GC512C (id-tc26-gost-3410-2012-512-paramSetC) is the 512-bit GOST curve with a twisted Edwards form.
GC512C is a short Weierstrass curve y² = x³ + ax + b over a 512-bit prime field with a 510-bit prime-order subgroup and cofactor 4; its estimated security level is 256 bits. Status: secure, but regional or niche.
Published with GC256A in RFC 7836 §5.2, paramSetC has cofactor 4 and is birationally equivalent to a twisted Edwards curve, so implementations can use complete addition formulas. It shares the prime 2^512 − 569 with GC512A.
TLS lists it as group GC512C with signature scheme gostr34102012_512c (RFC 9189, RFC 9367).