Windows: Schannel error 40 and Internet Explorer

When I needed to access a secure page (HTTPS) from Internet Explorer 11 on a Windows 2008 R2 server, I always got a "Page cannot be displayed" error. I could, though, access that page from another machine or another browser on the same server. Looking in the Event Viewer I saw: Log Name: System Source: Schannel Date: 05.01.2015 12:11:58 Event ID: 36887 Task Category: None Level: Error Keywords: User: SYSTEM Description: The following fatal alert was received: 40. Schannel error 40 means: Read more [...]