You can't sign up for a CRM 2011 Online trial now. CRM 2013 solutions aren't backward-compatible with CRM 2011, though I imagine you could dig into the XML and make changes to push it back. I wouldn't recommend it, though.
If you need to develop for CRM 2011, your best bet is to set up a local development environment. Or, you could use Azure, set up some virtual servers, and install CRM 2011 on those virtual servers. No local resources needed.
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