no peer certificate available
No client certificate CA names sent
SSL handshake has read 0 bytes and written 305 bytes
New, (NONE), Cipher is (NONE)
Secure Renegotiation IS NOT supported
How can it be possible that the browser is connecting Ok and curl and Python are not? How should I fix this? Is this even my problem (or the owner of the API)?
At the time this question was asked, the site in question supported only a small selection of very weak cipher suites and had very little compatibility with modern user agents. Thus it was impossible for most browsers or even robots to negotiate a connection, let alone a secure one.
The site has been (mostly) fixed since; while it still has weak cipher suites and other problems, it should at least be functional.