The handful of investors who are able to get their hands on Twitter shares continue to have the utmost faith in the company. Another private market auction has taken place, and this time, eager supporters placed bids high enough to push Twitter’s valuation to $7.7 billion.

To put that in perspective: AOL’s market cap is about $2.1 billion right now, and IAC’s market cap is closer to $3.2 billion. Meanwhile, Yahoo’s market cap is $22.4 billion, but its stakes in Alibaba and Yahoo Japan contribute a great deal to that total.

Also, it’s important to remember that Twitter itself was just valued at $3.7 billion in mid-December when it raised $200 million from Kleiner Perkins Caufield Byers and a few other sources.

It’s hard to even guess what might happen next. We could make forecasts based on Twitter’s recent record of success, of course, but either in terms of percentages or absolute dollars, that sort of growth rate can’t be sustained forever. (Not that it needs to be.)

In any event, let’s consider a few more details concerning the auction that put Twitter’s value at $7.7 billion. It was conducted through Sharespost, it was oversubscribed, and individual shares sold for $34.50 each.

Biz Stone remains adamant that Twitter won’t seek more funding or go public anytime soon, by the way.