numsp512t1 is a 512-bit 'nothing up my sleeve' twisted Edwards curve proposed by Microsoft Research in 2014.
numsp512t1 is a twisted Edwards curve ax² + y² = 1 + dx²y² 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.
Over the same prime as numsp512d1, numsp512t1 is the twisted Edwards curve −x² + y² = 1 + dx²y² with the smallest d for which both the curve and its twist have order four times a prime (draft-black-numscurves, Appendix A). Its cofactor is 4 and its security about 256 bits.
Like the Weierstrass NUMS curves it was never standardised; Microsoft Research's MSR ECCLib implements it.