Sadly, the answer isn't so simple, except to say: it is not a cookie.
The webpage _probably_ uses "Basic" authentication, but may use other forms.
As far as providing authentication information to webclient, you neglected to mention which language you are programming in.
Here is an article that may answer your question if you are using a .NET language: HTTP GET with .NET WebClient
And if you need more gory details on WebClient, here is the MSDN page on WebClient
]. Even so, you may need to provide more details when you create your Credentials to give your WebClient, which is discussed on this MSDN page on adding to the CredentialsCache
[UPDATE:] Often, after initial authentication, the server will send back a cookie with a SESSION ID NUMBER. Each further page access from the same browser, in the same session, will send this session ID cookie, so the server knows the access is already authenticated.