c# programmatically retrieve AWS cognito authorization code

I've been scratching my head with this authflow. I'm able to use Cognito's built hosted UI to return the authorization code, but I haven't figure out how to do this programmatically as we are hosting our own UI for the login.

I'm trying to do what the below link does but in c#, where I accept a user name and password and return the authorization code.

https://.auth.us-west-2.amazoncognito.com/oauth2/authorize?client_id=&redirect_uri=https://localhost:5001&scope=openid&response_type=code

I have tried a number of options to get this working, but so far I haven't been able to figure out how to get the authorization code.

AmazonCognitoIdentityProviderClient provider = new AmazonCognitoIdentityProviderClient(new Amazon.Runtime.AnonymousAWSCredentials(), RegionEndpoint.USWest2);
var userPool = new CognitoUserPool(_userPool, _clientId, provider, _settings.Value.AppClientSecret);


var user = new CognitoUser(username, _clientId, userPool, provider, _settings.Value.AppClientSecret);

var authRequest = new InitiateSrpAuthRequest()
{
    Password = password
};

try
{
    var authResponse = await user.StartWithSrpAuthAsync(authRequest);

    if (authResponse.ChallengeName == ChallengeNameType.NEW_PASSWORD_REQUIRED)
    {
        throw new Exception("User must change password.");
    }

    var timeSpan = TimeSpan.FromSeconds(authResponse.AuthenticationResult.ExpiresIn);
    var expiry = DateTimeOffset.Now + timeSpan;
}
catch (Exception e)
{
    Console.WriteLine(e);
    throw;
}