My understanding is that during ssl negotiation, the client (i.e. curl) sends a list of ciphers to the server, and the server replies with its preferred choice.
How do I see the list of ciphers that curl is sending?
There is a website that offers curl cipher requestion detection as a service:
However, it does not accept all ciphers - if one of the ciphers they accept is not on the list that your curl is sending, then you will not be able to get a response at all.