Trying to understand the use of ECC in TLS certificates I was looking the certificate of this website: https://www.cloudflare.com that has an ECC based certification. 

I'm just curious to know if is possible to understand which elliptic curve is used and which point is used.

Another thing: I don't understand why in the certificate there is a RSA 2048 public key and not an ECC key.
ECC is indeed used by CloudFlare's website but only for the session key agreement. The authentication is performed using an RSA 2048 bit private key. The corresponding RSA public key is in the certificate. In other words, although ECC is being used, it is not used for authentication and therefore not part of the certificate.

The ciphersuite is:

TLS_ECDHE_RSA_WITH_AES_128_GCM_SHA256


Which means TLS with ECDHE (ephemeral Elliptic Curve Diffie-Hellman) key agreement, RSA based authentication (and thus certificates). The ephemeral part means that no static private ECDH key is used on the server and no public ECDH key is therefore present in the certificate.

Or, as specified by RFC 4492 section 2.4:


  2.4 ECDHE_RSA
  
  This key exchange algorithm is the same as ECDHE_ECDSA except that
     the server's certificate MUST contain an RSA public key authorized
     for signing, and that the signature in the ServerKeyExchange message
     must be computed with the corresponding RSA private key.  The server
     certificate MUST be signed with RSA.


To state that the CloudFlare website is using ECC certificates (not certification, that term means something else) is therefore incorrect. It uses a cipher suite that performs ECDH key agreement.



The used explicit or named parameters are determined during the handshake. The client has the ability to include a list of supported curves, ordered to preference RFC 4492 section 5.1.1. The point format - uncompressed (default) or compressed - can also be indicated. As the EC points themselves are ephemeral (short-lived) you can only retrieve them by analyzing the handshake.



For completeness the rest of the ciphersuite: AES-128 bit encryption using GCM authenticated (AEAD) mode encryption. The final SHA-256 is used as definition of the keyed hash (HMAC) used for key generation (or key derivation) and validation.