{
  "source": "G. Nebe and N. J. A. Sloane, A Catalogue of Lattices",
  "retrieved_utc": "2026-10-25",
  "comparison": "All 17 lower triangles agree with the live catalogue and the generator attached to T147. LAMBDA11/12/13 are MAX variants.",
  "matrices": {
    "LAMBDA9": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA9.html",
      "html_sha256": "1862395517dae8af9d7951443a7813948f182ce3b8d8a350cebc1e93c2ac2a75"
    },
    "LAMBDA10": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA10.html",
      "html_sha256": "10a1fa86d38c92c30d4df0f95169d0fee64e3584bc7316e35b19d0c325229c1a"
    },
    "LAMBDA11": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA11.html",
      "html_sha256": "f8f5a48692e28ec52d35b27acd872c1fb2247b87c5fe509d0c286ad94d8522a3"
    },
    "LAMBDA12": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA12.html",
      "html_sha256": "195df1de81902ca330a0489ecb26d6ed1f24740abb3ed87dfc9ec1be0127c36a"
    },
    "LAMBDA13": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA13.html",
      "html_sha256": "aaa416154b9550ac8c773f0297506e9e4ac4813238062638f4eb2e0b1939ba2f"
    },
    "LAMBDA14": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA14.html",
      "html_sha256": "7ee40a9247c4931a3063b5a33f87d4f5c9524dfaf388228053d4c5ce076887b1"
    },
    "LAMBDA15": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA15.html",
      "html_sha256": "d6f17507cdf3a453aab0d73408a157d4f1ac96324f4a85b004674564ba775c88"
    },
    "LAMBDA16": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA16.html",
      "html_sha256": "b07c9ec5b770bf2a2ef05936cd04a15ebab7627654e9c54bc07d141e23bcadf7"
    },
    "LAMBDA17": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA17.html",
      "html_sha256": "cc3b101917f737ca7f38e550af32a6433c546872e67715923ecbf75357dce36b"
    },
    "LAMBDA18": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA18.html",
      "html_sha256": "da32049d0cb4b1173f3f63c913e1f6ffe957eb65e1645a6c77b3e816fd98e36e"
    },
    "LAMBDA19": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA19.html",
      "html_sha256": "aa9c0c5dc24d3a12cf6203c27622b464bb1d7f9dd7784080f304e69a8feb8e78"
    },
    "LAMBDA20": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA20.html",
      "html_sha256": "a851e5e03638e275c913ba87ab37ecf6550df1ab98ba40c37cb8a6775ddddadb"
    },
    "LAMBDA21": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA21.html",
      "html_sha256": "317eb3c36c5600947e826d4e835b32027667f191487f8426588c0a06fd5c2c04"
    },
    "LAMBDA22": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA22.html",
      "html_sha256": "b4e4f08d2c4a4926599b6551ab852b578877f7c3cbebbfed57ea8b8924e3aab4"
    },
    "LAMBDA23": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/LAMBDA23.html",
      "html_sha256": "6b12d834cddfde6445f9107aba15754070917552582dbb8419a807cd18c597ce"
    },
    "K12": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/K12.html",
      "html_sha256": "163e03dfa9a4ab07675daa6e97a371bcfdb38f6195c311c63c699872b3e486c9"
    },
    "Leech": {
      "url": "https://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/Leech.html",
      "html_sha256": "0d5967713c09e2fda1ba06fc183ca376eccc73b9e4612e88d36c5fe70d13479c"
    }
  },
  "published_group_orders": {
    "E6.b": 103680,
    "E7.b": 2903040,
    "E8.b": 696729600,
    "Leech.b": 8315553613086720000
  },
  "independent_sources": {
    "Barnes-Wall": "https://oeis.org/A014116",
    "Coxeter-Todd": "https://neilsloane.com/doc/Me107.pdf",
    "Coxeter-Todd-doi": "10.1017/S0305004100060746",
    "Coxeter-Todd-note": "Page 429 gives complex group order 39191040 and an index-two real extension. Its printed final factor 8 in the real order is erroneous: doubling equation (16) gives final factor 7 and real order 78382080. The page was checked visually.",
    "PARI": "https://pari.math.u-bordeaux.fr/dochtml/html-stable/Linear_algebra__Vectors__matrices_and_sets.html#qfauto"
  }
}