c# - WebRequest HTTP POST with Cookie (port from curl script)

The IBM RTC RESTful api gives an example of a shell script for authenticating with the server:

COOKIES=./cookies.txt

USER=my_user
PASSWORD=my_password
HOST="https://myJazzServer:9092/jazz"

curl -k -c $COOKIES "$HOST/authenticated/identity"

curl -k -L -b $COOKIES -c $COOKIES -d j_username=$USER -d j_password=$PASSWORD "$HOST/authenticated/j_security_check"

This works perfectly, however i need to authenticate with the server using c#.

So far i have the following, but it isn't working (returns the authorization failed page):

    CookieContainer _cookie;

    public string _RTC()
    {
        HttpWebRequest request = (HttpWebRequest)WebRequest.Create("https://myJazzServer.com:9092/jazz/authenticated/identity");
        if (_cookie == null)
        {
            _cookie = new CookieContainer();
        }
        string a;
        request.CookieContainer = _cookie;
        using (var response = request.GetResponse())
        {
            using (StreamReader sr = new StreamReader(response.GetResponseStream()))
            {
                a = sr.ReadToEnd();
            }
        }




        byte[] data = (new ASCIIEncoding()).GetBytes("j_username=myUser&j_password=MyPass");

        request = (HttpWebRequest)WebRequest.Create("https://myJazzServer.com:9092/jazz/authenticated/j_security_check");

        request.Method = "POST";
        request.ContentType = "text/html";
        request.ContentLength = data.Length;
        request.CookieContainer = _cookie;
        Stream reqStream = request.GetRequestStream();
        reqStream.Write(data,0,data.Length);

        string b;

        using (var response = request.GetResponse())
        {
            using (var reader = new StreamReader(response.GetResponseStream()))
            {
                b = reader.ReadToEnd();
            }
        }
    }