Families of elliptic curves with rational 3-torsion

@inproceedings{Moody2012FamiliesOE,
  title={Families of elliptic curves with rational 3-torsion},
  author={Dustin Moody and Hongfeng Wu},
  booktitle={J. Math. Cryptol.},
  year={2012}
}
Abstract. In this paper we look at three families of elliptic curves with rational 3-torsion over a finite field. These families include Hessian curves, twisted Hessian curves, and a new family we call generalized DIK curves. We find the number of -isogeny classes of each family, as well as the number of -isomorphism classes of the generalized DIK curves. We also include some formulas for efficient computation on these curves, improving upon known results. In particular, we find better formulas… 
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