GC512A (id-tc26-gost-3410-12-512-paramSetA) is a 512-bit curve of GOST R 34.10-2012.
GC512A is a short Weierstrass curve y² = x³ + ax + b over a 512-bit prime field with a 512-bit prime-order subgroup and cofactor 1; its estimated security level is 256 bits. Status: secure, but regional or niche.
GOST R 34.10-2012 added 512-bit signature keys. paramSetA, published in RFC 7836 §5.1.1, is y² = x³ − 3x + b over the prime 2^512 − 569 and has prime order, for about 256 bits of security.
Signatures use the 512-bit Streebog hash; TLS lists the curve as group GC512A with signature scheme gostr34102012_512a (RFC 9189, RFC 9367).