## Results (1-50 of at least 1000)

Label Polynomial Discriminant Galois group Class group
8.0.221445125.1 $x^{8} - 3 x^{7} + 7 x^{6} - 15 x^{5} + 18 x^{4} - 16 x^{3} + 13 x^{2} - 5 x + 3$ $5^{3}\cdot 11^{6}$ $C_4\wr C_2$ (as 8T17) trivial
8.0.3055942725.1 $x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 14 x^{4} - 21 x^{3} + 30 x^{2} - 20 x + 37$ $3\cdot 5^{2}\cdot 11^{6}\cdot 23$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.4296035425.1 $x^{8} - 2 x^{7} - 9 x^{6} + 18 x^{5} + 27 x^{4} - 50 x^{3} - 23 x^{2} - 4 x + 69$ $5^{2}\cdot 11^{6}\cdot 97$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.5536128125.1 $x^{8} - 2 x^{7} + 4 x^{6} - 18 x^{5} + 39 x^{4} - 3 x^{3} - 28 x^{2} - 5 x + 71$ $5^{5}\cdot 11^{6}$ $C_4\wr C_2$ (as 8T17) $[2]$
8.0.6887829168.1 $x^{8} + 9 x^{6} - 11 x^{5} + 18 x^{4} - 33 x^{3} + 49 x^{2} - 33 x + 9$ $2^{4}\cdot 3^{5}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$
8.0.8193469625.2 $x^{8} - x^{7} + 9 x^{6} + 31 x^{4} + 92 x^{2} - 28 x + 81$ $5^{3}\cdot 11^{6}\cdot 37$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.11337990400.5 $x^{8} - 11 x^{6} + 55 x^{4} - 121 x^{2} + 121$ $2^{8}\cdot 5^{2}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.17937055125.3 $x^{8} - 3 x^{7} - 4 x^{6} + 29 x^{5} - 26 x^{4} - 49 x^{3} + 112 x^{2} - 60 x + 201$ $3^{4}\cdot 5^{3}\cdot 11^{6}$ $C_4\wr C_2$ (as 8T17) $[2, 2]$
8.0.23428894225.1 $x^{8} + 3 x^{6} + 13 x^{4} - 11 x^{3} + 12 x^{2} + 5$ $5^{2}\cdot 11^{6}\cdot 23^{2}$ $V_4^2:(S_3\times C_2)$ (as 8T41) $[2]$
8.0.24250898529.1 $x^{8} - x^{7} - 20 x^{6} + 19 x^{5} + 131 x^{4} - 137 x^{3} - 344 x^{2} + 437 x + 643$ $3^{4}\cdot 11^{6}\cdot 13^{2}$ $Q_8:C_2$ (as 8T11) $[2]$
8.0.27503484525.1 $x^{8} - 2 x^{7} + 15 x^{6} - 18 x^{5} + 94 x^{4} - 25 x^{3} + 137 x^{2} + 6 x + 137$ $3^{3}\cdot 5^{2}\cdot 11^{6}\cdot 23$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.27551316672.2 $x^{8} - 3 x^{7} + 22 x^{6} - 68 x^{5} + 197 x^{4} - 406 x^{3} + 726 x^{2} - 463 x + 97$ $2^{6}\cdot 3^{5}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$
8.0.34013971200.2 $x^{8} - 121 x^{2} + 363$ $2^{8}\cdot 3\cdot 5^{2}\cdot 11^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.34013971200.3 $x^{8} + 121 x^{2} + 363$ $2^{8}\cdot 3\cdot 5^{2}\cdot 11^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.36281569280.2 $x^{8} - 2 x^{7} + 2 x^{6} - 26 x^{5} + 137 x^{4} - 358 x^{3} + 538 x^{2} - 444 x + 157$ $2^{12}\cdot 5\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial
8.0.36735088896.11 $x^{8} - 4 x^{7} + x^{6} + 27 x^{4} + 5 x^{2} + 58 x + 47$ $2^{8}\cdot 3^{4}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$
8.0.42172009605.4 $x^{8} + 4 x^{6} - 11 x^{5} - 5 x^{4} + 11 x^{3} + 4 x^{2} + 1$ $3^{2}\cdot 5\cdot 11^{6}\cdot 23^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.47784314853.1 $x^{8} - x^{7} - 9 x^{6} + 41 x^{5} + 76 x^{4} - 489 x^{3} + 393 x^{2} + 96 x + 93$ $3^{6}\cdot 11^{6}\cdot 37$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$
8.0.48980118528.4 $x^{8} + 3 x^{6} + 13 x^{4} - 66 x^{3} + 56 x^{2} - 44 x + 60$ $2^{10}\cdot 3^{3}\cdot 11^{6}$ $S_4\wr C_2$ (as 8T47) trivial
8.0.56689952000.1 $x^{8} - 11 x^{6} + 22 x^{4} + 605$ $2^{8}\cdot 5^{3}\cdot 11^{6}$ $C_4\wr C_2$ (as 8T17) $[2]$
8.0.58116058605.1 $x^{8} + 3 x^{6} - 11 x^{5} + 24 x^{4} - 21 x^{2} + 27$ $3^{8}\cdot 5\cdot 11^{6}$ $S_4\wr C_2$ (as 8T47) trivial
8.0.63281930481.1 $x^{8} - x^{7} + 24 x^{6} - 25 x^{5} + 241 x^{4} - 159 x^{3} + 1152 x^{2} - 201 x + 2271$ $3^{6}\cdot 7^{2}\cdot 11^{6}$ $Q_8:C_2$ (as 8T11) $[2]$
8.0.74449851025.1 $x^{8} - x^{7} - 2 x^{6} - 22 x^{5} + 20 x^{4} - 11 x^{3} + 180 x^{2} - 94 x + 873$ $5^{2}\cdot 11^{6}\cdot 41^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.76398568125.1 $x^{8} - 2 x^{7} + 10 x^{6} - 5 x^{5} + 60 x^{4} - 177 x^{3} - 26 x^{2} - 215 x + 885$ $3\cdot 5^{4}\cdot 11^{6}\cdot 23$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.76644815104.3 $x^{8} - 2 x^{7} + 2 x^{6} - 4 x^{5} - 6 x^{4} - 50 x^{3} + 285 x^{2} - 378 x + 157$ $2^{8}\cdot 11^{6}\cdot 13^{2}$ $Q_8:C_2$ (as 8T11) trivial
8.4.82653950016.1 $x^{8} - 3 x^{7} + 9 x^{6} - 3 x^{5} - 15 x^{4} + 36 x^{3} - 90 x^{2} - 162 x - 54$ $2^{6}\cdot 3^{6}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.102041913600.2 $x^{8} + 44 x^{4} - 363 x^{2} + 1089$ $2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$
8.0.102041913600.3 $x^{8} - 11 x^{6} + 44 x^{4} + 1089$ $2^{8}\cdot 3^{2}\cdot 5^{2}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$
8.0.110205266688.1 $x^{8} - 22 x^{6} + 121 x^{4} + 363$ $2^{8}\cdot 3^{5}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$
8.0.112501209744.1 $x^{8} - 3 x^{7} - 22 x^{6} + 20 x^{5} + 175 x^{4} + 386 x^{3} + 682 x^{2} + 516 x + 372$ $2^{4}\cdot 3^{4}\cdot 7^{2}\cdot 11^{6}$ $Q_8:C_2^2$ (as 8T22) $[2]$
8.0.116101021696.3 $x^{8} - 22 x^{6} + 242 x^{4} - 242 x^{2} + 121$ $2^{16}\cdot 11^{6}$ $Q_8:C_2$ (as 8T11) trivial
8.0.138403203125.1 $x^{8} - 2 x^{7} + 3 x^{6} + 11 x^{5} + 45 x^{4} + 66 x^{3} + 58 x^{2} + 13 x + 1$ $5^{7}\cdot 11^{6}$ $C_4\wr C_2$ (as 8T17) $[8]$
8.0.138403203125.2 $x^{8} - 2 x^{7} + 8 x^{6} - 24 x^{5} + 50 x^{4} - 39 x^{3} + 83 x^{2} - 87 x + 26$ $5^{7}\cdot 11^{6}$ $C_4\wr C_2$ (as 8T17) $[8]$
8.4.146940355584.2 $x^{8} - x^{7} - 10 x^{6} + 6 x^{5} + 43 x^{4} - 85 x^{3} + 36 x^{2} + 4 x - 2$ $2^{10}\cdot 3^{4}\cdot 11^{6}$ $V_4^2:(S_3\times C_2)$ (as 8T41) trivial
8.0.154170096025.2 $x^{8} - x^{7} - 11 x^{6} + 37 x^{5} + 107 x^{4} - 230 x^{3} - 352 x^{2} + 1216 x + 1808$ $5^{2}\cdot 11^{6}\cdot 59^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.164799462025.1 $x^{8} - x^{7} + 15 x^{5} + 41 x^{4} - 219 x^{3} + 242 x^{2} + 1029 x + 1269$ $5^{2}\cdot 11^{6}\cdot 61^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.170069856000.2 $x^{8} - 11 x^{6} + 121 x^{4} - 605 x^{2} + 1815$ $2^{8}\cdot 3\cdot 5^{3}\cdot 11^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.170069856000.4 $x^{8} + 11 x^{6} + 121 x^{4} + 605 x^{2} + 1815$ $2^{8}\cdot 3\cdot 5^{3}\cdot 11^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$
8.0.172195729200.1 $x^{8} - 3 x^{7} - 13 x^{5} + 21 x^{4} + 144 x^{3} + 286 x^{2} + 516 x + 372$ $2^{4}\cdot 3^{5}\cdot 5^{2}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2, 2]$
8.0.172195729200.2 $x^{8} - 3 x^{7} + 22 x^{6} - 35 x^{5} + 164 x^{4} - 175 x^{3} + 561 x^{2} - 298 x + 724$ $2^{4}\cdot 3^{5}\cdot 5^{2}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2, 2]$
8.2.172337454080.1 $x^{8} - 2 x^{7} + 3 x^{6} - 10 x^{4} + 22 x^{3} - 30 x^{2} + 24 x - 10$ $-\,2^{10}\cdot 5\cdot 11^{6}\cdot 19$ $S_4\wr C_2$ (as 8T47) trivial
8.0.181407846400.3 $x^{8} - 22 x^{6} + 220 x^{4} - 968 x^{2} + 1936$ $2^{12}\cdot 5^{2}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[3]$
8.0.204836740625.1 $x^{8} - 2 x^{7} + 2 x^{6} - 15 x^{5} + 49 x^{4} - 138 x^{3} + 252 x^{2} + 568 x + 2544$ $5^{5}\cdot 11^{6}\cdot 37$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$
8.0.223260975025.3 $x^{8} - x^{7} - 24 x^{6} + 22 x^{5} + 262 x^{4} - 99 x^{3} - 1250 x^{2} + 126 x + 2259$ $5^{2}\cdot 11^{6}\cdot 71^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.2.263459465676.3 $x^{8} - x^{7} - 2 x^{6} - 11 x^{5} - 13 x^{4} - 11 x^{3} + 4 x^{2} + 5 x + 4$ $-\,2^{2}\cdot 3^{7}\cdot 11^{6}\cdot 17$ $S_4\wr C_2$ (as 8T47) $[2]$
8.0.283449760000.6 $x^{8} - 11 x^{6} + 154 x^{4} - 1210 x^{2} + 3025$ $2^{8}\cdot 5^{4}\cdot 11^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) $[2]$
8.2.293880711168.1 $x^{8} - 11 x^{6} + 77 x^{4} - 121 x^{2} - 242$ $-\,2^{11}\cdot 3^{4}\cdot 11^{6}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$
8.2.293880711168.2 $x^{8} - x^{7} + 12 x^{6} - 5 x^{5} + 65 x^{4} - 8 x^{3} + 102 x^{2} - 106 x - 2$ $-\,2^{11}\cdot 3^{4}\cdot 11^{6}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$
8.2.293880711168.3 $x^{8} - 4 x^{7} + 5 x^{6} + 32 x^{5} - 69 x^{4} + 102 x^{3} + 12 x^{2} + 20 x + 4$ $-\,2^{11}\cdot 3^{4}\cdot 11^{6}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$
8.2.293880711168.4 $x^{8} - x^{7} + x^{6} - 5 x^{5} + 21 x^{4} - 85 x^{3} + 157 x^{2} - 161 x + 64$ $-\,2^{11}\cdot 3^{4}\cdot 11^{6}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$