numsp512d1 is a 512-bit 'nothing up my sleeve' Weierstrass curve proposed by Microsoft Research in 2014.
numsp512d1 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.
The NUMS curves (Bos, Costello, Longa and Naehrig, 2014; draft-black-numscurves) were generated deterministically so that no constant needs explaining: p = 2^512 − c with the smallest c that makes p prime and p ≡ 3 (mod 4), then the smallest b for which y² = x³ − 3x + b and its twist both have prime order. numsp512d1 is that prime-order Weierstrass curve, at about 256 bits of security.
The Internet-Draft expired in 2015 without becoming an RFC and no protocol registry lists the curves; Microsoft Research's MSR ECCLib implements them. The twisted Edwards NUMS curve over the same prime is numsp512t1.