I have the following code to align several equations:

```
\begin{aligned}
s_{1} & :=\sum_{1 \leq j \leq m} X_{j} \\
s_{2} & :=\sum_{1 \leq j<k \leq m} X_{j} \cdot X_{k} \\
      & \vdots \\
s_{k} & :=\sum_{1 \leq j_{1}<j_{2}<\cdots<j_{k} \leq m} X_{j_{1}} \cdot X_{j_{2}} \cdot \cdots \cdot X_{j_{k}} \\
      & \vdots \\
s_{m} & :=X_{1} X_{2} \cdots X_{m}
\end{aligned}

```

![LaTeX output of above code with only minimal.cls and amsmath.sty](https://i.stack.imgur.com/zCPh2.png)

I would like to ask why the colon does not align with the vdots and a solution for it.