Background:

Elliptic curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. One of the main benefits in comparison with non-ECC cryptography [..] is the same level of security provided by keys of smaller size. from its Wikipedia entry 2015-11-05

Function	Protocol	Curve	OpenPGP spec.	Library dependency	Token
Signature	ECDSA	NIST ECC: P-256	RFC6637		Gnuk 1.2
Signature	ECDSA	NIST ECC: P-384	RFC6637
Signature	ECDSA	NIST ECC: P-521	RFC6637
Signature	ECDSA	ECC Brainpool: brainpoolP256r1
Signature	ECDSA	ECC Brainpool: brainpoolP384r1
Signature	ECDSA	ECC Brainpool: brainpoolP512r1
Signature	ECDSA	SECG: secp256k1		libgcrypt 1.7	Gnuk 1.2
Signature	EdDSA	RFC8032: Ed25519	RFC4880bis draft		Gnuk 1.2
Encryption	ECDH	NIST ECC: P-256	RFC6637		Gnuk 1.2
Encryption	ECDH	NIST ECC: P-384	RFC6637
Encryption	ECDH	NIST ECC: P-521	RFC6637
Encryption	ECDH	ECC Brainpool: brainpoolP256r1
Encryption	ECDH	ECC Brainpool: brainpoolP384r1
Encryption	ECDH	ECC Brainpool: brainpoolP512r1
Encryption	ECDH	SECG: secp256k1		libgcrypt 1.7	Gnuk 1.2
Encryption	ECDH	RFC7748: Curve25519		libgcrypt 1.7	Gnuk 1.2