How to identify elliptic curve name from an Openssl certificate?

I've an OpenSSL certificate in .cer format, most probably generated with openssl ecparam command and having ciphers one from

TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384

or

TLS_DH_RSA_WITH_AES_256_GCM_SHA384

or

TLS_ECDHE_ECDSA_WITH_AES_256_CBC_SHA384,

because only these three ciphers are listed in my server.

How can I identify using openssl command which curve is being used in my certificate?

You can use the openssl x509 command with -text output. The curve name is part of the subject public key info.

$ openssl x509 -in stackoverflow-com.cer-text
Certificate:
    Data:
        Version: 3 (0x2)
        Serial Number:
            04:0f:a0:c7:81:0b:66:11:f4:69:fd:c8:ce:2e:2b:a6:43:7d
        Signature Algorithm: ecdsa-with-SHA384
        Issuer: C=US, O=Let's Encrypt, CN=E6
        Validity
            Not Before: Sep  6 18:59:06 2024 GMT
            Not After : Dec  5 18:59:05 2024 GMT
        Subject: CN=stackoverflow.com
        Subject Public Key Info:
            Public Key Algorithm: id-ecPublicKey
                Public-Key: (256 bit)
                pub:
                    04:1b:87:f7:7e:8a:18:f6:1e:15:18:31:b1:d3:9a:
                    f3:11:06:0d:51:3c:d7:25:ab:5c:d5:79:dd:51:97:
                    2a:11:a6:f8:4d:5a:84:08:a1:dc:27:a3:59:ce:31:
                    e0:b8:b6:aa:79:5a:f9:06:11:75:e4:f1:3c:13:3b:
                    5f:ac:99:29:b1
                ASN1 OID: prime256v1
                NIST CURVE: P-256       <<<---- curve name
[...]