Why does batchnorm1d in Pytorch compute 0 with the following example (2 lines of code)?

Here is the code

import torch
import torch.nn as nn
x = torch.Tensor([[1, 2, 3], [1, 2, 3]])
print(x)
batchnorm = nn.BatchNorm1d(3, eps=0, momentum=0)
print(batchnorm(x))

Here is what is printed

tensor([[1., 2., 3.],
        [1., 2., 3.]])
tensor([[0., 0., 0.],
        [0., 0., 0.]], grad_fn=NativeBatchNormBackward)

What I am expecting is the following:

Using hand calculation, let $x = (1,2,3)$, then $E(x) = (1+2+3)/3 = 2$ and $Var(x) = (1^2 + 2^2 + 3^2) /3 - (2)^2 = 0.9999...$, so that the final output looks like $y \approx (1,2,3) - 2/\sqrt{1} = (-1, 0, 1)$

So, I am expecting the output to the batchnorm be

tensor([[-1., 0., 1.],
        [-1., 0., 1.]])

Can someone please explain where I went wrong?