Q(rt5) Disc=5 e=(1+rt5)/2 -------------------- n=4 Gram Matrix A= [2,e,e,e] [e,2,1,1] [e,1,2,1] [e,1,1,2] h=1 Automorphism group size: [14400] Trivial case. -------------------- n=8 Gram Matrix A oplus A h=2 Automorphism group sizes: [414720000,696729600] Neighbour Matrices: N(P)=4 [3650,1875] [3150,2375] CharPoly = (x-5525)*(x-500) N(P)=9 [378600 220000] [369600 229000] CharPoly = (x-598600)*(x-9000) N(P)=5 [12456,7200] [12096,7560] CharPoly = (x-19656)*(x-360) -------------------- n=12 Gram Matrix A oplus A oplus A h=15 (takes a few minutes) Automorphism group sizes: [17915904000000,10032906240000,663552000,2488320000,127401984,870912000, 980995276800,10749542400,240000000,5760000,7962624,2703360,101606400, 2239488,72576000] Neighbour Matrices: N(P)=4 [10875,5625,810000,432000,140625,0,0,0,0,0,0,0,0,0,0] [3150,9600,453600,0,236250,518400,10125,168000,0,0,0,0,0,0,0] [30,30,47600,11400,30750,24000,75,2400,25920,659520,228000,27000,78400,264000,0] [60,0,42750,36975,16875,16000,0,0,51840,864000,80000,50625,0,240000,0] [1,3,5904,864,39195,9216,6,1824,0,359424,220800,168480,46080,542720,4608] [0,45,31500,5600,63000,39800,200,3150,0,589680,225750,0,104400,336000,0] [0,990,110880,0,46200,225280,15039,66528,0,0,123200,0,811008,0,0] [0,180,38880,0,153900,38880,729,17868,0,466560,291600,0,217728,172800,0] [0,0,9375,5000,0,0,0,0,34750,412500,156250,312500,0,468750,0] [0,0,5725,2000,16250,3900,0,250,9900,353850,182500,292500,22250,510000,0] [0,0,2736,256,13800,2064,1,216,5184,252288,192340,362880,21888,538560,6912] [0,0,110,55,3575,0,0,0,3520,137280,123200,554105,3520,545600,28160] [0,0,12005,0,36750,12180,84,2058,0,392490,279300,132300,76258,455700,0] [0,0,891,216,9540,864,0,36,4374,198288,151470,451980,10044,555870,15552] [0,0,0,0,2625,0,0,0,0,0,63000,756000,0,504000,73500] CharPoly = (x-1399125)*(x-348900)*(x-27300)*(x-24000)*(x-21300)*(x-18300)* (x-10800)*(x-9600)*(x-7200)*(x-900)*(x+6000)* (x^2-178500*x+7947360000)*(x^2-17700*x+60120000) N(P) = 5 [37260,21600,2592000,3110400,0,2592000,0,0,746496,3110400,0,0,0,0,0] [12096,21996,4717440,0,0,1036800,129600,403200,0,1741824,0,0,4147200,0,0] [96,312,215580,100160,414000,208000,200,19200,103680,5315328,1384000,648000,441600,3360000,0] [432,0,375600,162420,0,72000,0,0,419904,6004800,1560000,1215000,240000,2160000,0] [0,0,79488,0,149580,34560,288,6912,82944,2778624,2234880,2280960,414720,4147200,0] [126,90,273000,25200,236250,163500,1830,20160,136080,4430160,2520000,680400,825360,2898000,0] [0,12672,295680,0,2217600,2061312,36588,354816,0,4257792,0,0,2973696,0,0] [0,432,311040,0,583200,248832,3888,88236,0,4292352,2721600,0,1368576,2592000,0] [10,0,37500,40500,156250,37500,0,0,130896,3330000,937500,2812500,0,4687500,40000] [1,1,46140,13900,125625,29300,25,2300,79920,2788344,1595000,2821500,189300,4490000,28800] [0,0,16608,4992,139680,23040,0,2016,31104,2204928,1450380,3265920,150144,4838400,82944] [0,0,2640,1320,48400,2112,0,0,31680,1324224,1108800,4636260,42240,4787200,225280] [0,42,67620,9800,330750,96292,308,12936,0,3339252,1915900,1587600,439656,4410000,0] [0,0,11340,1944,72900,7452,0,540,43740,1745712,1360800,3965760,97200,4762800,139968] [0,0,0,0,0,0,0,0,12096,362880,756000,6048000,0,4536000,495180] CharPoly = (x-12210156)*(x-2446380)*(x-107100)*(x-90900)*(x-45900)^2* (x-27900)*(x-17100)*(x+13500)*(x+62100)*(x+351540)* (x^2-989640*x+244741986000)*(x^2-24840*x+49410000) -------------------- n=16 Gram Matrix A oplus A oplus A oplus A Mass = 1878135.63887917741408030697385 Too big.