Just noticed this today whilst trying to download Freya.
(Note: I have changed the actual code)
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It's a time-code that stops hotlinking. It's not tracked, although your button click is.
Hi there! I built both the system to generate those links and manage the delivery network that delivers the downloads, so I'm quite qualified to answer this, although Ravan has it mostly covered.
The elementary.io website is actually open-source in itself, and the code that generates (most) of this link can be seen in /_backend/classify.current.php, Line 14. That line is this:
$download_link = '//'.$region.'.dl.elementary.io/download/'.base64_encode(time()).'/';
You see the bit about time in the variable? It's basically encoding the time, and the download server decodes it, and checks it's within the last few days. If not, it tells you to get a new link. This is to combat hotlinking leeching bandwidth off of our servers, something several sites had been doing previously. This is why you get
405: Not Allowed, the link expired.