How do I create 256 bit self-signed certificate key with OpenSSL?
CodesInChaos was right. I should have edited the configuration of the server. I added the SSLCipherSuite line in Apache config and it worked:
SSLCipherSuite AES256-SHA
Common misunderstanding, SSL certificates don't dictate cipher strength a web site uses, the Web server SSL configuration does. There are two types of Certificates, signed with RSA or EC. If you want to use SSL Ciphers with ECDH, then you need an EC signed cert, otherwise RSA certs will only be able to use RSA ciphers.