Q(rt13) Disc=13 -------------------- n=4 Gram Matrix A= [4,2,-2,-rt13] [2,2,-1,1/2*(-rt13-1)] [-2,-1,2,1/2*(rt13+1)] [-rt13,1/2*(-rt13-1),1/2*(rt13+1),4] h=1 Automorphism group size: [576] Trivial case. -------------------- n=8 Gram Matrix A oplus A h=12 Automorphism group sizes: [696729600, 622080, 663552, 27648, 5760, 2592, 20736, 311040, 1728, 768, 2880, 4368] Neighbour Matrices: N(P)=4 [ 135 2240 3150 0 0 0 0 0 0 0 0 0] [ 2 297 90 540 2916 1440 240 0 0 0 0 0] [ 3 96 194 48 1152 2304 768 192 768 0 0 0] [ 0 24 2 555 480 1344 108 0 1056 1764 192 0] [ 0 27 10 100 1028 840 180 0 880 2220 0 240] [ 0 6 9 126 378 965 87 12 972 2106 540 324] [ 0 8 24 81 648 696 594 0 288 2754 432 0] [ 0 0 90 0 0 1440 0 215 2160 0 1620 0] [ 0 0 2 66 264 648 24 12 1257 2160 624 468] [ 0 0 0 49 296 624 102 0 960 2502 608 384] [ 0 0 0 20 0 600 60 15 1040 2280 1030 480] [ 0 0 0 0 182 546 0 0 1183 2184 728 702] CharPoly = (x-5525)(x-1349)(x-595)(x-296)(x-189)(x-164)(x-10)(x^2+9x-918)(x^3-1355x^2+542400x-58986000) N(P)=3 [ 0 1120 0 0 0 0 0 0 0 0 0 0] [ 1 81 0 270 648 0 120 0 0 0 0 0] [ 0 0 32 0 576 512 0 0 0 0 0 0] [ 0 12 0 100 192 128 0 0 400 288 0 0] [ 0 6 5 40 199 200 60 0 160 450 0 0] [ 0 0 2 12 90 284 0 0 120 432 72 108] [ 0 4 0 0 216 0 108 0 144 648 0 0] [ 0 0 0 0 0 0 0 40 1080 0 0 0] [ 0 0 0 25 48 80 12 6 301 432 144 72] [ 0 0 0 8 60 128 24 0 192 500 128 80] [ 0 0 0 0 0 80 0 0 240 480 200 120] [ 0 0 0 0 0 182 0 0 182 455 182 119] CharPoly = (x-1120)(x-337)(x-103)(x-4)(x+11)(x+40)^2(x^2-27x-756)(x^3-464x^2+62640x-2124288) -------------------- n=12 Gram Matrix A oplus A oplus A Mass = 70058445.87 Too big