brainpoolP320r1 is the 320-bit Brainpool curve of RFC 5639, with parameters derived verifiably from the digits of π and e.
brainpoolP320r1 is a short Weierstrass curve y² = x³ + ax + b over a 320-bit prime field with a 320-bit prime-order subgroup and cofactor 1; its estimated security level is 160 bits. Status: secure, but regional or niche.
The Brainpool curves (RFC 5639) were generated in a verifiably pseudo-random way: the primes come from the digits of π and the curve coefficients from the digits of e, so anyone can recompute them (RFC 5639 Appendix A). brainpoolP320r1 is the 320-bit random curve; it has prime order (cofactor 1) and about 160 bits of security.
COSE registers ESB320 — ECDSA with brainpoolP320r1 and SHA-384 (RFC 9864) — and the curve identifier 257 for ISO/IEC 18013-5 mobile driving licences. NIST SP 800-186 allows the Brainpool curves for interoperability.