sect409k1 (NIST K-409) is a Koblitz curve over the binary field GF(2^409); NIST has deprecated it.
sect409k1 is a binary Weierstrass curve y² + xy = x³ + ax² + b over the binary field GF(2^409) with a 407-bit prime-order subgroup and cofactor 4; its estimated security level is 192 bits. Status: deprecated, do not use for new keys.
Koblitz curves are binary curves y² + xy = x³ + ax² + 1 with a = 0 or 1; their Frobenius endomorphism lets implementations replace point doublings with cheap squarings (τ-adic scalar multiplication). sect409k1 uses a = 0, the degree-409 reduction polynomial f shown above and cofactor 4, for about 192 bits of security.
FIPS 186-2 to 186-4 listed it as K-409. NIST SP 800-186 (2023) deprecates every curve over a binary field, and RFC 8422 deprecated them for TLS. OpenSSL can be built without binary-curve support (no-ec2m).