It works like a charm, thanks for the explanation! As someone mentioned below, you need to open port 8888 to the outside world in the EC2 configuration.
To do this, do the following (note that I am no network security expert): In the EC2 console, go to Network & Security > Security Groups. Select your instance and click on the Inbound tab. Click on Edit > Add Rule. Add a custom rule, with port range 8888, source: anywhere, tag: jupyter.
Hope that helps someone :)