.
        sections (array): An array of size (batch_size) useful to unflatten
                    the output of this function.
                    See numpy.split for the meaning of sections.
        pad (bool): no effect here
    Returns:
        matrix: The connected states x', flattened together in a single matrix.
        array: An array containing the matrix elements :math:`O(x,x')` associated to each x'.
    """
    x = concrete_or_error(
        np.asarray,
        x,
        NumbaOperatorGetConnDuringTracingError,
        self,
    )
    return self._flattened_kernel(x, sections, self.edges, self._h, self._J)