## Results (1-50 of 363306 matches)

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Label Polynomial Discriminant Galois group Class group
18.0.923324627983045303.1 $x^{18} - 4 x^{17} + 10 x^{16} - 17 x^{15} + 24 x^{14} - 28 x^{13} + 28 x^{12} - 22 x^{11} + 14 x^{10} - 8 x^{9} + 5 x^{8} - 3 x^{7} + 2 x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 2 x^{2} + 1$ $-\,31^{6}\cdot 463\cdot 1499^{2}$ $C_2\times S_4^3.S_4$ (as 18T912) trivial
18.0.111...168.1 $x^{18} - 4 x^{17} + 14 x^{16} - 31 x^{15} + 64 x^{14} - 100 x^{13} + 146 x^{12} - 176 x^{11} + 202 x^{10} - 205 x^{9} + 202 x^{8} - 176 x^{7} + 146 x^{6} - 100 x^{5} + 64 x^{4} - 31 x^{3} + 14 x^{2} - 4 x + 1$ $-\,2^{12}\cdot 3^{9}\cdot 7^{12}$ $S_3 \times C_3$ (as 18T3) trivial
18.0.118...699.1 $x^{18} - 5 x^{17} + 16 x^{16} - 39 x^{15} + 80 x^{14} - 141 x^{13} + 221 x^{12} - 312 x^{11} + 400 x^{10} - 465 x^{9} + 489 x^{8} - 463 x^{7} + 395 x^{6} - 300 x^{5} + 195 x^{4} - 101 x^{3} + 38 x^{2} - 9 x + 1$ $-\,7^{4}\cdot 139\cdot 1373^{4}$ $C_2^9.A_9$ (as 18T966) trivial
18.0.119...867.1 $x^{18} - 4 x^{17} + 9 x^{16} - 14 x^{15} + 17 x^{14} - 16 x^{13} + 15 x^{12} - 23 x^{11} + 45 x^{10} - 65 x^{9} + 62 x^{8} - 40 x^{7} + 29 x^{6} - 39 x^{5} + 49 x^{4} - 41 x^{3} + 22 x^{2} - 7 x + 1$ $-\,31^{6}\cdot 67^{5}$ $C_6\wr S_3$ (as 18T284) trivial
18.0.141...707.1 $x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} + 12 x^{14} - 15 x^{13} + 21 x^{12} - 29 x^{11} + 36 x^{10} - 38 x^{9} + 36 x^{8} - 32 x^{7} + 31 x^{6} - 32 x^{5} + 30 x^{4} - 23 x^{3} + 13 x^{2} - 5 x + 1$ $-\,23^{6}\cdot 43^{3}\cdot 347^{2}$ $D_6\wr S_3$ (as 18T556) trivial
18.0.154...467.1 $x^{18} + 9 x^{16} - 9 x^{15} + 36 x^{14} - 63 x^{13} + 109 x^{12} - 189 x^{11} + 252 x^{10} - 335 x^{9} + 378 x^{8} - 378 x^{7} + 334 x^{6} - 243 x^{5} + 147 x^{4} - 67 x^{3} + 21 x^{2} - 3 x + 1$ $-\,3^{21}\cdot 23^{6}$ $C_3^2:D_6$ (as 18T57) trivial
18.0.167...571.1 $x^{18} - 2 x^{17} + x^{16} + 5 x^{15} - 10 x^{14} + 5 x^{13} + 13 x^{12} - 29 x^{11} + 24 x^{10} + 9 x^{9} - 48 x^{8} + 56 x^{7} - 16 x^{6} - 44 x^{5} + 74 x^{4} - 60 x^{3} + 29 x^{2} - 8 x + 1$ $-\,139\cdot 367^{2}\cdot 299401^{2}$ $C_2^9.S_9$ (as 18T968) trivial
18.0.196...487.1 $x^{18} - x^{17} - 7 x^{15} + 5 x^{14} + 6 x^{13} + 21 x^{12} - 29 x^{11} - 13 x^{10} - 11 x^{9} + 49 x^{8} - 8 x^{7} - 3 x^{6} - 24 x^{5} + 14 x^{4} + 3 x^{3} - 3 x + 1$ $-\,31^{6}\cdot 1303^{3}$ $S_3\wr S_3$ (as 18T314) trivial
18.0.199...128.1 $x^{18} - 6 x^{17} + 24 x^{16} - 68 x^{15} + 159 x^{14} - 300 x^{13} + 479 x^{12} - 630 x^{11} + 702 x^{10} - 636 x^{9} + 480 x^{8} - 270 x^{7} + 114 x^{6} - 12 x^{5} - 12 x^{4} + 14 x^{3} - 3 x^{2} + 1$ $-\,2^{18}\cdot 3^{27}$ $S_3 \times C_6$ (as 18T6) trivial
18.0.252...912.1 $x^{18} - 9 x^{17} + 36 x^{16} - 81 x^{15} + 105 x^{14} - 63 x^{13} - 21 x^{12} + 72 x^{11} - 63 x^{10} + 27 x^{9} - 6 x^{6} - 9 x^{5} + 18 x^{4} - 9 x^{2} + 3$ $-\,2^{12}\cdot 3^{31}$ $S_3 \times C_3$ (as 18T3) trivial
18.0.274...447.1 $x^{18} - 5 x^{17} + 12 x^{16} - 17 x^{15} + 12 x^{14} - 2 x^{13} + 8 x^{12} - 46 x^{11} + 111 x^{10} - 168 x^{9} + 188 x^{8} - 173 x^{7} + 137 x^{6} - 102 x^{5} + 70 x^{4} - 40 x^{3} + 19 x^{2} - 5 x + 1$ $-\,23^{6}\cdot 2647^{3}$ $S_3\wr S_3$ (as 18T314) trivial
18.0.319...743.1 $x^{18} - 5 x^{17} + 15 x^{16} - 36 x^{15} + 75 x^{14} - 137 x^{13} + 221 x^{12} - 312 x^{11} + 384 x^{10} - 411 x^{9} + 384 x^{8} - 312 x^{7} + 221 x^{6} - 137 x^{5} + 75 x^{4} - 36 x^{3} + 15 x^{2} - 5 x + 1$ $-\,11^{6}\cdot 23^{9}$ $C_3^3:S_4$ (as 18T221) trivial
18.0.405...267.1 $x^{18} - 3 x^{15} + 15 x^{12} + 20 x^{9} + 33 x^{6} + 6 x^{3} + 1$ $-\,3^{39}$ $S_3 \times C_3$ (as 18T3) trivial
18.0.455...263.1 $x^{18} + 6 x^{16} - 2 x^{15} + 15 x^{14} - 10 x^{13} + 22 x^{12} - 20 x^{11} + 23 x^{10} - 20 x^{9} + 18 x^{8} - 10 x^{7} + 9 x^{6} - 2 x^{5} + 2 x^{4} - x^{3} - x + 1$ $-\,3^{9}\cdot 229\cdot 433^{3}\cdot 12457$ $C_3^6.S_4^2:D_4$ (as 18T951) trivial
18.2.483...741.1 $x^{18} - 3 x^{17} + 2 x^{16} - 5 x^{15} + 15 x^{14} - 6 x^{13} + 2 x^{12} - 29 x^{11} + 17 x^{10} + 11 x^{9} + 17 x^{8} - 29 x^{7} + 2 x^{6} - 6 x^{5} + 15 x^{4} - 5 x^{3} + 2 x^{2} - 3 x + 1$ $23^{6}\cdot 59^{2}\cdot 149\cdot 251^{2}$ $C_2\times S_4^3.S_4$ (as 18T912) trivial
18.0.504...712.1 $x^{18} - x^{15} + 2 x^{12} - 9 x^{9} + 12 x^{6} - 5 x^{3} + 1$ $-\,2^{12}\cdot 3^{21}\cdot 7^{6}$ $C_3^2:C_6$ (as 18T23) trivial
18.0.513...176.1 $x^{18} - 6 x^{17} + 16 x^{16} - 20 x^{15} - 2 x^{14} + 51 x^{13} - 87 x^{12} + 64 x^{11} + 16 x^{10} - 108 x^{9} + 181 x^{8} - 232 x^{7} + 253 x^{6} - 224 x^{5} + 154 x^{4} - 79 x^{3} + 29 x^{2} - 7 x + 1$ $-\,2^{12}\cdot 3^{12}\cdot 11^{9}$ $C_3^2:C_6$ (as 18T23) trivial
18.0.546...107.1 $x^{18} - 9 x^{17} + 35 x^{16} - 76 x^{15} + 100 x^{14} - 84 x^{13} + 57 x^{12} - 56 x^{11} + 62 x^{10} - 35 x^{9} + 3 x^{8} - 28 x^{7} + 63 x^{6} - 32 x^{5} - 10 x^{3} + 16 x^{2} - 7 x + 1$ $-\,3^{9}\cdot 23^{6}\cdot 37^{4}$ $C_3^3:D_6$ (as 18T137) trivial
18.0.558...424.1 $x^{18} - 2 x^{17} + 5 x^{16} - 7 x^{15} + 10 x^{14} - 13 x^{13} + 17 x^{12} - 24 x^{11} + 28 x^{10} - 28 x^{9} + 25 x^{8} - 24 x^{7} + 28 x^{6} - 31 x^{5} + 29 x^{4} - 22 x^{3} + 13 x^{2} - 5 x + 1$ $-\,2^{12}\cdot 3^{12}\cdot 37^{6}$ $C_3\wr D_4$ (as 18T189) trivial
18.0.610...264.1 $x^{18} + 5 x^{16} + 12 x^{14} + 29 x^{12} + 55 x^{10} + 57 x^{8} + 39 x^{6} + 22 x^{4} + 8 x^{2} + 1$ $-\,2^{18}\cdot 13^{12}$ $S_3 \times C_3$ (as 18T3) trivial
18.0.622...163.1 $x^{18} - 4 x^{15} + 6 x^{12} - 5 x^{9} + 6 x^{6} - 4 x^{3} + 1$ $-\,3^{21}\cdot 29^{6}$ $C_3^3:D_6$ (as 18T119) trivial
18.2.642...321.1 $x^{18} - 2 x^{17} - x^{16} + 6 x^{15} - 4 x^{14} - 10 x^{13} + 11 x^{12} + 9 x^{11} - 16 x^{10} - 5 x^{9} + 16 x^{8} + 5 x^{7} - 15 x^{6} - 5 x^{5} + 12 x^{4} + x^{3} - 5 x^{2} + 1$ $23^{6}\cdot 208333^{2}$ $A_4^3.(C_2\times S_4)$ (as 18T776) trivial
18.0.664...399.1 $x^{18} - 9 x^{17} + 42 x^{16} - 132 x^{15} + 310 x^{14} - 574 x^{13} + 865 x^{12} - 1082 x^{11} + 1139 x^{10} - 1020 x^{9} + 787 x^{8} - 532 x^{7} + 321 x^{6} - 174 x^{5} + 85 x^{4} - 37 x^{3} + 14 x^{2} - 4 x + 1$ $-\,17^{2}\cdot 43^{2}\cdot 2311\cdot 73363^{2}$ $C_2^9.S_9$ (as 18T968) trivial
18.2.718...137.1 $x^{18} - 5 x^{17} + 12 x^{16} - 22 x^{15} + 39 x^{14} - 63 x^{13} + 85 x^{12} - 97 x^{11} + 99 x^{10} - 98 x^{9} + 91 x^{8} - 71 x^{7} + 53 x^{6} - 44 x^{5} + 29 x^{4} - 15 x^{3} + 10 x^{2} - 4 x + 1$ $7^{12}\cdot 113\cdot 2143^{2}$ $C_2\times S_4^3.A_4$ (as 18T879) trivial
18.0.817...000.1 $x^{18} + x^{16} - 6 x^{14} - 5 x^{12} + 2 x^{10} + 7 x^{8} + 18 x^{6} + 7 x^{4} - 3 x^{2} + 1$ $-\,2^{6}\cdot 5^{8}\cdot 83^{6}$ $C_6^2:D_6$ (as 18T156) trivial
18.2.867...481.1 $x^{18} - x^{17} + 2 x^{16} - 5 x^{15} + x^{14} - 6 x^{13} + 2 x^{12} + 4 x^{10} + 3 x^{9} + 4 x^{8} + 2 x^{6} - 6 x^{5} + x^{4} - 5 x^{3} + 2 x^{2} - x + 1$ $41^{3}\cdot 11221481^{2}$ $C_2^9.S_9$ (as 18T968) trivial
18.2.897...489.1 $x^{18} - x^{17} + 3 x^{15} - x^{14} + x^{13} + 7 x^{12} + 2 x^{11} + 3 x^{10} + 11 x^{9} + 3 x^{8} + 2 x^{7} + 7 x^{6} + x^{5} - x^{4} + 3 x^{3} - x + 1$ $7^{12}\cdot 41^{3}\cdot 97^{2}$ $D_6\wr C_3$ (as 18T472) trivial
18.0.928...243.1 $x^{18} - 9 x^{16} - 11 x^{15} + 21 x^{14} + 69 x^{13} + 54 x^{12} - 75 x^{11} - 219 x^{10} - 205 x^{9} - 6 x^{8} + 231 x^{7} + 342 x^{6} + 303 x^{5} + 201 x^{4} + 103 x^{3} + 39 x^{2} + 9 x + 1$ $-\,3^{21}\cdot 31^{6}$ $C_3^2:D_6$ (as 18T57) trivial
18.0.929...543.1 $x^{18} - 4 x^{17} + 10 x^{16} - 21 x^{15} + 37 x^{14} - 58 x^{13} + 80 x^{12} - 97 x^{11} + 107 x^{10} - 106 x^{9} + 92 x^{8} - 71 x^{7} + 52 x^{6} - 39 x^{5} + 30 x^{4} - 20 x^{3} + 11 x^{2} - 4 x + 1$ $-\,7^{15}\cdot 1399^{2}$ $S_3^3:C_6$ (as 18T286) trivial
18.0.965...875.1 $x^{18} - 9 x^{17} + 36 x^{16} - 78 x^{15} + 84 x^{14} - 111 x^{12} + 90 x^{11} + 72 x^{10} - 156 x^{9} + 45 x^{8} + 81 x^{7} - 57 x^{6} - 27 x^{5} + 36 x^{4} - 9 x^{2} + 3$ $-\,3^{31}\cdot 5^{6}$ $S_3 \times C_6$ (as 18T6) trivial
18.0.103...863.1 $x^{18} - 4 x^{17} + 11 x^{16} - 22 x^{15} + 36 x^{14} - 53 x^{13} + 80 x^{12} - 116 x^{11} + 154 x^{10} - 173 x^{9} + 154 x^{8} - 116 x^{7} + 80 x^{6} - 53 x^{5} + 36 x^{4} - 22 x^{3} + 11 x^{2} - 4 x + 1$ $-\,7^{8}\cdot 23^{9}$ $C_9:C_6$ (as 18T18) trivial
18.0.104...432.1 $x^{18} - 4 x^{17} + 11 x^{16} - 20 x^{15} + 31 x^{14} - 41 x^{13} + 56 x^{12} - 69 x^{11} + 64 x^{10} - 59 x^{9} + 49 x^{8} - 48 x^{7} + 28 x^{6} - 5 x^{5} + 17 x^{4} - 5 x^{3} - 2 x^{2} - x + 1$ $-\,2^{8}\cdot 3^{9}\cdot 113^{6}$ $C_3^2:D_6$ (as 18T52) trivial
18.0.108...103.1 $x^{18} - 3 x^{17} + 6 x^{16} - 6 x^{15} - 2 x^{14} + 21 x^{13} - 47 x^{12} + 61 x^{11} - 35 x^{10} - 37 x^{9} + 119 x^{8} - 155 x^{7} + 130 x^{6} - 79 x^{5} + 43 x^{4} - 27 x^{3} + 16 x^{2} - 6 x + 1$ $-\,7^{15}\cdot 1511^{2}$ $S_3^3:C_6$ (as 18T286) trivial
18.2.109...009.1 $x^{18} - 2 x^{17} + 4 x^{15} - 7 x^{14} + x^{13} + 7 x^{12} + 2 x^{11} - 10 x^{10} + x^{9} + 20 x^{8} - 22 x^{7} - 2 x^{6} + 7 x^{5} + 2 x^{4} - 10 x^{3} + 11 x^{2} - 5 x + 1$ $43^{2}\cdot 83\cdot 107\cdot 311^{2}\cdot 2621^{2}$ $C_2^9.S_9$ (as 18T968) trivial
18.2.109...837.1 $x^{18} - x^{17} + 3 x^{16} - 5 x^{15} + 4 x^{14} - 6 x^{13} - 5 x^{12} - 2 x^{11} - 16 x^{10} + x^{9} - 16 x^{8} - 2 x^{7} - 5 x^{6} - 6 x^{5} + 4 x^{4} - 5 x^{3} + 3 x^{2} - x + 1$ $53\cdot 453771377^{2}$ $C_2^9.S_9$ (as 18T968) trivial
18.2.109...889.1 $x^{18} - x^{16} - 4 x^{15} - x^{14} + 3 x^{13} + 9 x^{12} + x^{11} - 2 x^{10} - 13 x^{9} - 2 x^{8} + x^{7} + 9 x^{6} + 3 x^{5} - x^{4} - 4 x^{3} - x^{2} + 1$ $23^{6}\cdot 379^{2}\cdot 719^{2}$ $A_4^3.(C_2\times S_4)$ (as 18T776) trivial
18.0.111...771.1 $x^{18} - 8 x^{17} + 28 x^{16} - 54 x^{15} + 55 x^{14} - 8 x^{13} - 55 x^{12} + 69 x^{11} - 19 x^{10} - 37 x^{9} + 44 x^{8} - 16 x^{7} - 6 x^{6} + 15 x^{5} - 14 x^{4} + 3 x^{3} + 7 x^{2} - 5 x + 1$ $-\,3^{4}\cdot 11^{5}\cdot 31^{8}$ $C_6^3:S_4$ (as 18T485) trivial
18.0.114...403.1 $x^{18} - 4 x^{17} + 7 x^{16} - 9 x^{15} + 15 x^{14} - 24 x^{13} + 28 x^{12} - 30 x^{11} + 36 x^{10} - 39 x^{9} + 36 x^{8} - 30 x^{7} + 28 x^{6} - 24 x^{5} + 15 x^{4} - 9 x^{3} + 7 x^{2} - 4 x + 1$ $-\,23^{6}\cdot 43^{2}\cdot 347^{3}$ $D_6\wr S_3$ (as 18T556) trivial
18.2.116...689.1 $x^{18} - 4 x^{17} + 4 x^{16} + 9 x^{15} - 27 x^{14} + 17 x^{13} + 26 x^{12} - 46 x^{11} + 12 x^{10} + 20 x^{9} - 12 x^{8} + 15 x^{7} - 48 x^{6} + 48 x^{5} - x^{4} - 29 x^{3} + 20 x^{2} - 5 x + 1$ $5881\cdot 44555813^{2}$ $C_2^9.S_9$ (as 18T968) trivial
18.0.122...031.1 $x^{18} - 3 x^{17} - 3 x^{16} + 9 x^{15} + 24 x^{14} - 30 x^{13} - 78 x^{12} + 60 x^{11} + 141 x^{10} - 56 x^{9} - 150 x^{8} + 12 x^{7} + 81 x^{6} + 12 x^{5} - 15 x^{4} - 3 x^{3} + 3 x^{2} + 3 x + 1$ $-\,3^{33}\cdot 13^{3}$ $S_3^2:C_6$ (as 18T93) trivial
18.0.126...967.1 $x^{18} - 3 x^{17} + 6 x^{16} - 7 x^{15} + 4 x^{14} + 2 x^{13} - 4 x^{12} - 3 x^{11} + 14 x^{10} - 19 x^{9} + 17 x^{8} - 6 x^{7} - 10 x^{6} + 18 x^{5} - 9 x^{4} - 6 x^{3} + 10 x^{2} - 5 x + 1$ $-\,23^{9}\cdot 2647^{2}$ $S_3\wr S_3$ (as 18T319) trivial
18.0.128...283.1 $x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} + 3 x^{14} + 18 x^{13} - 47 x^{12} + 90 x^{11} - 87 x^{10} + 43 x^{9} + 63 x^{8} - 186 x^{7} + 274 x^{6} - 270 x^{5} + 198 x^{4} - 106 x^{3} + 39 x^{2} - 9 x + 1$ $-\,3^{27}\cdot 1297^{2}$ $S_3^3:C_6$ (as 18T286) trivial
18.0.129...896.1 $x^{18} - 9 x^{17} + 41 x^{16} - 124 x^{15} + 276 x^{14} - 476 x^{13} + 646 x^{12} - 678 x^{11} + 517 x^{10} - 231 x^{9} - 15 x^{8} + 98 x^{7} - 48 x^{6} - 18 x^{5} + 36 x^{4} - 22 x^{3} + 9 x^{2} - 3 x + 1$ $-\,2^{16}\cdot 11^{9}\cdot 17^{4}$ $C_3^3:S_3$ (as 18T88) trivial
18.0.134...623.1 $x^{18} - 6 x^{17} + 15 x^{16} - 23 x^{15} + 37 x^{14} - 78 x^{13} + 152 x^{12} - 240 x^{11} + 302 x^{10} - 308 x^{9} + 300 x^{8} - 298 x^{7} + 220 x^{6} - 85 x^{5} + 25 x^{4} - 26 x^{3} + 12 x^{2} + 1$ $-\,7^{15}\cdot 41^{4}$ $C_3^3:C_6$ (as 18T85) trivial
18.0.135...707.1 $x^{18} - 6 x^{17} + 9 x^{16} + 14 x^{15} - 42 x^{14} - 21 x^{13} + 131 x^{12} - 51 x^{11} - 162 x^{10} + 126 x^{9} + 108 x^{8} - 138 x^{7} - 18 x^{6} + 84 x^{5} - 33 x^{4} - 11 x^{3} + 15 x^{2} - 6 x + 1$ $-\,3^{27}\cdot 11^{6}$ $S_3 \times C_6$ (as 18T6) trivial
18.0.139...207.1 $x^{18} - x^{17} + 4 x^{15} - 5 x^{14} + x^{13} + 6 x^{12} - 9 x^{11} + 7 x^{10} + x^{9} - 12 x^{8} + 11 x^{7} - 2 x^{6} - 5 x^{5} + 6 x^{4} - x^{3} - x^{2} - x + 1$ $-\,11^{4}\cdot 23^{11}$ $C_3^3:S_4$ (as 18T217) trivial
18.0.141...912.1 $x^{18} - 7 x^{17} + 29 x^{16} - 86 x^{15} + 204 x^{14} - 403 x^{13} + 684 x^{12} - 1007 x^{11} + 1301 x^{10} - 1479 x^{9} + 1488 x^{8} - 1316 x^{7} + 1016 x^{6} - 673 x^{5} + 378 x^{4} - 171 x^{3} + 58 x^{2} - 10 x + 1$ $-\,2^{12}\cdot 3^{6}\cdot 7^{15}$ $S_3 \times C_6$ (as 18T6) trivial
18.0.149...783.1 $x^{18} - x^{17} - x^{16} + x^{15} + 3 x^{14} + 2 x^{13} - 5 x^{12} + 4 x^{11} + 5 x^{10} + 5 x^{9} + 6 x^{8} - 4 x^{7} + 8 x^{6} - 5 x^{5} + 5 x^{4} + x^{3} + 2 x^{2} - x + 1$ $-\,23^{9}\cdot 2879^{2}$ $S_3\wr S_3$ (as 18T319) trivial
18.2.153...696.1 $x^{18} + 5 x^{16} + 5 x^{14} - 8 x^{12} - 8 x^{10} + 17 x^{8} + 19 x^{6} + x^{4} - 2 x^{2} - 1$ $2^{18}\cdot 37^{6}\cdot 151^{2}$ $S_3^3:S_4$ (as 18T483) trivial
18.0.162...343.1 $x^{18} - x^{17} - 5 x^{16} + 9 x^{15} + 2 x^{14} - 32 x^{13} + 37 x^{12} + 40 x^{11} - 100 x^{10} + 31 x^{9} + 83 x^{8} - 97 x^{7} + 27 x^{6} + 18 x^{5} - 15 x^{4} + 5 x^{2} - 3 x + 1$ $-\,7^{15}\cdot 43^{4}$ $C_3^3:C_6$ (as 18T85) trivial
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