The table below lists ordinary elliptic curves defined over a prime field F_p with 171 < log₂(p) < 192. Each curve has prime order N and embedding degree k=6 (i.e. p⁶ is congruent to 1 mod N and no smaller power of p has this property). These parameters yield a pairing-friendly curve at or above the 80-bit security level (See Freeman, Scott, and Teske, A taxonomy of pairing-friendly curves, 2006).

The data is organized according to the negative fundamental discriminant D satisfying 4p=t²− v²D, where N=p+1-t. The endomorphism ring of the corresponding curve is isomorphic to the imaginary quadratic order with discrminant D (the ring of integers of the number field Q[√D], since D is fundamental). Attached to each entry is a file containing a complete list of all such curves (up to isomorphism).

The values of D were obtained using the method of Karabina and Teske described in On prime-order elliptic curves with embedding degree 3, 4, and 6, ANTS VIII, (2008). The curves were constructed by computing the Hilbert class polynomial modulo p, using the algorithm described in Computing Hilbert class polynomials with the Chinese Remainder Theorem.