@article{42796,
  abstract     = {{We give an enumeration of all positive definite primitive Z-lattices in dimension n ≥ 3 whose genus consists of a single isometry class. This is achieved by using bounds obtained from the Smith–Minkowski–Siegel mass formula to computationally construct the square-free determinant lattices with this property, and then repeatedly calculating pre-images under a mapping first introduced by G. L. Watson.

We hereby complete the classification of single-class genera in dimensions 4 and 5 and correct some mistakes in Watson’s classifications in other dimensions. A list of all single-class primitive Z-lattices has been compiled and incorporated into the Catalogue of Lattices.}},
  author       = {{Lorch, David and Kirschmer, Markus}},
  issn         = {{1461-1570}},
  journal      = {{LMS Journal of Computation and Mathematics}},
  keywords     = {{Computational Theory and Mathematics, General Mathematics}},
  pages        = {{172--186}},
  publisher    = {{Wiley}},
  title        = {{{Single-class genera of positive integral lattices}}},
  doi          = {{10.1112/s1461157013000107}},
  volume       = {{16}},
  year         = {{2013}},
}