With OpenSSL and ECDHE, how to show the actual curve being used?
You can make OpenSSL print out the handshake messages with the -msg parameter:

openssl s_client -msg -connect myserver.net:443


Then look for the ServerKeyExchange message. Here is an example:

&lt;&lt;&lt; TLS 1.2 Handshake [length 014d], ServerKeyExchange
    0c 00 01 49 03 00 17 41 04 6b d8 6e 14 1c 9b 12
    4d 58 29 20 e8 e2 1a 24 0d da 8f 38 1a 5d 85 2b
    2b 70 61 97 3b a7 5b fd b6 14 b3 5d f0 dd ea 7b
    68 d9 eb bc b2 59 32 52 9d 8e 9c 97 c0 d4 45 4c
    (...)


This can be analyzed, using RFC 5246 and RFC 4492 as references. In this case:


0c: this is a ServerKeyExchange message (described in section 5.4 of RFC 4492)
00 01 49: of length 0x000149 bytes (329 bytes)
03: the curve type is "named_curve"
00 17: the curve is secp256r1 (curve identifiers are in section 5.1.1, identifier 0x0017 is 23 in decimal).


secp256r1 is also known as P-256, one of the 15 curves standardized by NIST in FIPS 186-4. In fact this is the curve that almost everybody uses.