Swedish citizen applying for Chinese Visa in Tokyo

I am a Swedish exchange student living in Tokyo and would like to visit Shanghai. I have an alien registration card which does not expire until late December and I want to go there in March. Can I apply directly at the Chinese Embassy here in Tokyo and what would the cost be? I will stay with friends living in Shanghai and I've heard that they can write me an invitation letter, is this true and what other documents would I need?
Many thanks in advance.