This is a list of the 556-560 26 dimensional even lattices of det 3 with no norm 6 roots. There are also 121 with norm 6 roots, corresponding to the 121 even 25 dimensional lattices of det 2, which have an index 2 sublattice equal to the 25 dimensional lattice of determiannt 2 plus a lattice generated by a norm 6 vector. . There are 4 or 5 ambiguities in these tables, mostly where 1 line might possibly correspond to 2 lattices rather than 1 lattice. So the total number of 26 dimensional even lattices of det 3 is in the range 677-681. The lines give the height (= number of roots/6), the Dynkin diagram arranged into orbits under the automorphism group, and the order of the automorphism group modulo the reflection group and -1, and occasionally a comment about a possible ambiguity (or error...). To do: resolve 5 ambiguities. check mass formula. 0 None 634023936 (^3D_4(2).3) 1 a2 138568320 (2.3^6.M12) 1 a1^3 756000 2 a1^3a2 241920 2 a1^6 11520 2 a3 244823040 3 a1^6a2 2160 3 a1^9 648 4 a1^12 192 4 a1^12 27648 4 a1^6a2^2 480 4 a1^6a3 23040 4 a1^9a2 108 4 a1^2a1^7a2 336 4 a2^4 186624 4 d4 55180984320 5 a1^12a2 240 5 a1^4a1^8a2 a2 48 5 a1^6a2^3 72 5 a1a1^8a2^2 16 5 a1^9a3 432 6 a1^4a1^8a2^2 32 6 a1^4a1^8a3 192 6 a1^2a1^10a3 240 6 a1^3a1^12a2 432 6 a1^6a2^2a3 96 6 a1^6a2a2^3 12 6 a1^2a1^4a2^4 48 6 a1^8a4 40320 6 a1a1^4a1^4a2a2^2 8 6 a1^9a2^3 18 6 a1a1^8a2a3 32 7 a1^11a4 660 7 a1^3a2^6 24 7 a1a1^2a1^3a2^3a3 6 7 a1a1^5a2^5 5 7 a1^6a2^2a2^3 12 7 a1a1^2a1^2a1^4a2^2a3 4 7 a1^9a2a2^3 108 7 a1^3a1^3a1^3a2a2^3 6 7 a2^7 2160 8 a1^12a2^2a3 48 8 a1^4a1^8a3^2 64 8 a1^12d4 6912 8 a1^14a4 336 8 a1^18a3 2160 8 a1^3a2a2^4a3 24 8 a1^3a2^2a2^3a3 6 8 a1^3a2a2^6 12 8 a1^2a1^4a2^2a3^2 a3 4 8 a1^2a1^4a2^2a3^2 a3 8 8 a1^2a1^4a2^4a3 16 8 a1a1a1^2a1^2a2a2a2^2a3 2 8 a1^2a1^2a1^2a2^2a2^2a3 4 8 a1^6a2a2^2a2^3 6 8 a1^6a2^6 24 8 a1^6a3^3 192 8 a1^8a2^2a4 32 8 a1a1^2a1^6a2^3a3 12 8 a1^3a1^3a1^3a2^3a3 6 8 a1^3a1^6a2a3a3 12 8 a2^6a3 240 9 a1a1^2a2^2a2^2a3^2 2 9 a1a1^2a2a2a2^2a2^2a3 a3 2 9 a1a1^4a2^4a4 a4 8 9 a1a1a1a1a1a1a2a2a2a3a3 1 9 a1^2a1^4a2a2^2a3^2 4 9 a1^2a1^4a2a2^4a3 4 9 a1^3a1^3a2^2a2^3a3 6 9 a1^6a2^3a2^4 24 9 a1^3a1^3a2a3^3 6 9 a1a1a1^6a2^3a4 6 9 a2^9 216 10 a1^2a2^4a3a4 16 10 a1^2a2^3a2^3a4 6 10 a1a1^2a2a2^2a3a3a3 2 10 a1^3a2^3a3^3 6 10 a1a1^2a2a2^2a3a3^2 4 (?might be 2 lattices a1^3a2^3a3^3 with groups 6,12) 10 a1a1^2a2a2^2a2^2a3^2 2 10 a1a1^2a2a2^2a2^2a3a3 2 10 a1a1^2a2a2^4a3a3 4 10 a1a1^2a1^2a2a2^2a3a4 2 (corrected by Megarbane 2016) 10 a1a1^4a2a2^4a4 4 10 a1a1a1^2a1^2a2^2a3a3a3 2 10 a1^2a1^4a2^2a3a3^2 8 10 a1^6a2^2a3^3 24 10 a1^2a1^2a1^2a2^2a2^2a3^2 4 10 a1^2a1^4a2^4a3a3 8 10 a1^6a2^4d4 48 10 a1a1^2a1^3a3a3^3 12 (corrected by Thomas Megarbane) 10 a1^2a1^2a1^4a2^2a3a4 4 10 a1^4a1^4a3^2a4 16 10 a1^9a2^2a5 144 10 a1^9a2^3d4 108 10 a1^3a1^3a1^3a2a3^3 6 10 a2a2^9 108 (?Might be 2 lattices a2^10 with groups 1080,120) 10 a2^2a2^2a3^3 24 10 a2^6d4 4320 11 a1a1a2a2^2a3^2a4 2 11 a1^2a2a2^2a2^2a3a4 2 11 a1a1a1a2a2a3a3a3a3 1 11 a1^3a2a2a3a3^3 3 11 a1a1^2a2a2a2^2a3a3^2 2 11 a1a1^2a2a2a2^2a3a3^2 2 11 a1a1a1a1a1a2a2a3a3a4 1 11 a1a1a1a1^2a2^2a3^2a4 2 11 a1a1a1a1a1a2a2a2a2a3a4 1 11 a1^2a1^3a2^6a4 12 11 a1^6a2^4a5 12 11 a2^3a3a3^3 6 11 a2a2^6a3^2 6 12 a1^12a3^2d4 96 12 a1^16d5 11520 12 a1a1a2a2a3a3a3a4 1 12 a1^2a2^2a3a3^2a4 4 12 a1a1a2a2a2a2a3a3a4 1 12 a1^2a2a2a2^2a3^2a4 2 12 a1^2a2^2a2^2a3^2a4 4 12 a1^2a2^4a3^2a4 8 12 a1^3a2^3a3a3d4 6 12 a1a1a1a2a2^2a3a3a3^2 2 12 a1a1^2a2^2a2^2a3a5 4 12 a1a1^2a2a2^4a3d4 4 12 a1a1^2a2a3a3a3a3^2 2 12 a1^4a2^2a3a4^2 4 12 a1^2a1^2a2^2a3a4^2 4 12 a1^2a1^2a2a2a2^2a4^2 2 12 a1a1^2a1^2a2a2^2a3^2a4 2 12 a1a1^2a1^2a2a3a3^2a4 2 12 a1a1^2a1^2a2a3a3^2a4 2 12 a1^2a1^4a2^2a3^2d4 d4 8 12 a1^6a2^2a3a3^3 12 12 a1^6a2^3a3a5 12 12 a1a1^5a2^5a5 10 12 a1^2a1^4a3^3d4 48 12 a1^2a1^4a3a3^2a3^2 8 12 a1^2a1^6a3^3a4 12 12 a1a1^8a3^2a5 16 12 a2^2a2^4a3a3^2 8 (?Might be 2 lattices a2^6a3^3 with groups 12,24) 12 a2^7a5 42 12 a3^6 192 12 a3^6 24 13 a1a1a2a2a2a3a3a3a4 1 13 a1a1a2a2a2a3a3a3a4 1 13 a1^2a2a2^2a3a3^2a4 2 13 a1a1a2a3a3a3a3a4 1 13 a1^2a2a3^4a4 4 13 a1a1a1a2a2a2a3a3a5 1 13 a1a1^2a2a2^2a3^2a5 2 13 a1a1a1a1a2a2a2a3a4a4 1 13 a1a1a1a1a2a3a3a4a4 1 13 a1^4a2a3^2a4^2 4 13 a1^3a1^3a2a4^3 6 13 a1a2^2a3^2a4^2 2 13 a1a2a2a2a2a3a4a4 1 (Typo corrected by Megarbane 2016) 13 a2^13 5616 13 a2^8a5 48 13 a2a3^6 12 14 a1^2a2^2a3^2a4d4 2 14 a1^2a2^2a3^2a3^2a4 4 14 a1^2a2a2^2a3a4a5 2 14 a1^2a2^2a2^2a3a4d4 2 (Typo corrected by Megarbane 2016) 14 a1^2a3a3^2a3^2a4 2 14 a1a1^2a2^2a3a3^2a5 2 14 a1a1^2a2^2a3a3^2a5 4 14 a1^3a2^3a3^3d4 6 14 a1^3a2^3a4^3 3 14 a1a1^2a2a3^4d4 4 14 a1a1^2a2a3a4a4^2 2 14 a1^3a3^4a5 24 14 a1a1^2a3^2a3^2a5 4 14 a1^3a3a3^3a5 6 14 a1^4a2^2a4^2d4 8 14 a1^4a2^6d5 48 14 a1a1a1^2a3a3a3a4^2 2 14 a1a1^2a1^2a2^2a3a4a5 2 14 a1a1^2a1^2a2^2a3a4a5 2 14 a1a1^4a2^4a4a5 8 14 a1a1^2a1^2a2a3^2a4d4 2 14 a1^6a2^3a3a6 12 14 a1^3a1^3a2a3^3a5 3 14 a1^6a3a4^3 12 14 a1a2a2^2a3^2a4^2 2 14 a1a2a2^2a3a3a4^2 2 14 a1a2a3a3a3a4a4 1 14 a1a2a3a3^2a4^2 2 14 a2^2a3^2a3^2d4 4 14 a2^2a3a4^3 12 14 a2^4a3a3^4 24 14 a2a2^2a2^2a3a3a5 2 14 a2^7a6 42 14 a2a3^4a5 8 14 a3^3a3^4 24 (?Might be 2 lattices a3^7 with groups 42,56) 15 a1a1a2a2a3a3a4a5 1 15 a1a1a2a2a3a3a4a5 1 15 a1a1a2a2a3a3a4a5 1 15 a1a1a3a3a3a4a5 1 15 a1a1a1a2a2a3a4a4a4 1 15 a1a1^2a2a2^2a3^2a6 2 15 a1^3a2a2^3a4^3 6 15 a1a1a1a3a3a4a4a4 1 15 a1a1a1^2a2^2a4^2a5 2 15 a1a2a2a3a3a3a4a4 1 15 a1a2a2^2a4^2a5 2 15 a2a2^2a3a4a4^2 1 15 a2a2^3a3^3a5 3 16 a1^2a2^2a3a4d4^2 2 16 a1^2a2a2^2a3a4a6 2 16 a1^2a2a2^2a4a5d4 2 16 a1a1a2a3a3a3a4a5 1 16 a1a1a2a3a3a3a4a5 1 16 a1^2a2a3a3^2a4a5 2 16 a1^2a3^2a3^2a4d4 2 16 a1a2^3a3a4^2d4 (Accidentally omitted: found by Megarbane 2016) 16 a1^2a3a4a4a4^2 2 16 a1a1^2a2^2a3a3a5d4 2 16 a1a1^2a2^2a3a3^2a6 2 16 a1a1^2a2a3^2a5^2 2 16 a1^3a2a4^3d4 6 16 a1a1^2a3a3^2a5d4 4 16 a1a1^2a3a3^4a5 4 16 a1^2a1^2a2^2a3a3^2d5 4 16 a1a1a1a1a2a3a4a4a5 1 16 a1^4a3^4d5 32 16 a1^2a1^4a3^2a5^2 4 16 a1^6a3^3d4^2 12 16 a1^9a5d4^2 72 16 a1a2a2a3a4a4a5 1 16 a1a2a2a3a4a4a5 1 16 a1a2^3a3^3d5 6 16 a1a2a3a3a4a4d4 1 16 a1a2a3a3a4^2d4 2 16 a1a3^2a4^2a5 4 16 a2^2a3a3a4a4^2 2 (Maybe a2^2 should be exchanged with a2a2 in 16 a2a2a3^2a4a4^2 2 these two...) 16 a2^2a3^3d4d4 12 16 a2^4d4^3 432 16 a2^2a2^4a5^2 4 16 a2a2^6a5d4 12 16 a2a3^3a5d4 6 16 a2a3^4a6 8 16 a3^3a4^3 3 16 a3^3a5^2 48 16 a3^6d4 48 17 a1a1a2a2a3a3a4a6 1 17 a1a1a2a3a4a5a5 1 17 a1^2a2a3a4a5^2 2 17 a1a1a3a3a3a4a6 1 17 a1a1a1a2a4a4a4a5 1 17 a1^3a2a4^3a5 3 17 a1a1a1^2a2^2a4^2a6 2 (Corrected by Megarbane 2016) 17 a1a2a3a3a4a4a5 1 17 a1a2a3^2a4^2a5 2 17 a1a4^5 5 17 a2a2a2a3a3a5a5 1 17 a2a2^2a3^2a5^2 2 17 a2a2^3a3^3a6 3 17 a2a3^3a4^3 6 17 a3^5a6 10 17 a3a4^3a5 3 18 a1^2a2^2a3a3^2a7 4 18 a1a1a2a2a3a4a4d5 1 18 a1^2a2a2^2a4a6d4 2 18 a1^2a2^2a2^2a4^2d5 4 18 a1a1a2a3a3a4a5d4 1 18 a1^2a3^2a4^2d5 4 18 a1^2a3^2a4a5a5 2 18 a1^2a3^2a4a5^2 4 18 a1a1^2a2a3^2a5a6 2 18 a1a1a1a2a3a5a5d4 1 18 a1^3a3^3a6d4 3 18 a1^3a3a4^3a5 6 18 a1a1^2a3a5a5^2 4 18 a1^4a2^4a4a7 8 18 a1^3a1^3a2a5^3 6 18 a1a2a2a3a4a4a6 1 18 a1a2a2a4a4a5d4 1 18 a1a2a4^2a5a5 2 18 a1a3a3a4a4a6 1 18 a1a3a3^2a4^2a5 2 18 a1a3a4a4a5d4 1 18 a2^2a3a3^2a4d5 2 18 a2^2a3a3^2a5^2 4 18 a2^3a5^3 6 18 a2^2a2^2a3a5a6 2 18 a2a3a4a4a4a5 1 19 a1a1a2a3a4a5a6 1 19 a1a1a2a3a4a5a6 1 19 a1a1a2a3a4a5a6 1 19 a1a1a2a3a4a5a6 1 19 a1a2a2a3a3a4a7 1 19 a1a2a3a3a4a4a6 1 19 a1a3a4a4a5a5 1 19 a1a3a4a4a5a5 1 19 a2^2a4a4^2a6 2 19 a2a2^3a5^3 6 20 a1^2a2a4^2a5d5 2 20 a1a1a3a3a4a5a6 1 20 a1^2a3a3^2a7d4 4 20 a1^2a3a4^2d4d5 2 20 a1^2a3a4a5^2d4 1 20 a1a1a1a2a3a4a4a7 1 20 a1a1a1a3a3a4a5d5 1 20 a1a1^2a3a5^2a6 2 20 a1^3a3a5d4^3 6 20 a1^2a1^2a2^2a5^2d5 4 20 a1^4a3^2d4^2d5 8 20 a1^4a3a5^2d5 8 20 a1a1^4a3^2a5a7 4 20 a1^6a3^4d6 48 20 a1a2^2a3a5d4d5 2 20 a1a2^2a4^2a6d4 2 20 a1a2a4a4a5a6 1 20 a1a3a3a3^2a5d5 2 20 a1a3a4a4a6d4 1 20 a1a4^2a5d4^2 2 20 a2^2a3^2a4d4d5 2 20 a2a2^2a5^2a6 2 20 a2^4a3^3d6 24 20 a2^4a3a6^2 4 20 a2a3a3a4a5d5 1 20 a2a3a3a5a5a5 1 20 a2a3a3a5a5^2 2 20 a2a3^2a6d4^2 2 20 a2a4a4^2a5d4 2 20 a3^2a4^2a7 4 20 a3^2a5a6d4 2 20 a3^4d4^3 24 20 a3a5^2d4^2 8 21 a1a1a2a3a4a6a6 1 21 a1^2a4^4a6 4 21 a1a1a4a5a5a6 1 21 a1a2a3a4a5a7 1 21 a1a3a4a4a5a6 1 21 a1a4^2a6^2 2 21 a2a2a3a5a5a6 1 21 a2a3^2a4^2a7 2 21 a2a5^4 4 22 a1^2a2a3^2a6a7 2 22 a1a1a2a3a5a7d4 1 22 a1a1a2a4a4a6d5 1 22 a1^2a3a3^2a4a8 2 22 a1^2a3a5a5a7 2 22 a1^2a4a6^2d4 2 22 a1a1^2a5^2a6d4 2 22 a1a2a3^2a4^2d6 2 22 a1a2a3a5a6d5 1 22 a1a2a4^2a6^2 2 22 a1a3a3a4a5a7 1 22 a1a4a4a4a5d5 1 22 a2^10e6 720 22 a2^2a4^2a7d4 2 22 a2^2a5a5^3 12 22 a2^3a5^3d4 6 22 a2^6a8d4 12 22 a2a3a3a4a6d5 1 22 a2a4^2a5a7 2 22 a3^2a6^2d4 4 22 a3a3^2a4^2a7 2 22 a3a4a5a5d5 1 22 a4a4a4a5a6 1 23 a1a1^2a2a6a6^2 2 23 a1^3a4^3a8 3 23 a1a2a3a4a6a7 1 23 a1a4a5a5a7 1 23 a2a2a3a3a5a8 1 23 a2a2a3a5a6a6 1 23 a2a5a5a5a6 1 23 a2a5^3a6 3 23 a3a6^3 6 24 a1^2a2a3a6d5^2 2 24 a1a1a3a5a6a7 1 24 a1^2a5a5a7d4 2 24 a1a1^2a2^2a5a7d5 2 24 a1a1^2a3^2a5d4d6 1 24 a1a2^2a4a5d5^2 2 24 a1a2a3a6^2d5 2 24 a1a2a4a4a7d5 1 24 a1a2a4a4a8d4 1 24 a1a2a5a6d4d5 1 24 a1a3a4^2a5d6 2 24 a1a3a4a5a7d4 1 24 a1a3a4a5d5d5 1 24 a1a4^2a5a8 2 24 a1a4a6a7d4 1 24 a2^2a3a5^2d6 4 24 a2^2a3a7d4d5 2 24 a2^4d5^3 24 24 a2a4^2a6a7 2 24 a2a4^2a6a7 2 24 a3^2a3^2a7d5 4 24 a3^6e6 24 24 a3a4a5a6d5 1 24 a3a5a5^2a6 2 24 a4^2d4d5^2 4 24 a4^3d4d6 6 24 a4a5^2d4d5 2 25 a1^2a2a6^2a7 2 25 a1a1a3a4a6a8 1 25 a1a4a5a6a7 1 25 a2a2^2a5^2a8 1 25 a2a3a4a7a7 1 26 a1^2a4^2a8d5 2 26 a1^2a4^2a4^2e6 4 26 a1a1a4a5a6d6 1 26 a1^3a4^3a9 6 26 a1a3a5a7a7 1 26 a1a5a6a6d5 1 26 a2^2a3a3a5a9 1 26 a2a2a3a5a6d6 1 26 a2a2a5a6a8 1 26 a2a3a6a7d5 1 26 a2a5^3d6 3 26 a3a3a5a5a8 1 26 a3a4a6^2d5 2 26 a5^2a7d5 2 27 a1a4a4a5a9 1 27 a1a4a6a6a7 1 27 a2a3a5a6a8 1 27 a5^3a8 3 28 a1^2a3^2d5^2d6 4 28 a1a1a3a4a6a9 1 28 a1a1a3a7a7d5 1 28 a1^2a7d4^2d6 4 28 a1a3a3^2a9d5 2 28 a1a3a4^2a5d7 2 28 a1a3a5d4d5d6 1 28 a1a3a6a8d5 1 28 a1a5a7d5^2 2 28 a1a5a8d4d5 1 28 a2^2a5a5d4e6 2 28 a2^4a5^2d7 8 28 a2a4a6d5d6 1 28 a2a5^3e6 6 28 a2a6a7d4d5 1 28 a3^3d4^2d7 12 28 a3a4^2a7d6 2 28 a4^2a7a8 2 28 a5a6a7d5 1 28 a5a9d4^2 4 28 a7^3 24 28 d4^2d5^3 12 28 d4^4e6 144 29 a1a1a6a7a8 1 29 a2a2a5a6a9 1 29 a2a3^2a8^2 2 29 a4a6a7^2 2 29 a5a5a6a8 1 30 a1a1a2a7a9d4 1 30 a1^2a5a7a9 1 30 a1a2a7^2d6 2 30 a1a4a6a7d6 1 30 a2a3a5a8d6 1 30 a2a4^2a10d4 2 30 a2a5a8^2 2 30 a3a3a6a6e6 1 30 a3a7a7^2 2 31 a1a3a4a6a10 1 32 a1^2a3a7d6^2 2 32 a1a1a4a7d5e6 1 32 a1^4a7^2e6 8 32 a1a4a4a10d5 1 32 a1a4a5a7d7 1 32 a1a4a9d5d5 1 32 a2^2a5a9d6 2 32 a2a4a6d5d7 1 32 a2a6a8a8 1 32 a2a6a8^2 2 32 a3a5^2d6^2 2 32 a4^2d5d5e6 2 32 a4a6a9d5 1 32 a4a8d5d6 1 32 a5a5a6a9 1 32 a5a5a8d6 1 32 a6^2d4d7 2 32 a7^3d4 6 32 a8d5^3 3 33 a1a5a7a10 1 33 a2a5a8a9 1 34 a1a8a9d5 1 34 a2^2a5^2a11 4 34 a3a6a10d5 1 34 a5^2a8e6 2 34 a5^2a8e6 2 35 a2a5a6a11 1 36 a1^2a5^2d5d8 2 36 a1^2a7a11d4 2 36 a1a1a7a8d7 1 36 a1a4^2a9d7 2 36 a1a5d5d6d7 1 36 a3^2a7d4d8 2 36 a3^2d6^2e6 4 36 a3a6a9e6 1 36 a4a6^2d8 2 36 a6a6d6e6 1 36 a7d5d6^2 2 36 a8^3 1 37 a1a4a9a10 1 37 a2a8^3 6 37 a7^2a10 2 38 a1a7a10d6 1 38 a2a5a11d6 1 38 a2a8a9d6 1 38 a3a3a8a11 1 38 a3a5^2a12 2 40 a1a6a12d5 1 40 a2^2a11d4e6 2 40 a2a2a8d7e6 1 40 a2^4e6^3 24 40 a2a10d5d7 1 40 a5^3d4e7 6 40 a8d4e6^2 2 41 a2a3a8a12 1 41 a6a8a11 1 42 a5a9a11 1 42 a6^3e7 3 42 a9a9e6 1 44 a1a13d5^2 2 44 a1a7d5^2e7 2 44 a1a9d6d8 1 44 a2a6a8d9 1 44 a3a7d7d8 1 44 a3d7^3 6 44 a5^2d6d9 2 44 a6a10d8 1 44 a8a11d6 1 44 d5^2d8e6 2 44 d5^3d9 6 45 a2a11^2 2 46 a1^2a9a13 2 46 a2a8^2e7 2 47 a5a6a14 1 48 a12d6e6 1 48 a1a4a13d7 1 48 a3a9d6e7 1 52 a1a9d5d10 1 52 a5^2d10e6 2 52 a5a14e6 1 52 a5d7e6e7 1 53 a2a8a15 1 54 a6a12e7 1 57 a11a14 1 60 a2a14d9 1 60 a7d7d11 1 60 a9d9e7 1 60 d9^2e6 2 62 a11a15 1 62 a2a17d6 1 64 a11e7^2 2 68 a3a11d12 1 76 a11d7e8 1 76 d13e6^2 2 76 e6^3e8 6 77 a6a20 1 78 a18e7 1 92 a11d15 1 117 a26 1