You are missing a }
to close the authenticate function.
Besides that your form and the submit button have the same id. It is in general a bad idea to have two html tags with the same id and this means that your function is called after clicking on the form.
You should wrap your script inside a $(document).ready.
$(document).ready(function() {
// your script.
});
This will prevent your script from running before the elements are loaded.
You should also prevent the form from submitting by ending the click function with a return false;
statement. This prevents the page refresh.
And I don't have experience with jsonp but it generates an error for me. I would suggest using normal json but I don't know your other plans with the script.