These are ordinary curves of with embedding degree 6, whose orders are prime or a prime multiplied by a small constant.
A type D curve is defined over some field F_q and has order h * r where r is a prime and h is a small constant. Over the field F_q6 its order is a multiple of r2.
Typically the order of the curve E is around 170 bits, as is F_q, the base field, thus qk is around the 1024-bit mark which is commonly considered good enough.
d_param struct fields:
q F_q is the base field n # of points in E(F_q) r large prime dividing n h n = h * r a E: y^2 = x^3 + ax + b b nk # of points in E(F_q^k) hk nk = hk * r * r coeff0 coefficients of a monic cubic irreducible over F_q coeff1 coeff2 nqr quadratic nonresidue in F_q
These were discovered by Miyaji, Nakabayashi and Takano, "New explicit conditions of elliptic curve traces for FR-reduction".