ECC is based on domain parameters defined by various standards. You can see the list of all available standards defined and recommended curves available in OpenSSL using the following command. (Once again, only partial output is shown here, and it is truncated in the middle.):
$ openssl ecparam -list_curves secp112r1 : SECG/WTLS curve over a 112 bit prime field secp112r2 : SECG curve over a 112 bit prime field secp128r1 : SECG curve over a 128 bit prime field secp128r2 : SECG curve over a 128 bit prime fieldsecp160k1 : SECG curve over a 160 bit prime field secp160r1 : SECG curve over a 160 bit prime field secp160r2 : SECG/WTLS curve over a 160 bit prime fieldsecp192k1 : SECG curve over a 192 bit prime fieldsecp224k1 : SECG curve ...
