Error when opening a SSL connection with httpclient

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SSL

When sending a request with the HttpClient class, we always get the 'The request was aborted: Could not create SSL/TLS secure channel' error. The code is part of a library and has successfully accessed other services before. That's why I suspect that something about the specific service we are trying to access is different and the question is how to identify that difference. The error message is not really helpful in that regard.

What I have tried:

The following code was compiled under .NET famework 4.5.1. I have read that switching to a higher framework version might fix the problem. I have NOT tried this yet, because this library is only part of a much larger solution and a version change involves a little more than just changing a setting in the current project.

This is how the HttpClient is initialized:

protected override void Initialize()
{
    base.Initialize();

    ServicePointManager.Expect100Continue = true;
    ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls12;
    //ServicePointManager.SecurityProtocol = SecurityProtocolType.Ssl3 | 
SecurityProtocolType.Tls | SecurityProtocolType.Tls11 | 
SecurityProtocolType.Tls12;

    handler = new HttpClientHandler()
    {
        ClientCertificateOptions = ClientCertificateOption.Automatic,
        UseDefaultCredentials = false,
        PreAuthenticate = false,
        Credentials = new NetworkCredential
                      (Parameter.Name, Parameter.Password)
    };

    client = new HttpClient(handler)
    {
        Timeout = new TimeSpan(0, 1, 0)
    };

    client.DefaultRequestHeaders.Accept.Add
    (new MediaTypeWithQualityHeaderValue("application/json"));

     Result.Succeeded = true;
}