Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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Label | Polynomial | Discriminant | Galois group | Class group |
---|---|---|---|---|
8.0.1257728.1 | $x^{8} - 2 x^{7} + 4 x^{5} - 4 x^{4} + 3 x^{2} - 2 x + 1$ | $2^{8}\cdot 17^{3}$ | $C_4\wr C_2$ (as 8T17) | trivial |
8.0.1265625.1 | $x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1$ | $3^{4}\cdot 5^{6}$ | $C_4\times C_2$ (as 8T2) | trivial |
8.0.1282789.1 | $x^{8} - x^{7} + 2 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - 2 x + 1$ | $1103\cdot 1163$ | $S_8$ (as 8T50) | trivial |
8.0.1327833.1 | $x^{8} - x^{7} + x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$ | $3^{4}\cdot 13^{2}\cdot 97$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.1342413.1 | $x^{8} - x^{7} + x^{6} + x^{4} - 2 x^{3} + 3 x^{2} - 3 x + 1$ | $3^{4}\cdot 16573$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.1361513.1 | $x^{8} - x^{7} + 2 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$ | $17\cdot 283^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.1385533.1 | $x^{8} - 2 x^{7} + 3 x^{6} - 3 x^{5} + x^{4} + 1$ | $29\cdot 47777$ | $S_8$ (as 8T50) | trivial |
8.0.1424293.1 | $x^{8} - 2 x^{7} + 2 x^{6} - x^{5} + x^{4} - x^{3} + 2 x^{2} - 2 x + 1$ | $13\cdot 331^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.1474013.1 | $x^{8} - x^{7} + x^{6} - x^{4} + x^{3} - x^{2} + 1$ | $617\cdot 2389$ | $S_8$ (as 8T50) | trivial |
8.0.1492101.1 | $x^{8} - x^{7} + x^{6} - 3 x^{5} + x^{4} - 2 x^{3} + 3 x^{2} + 1$ | $3^{4}\cdot 13^{2}\cdot 109$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.1513728.1 | $x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 3 x^{4} - 2 x^{3} + x^{2} + 2 x + 1$ | $2^{8}\cdot 3^{4}\cdot 73$ | $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) | trivial |
8.0.1520789.1 | $x^{8} - x^{7} - x^{6} + x^{4} - x^{2} + x + 1$ | $29\cdot 229^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.1578125.1 | $x^{8} - 2 x^{7} + 3 x^{5} - x^{4} - 3 x^{3} + 2 x + 1$ | $5^{6}\cdot 101$ | $((C_8 : C_2):C_2):C_2$ (as 8T27) | trivial |
8.0.1590773.1 | $x^{8} - x^{7} + 2 x^{5} - 2 x^{4} + x^{3} + x^{2} - 2 x + 1$ | $179\cdot 8887$ | $S_8$ (as 8T50) | trivial |
8.0.1601613.1 | $x^{8} - 2 x^{6} - 3 x^{5} + 3 x^{4} + 3 x^{3} - 2 x^{2} + 1$ | $3^{6}\cdot 13^{3}$ | $C_4\wr C_2$ (as 8T17) | trivial |
8.0.1740113.1 | $x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 4 x^{3} + 3 x^{2} - x + 1$ | $1740113$ | $S_8$ (as 8T50) | trivial |
8.0.1750329.1 | $x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{3} + 4 x^{2} - 3 x + 1$ | $3^{6}\cdot 7^{4}$ | $D_4$ (as 8T4) | trivial |
8.0.1763584.1 | $x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 3 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ | $2^{8}\cdot 83^{2}$ | $S_4\times C_2$ (as 8T24) | trivial |
8.0.1797309.1 | $x^{8} - 3 x^{7} + 6 x^{6} - 8 x^{5} + 10 x^{4} - 9 x^{3} + 7 x^{2} - 4 x + 1$ | $3^{4}\cdot 22189$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.1820637.1 | $x^{8} - x^{7} + x^{5} - x^{4} - 2 x^{3} + 2 x + 1$ | $3^{4}\cdot 7\cdot 13^{2}\cdot 19$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.1867553.1 | $x^{8} - x^{7} + x^{5} - 2 x^{4} + x^{3} + x^{2} - x + 1$ | $1867553$ | $S_8$ (as 8T50) | trivial |
8.0.1890625.1 | $x^{8} - 3 x^{7} + 6 x^{6} - 9 x^{5} + 9 x^{4} - 7 x^{3} + 4 x^{2} - x + 1$ | $5^{6}\cdot 11^{2}$ | $C_2^2:C_4$ (as 8T10) | trivial |
8.0.2067245.1 | $x^{8} - x^{7} + x^{6} - x^{4} + x^{2} - x + 1$ | $5\cdot 643^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.2105893.1 | $x^{8} - x^{7} + 2 x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - 2 x + 1$ | $29\cdot 72617$ | $S_8$ (as 8T50) | trivial |
8.0.2118069.1 | $x^{8} - x^{7} - x^{3} + 2 x^{2} - x + 1$ | $3^{4}\cdot 79\cdot 331$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.2149173.1 | $x^{8} - x^{7} - 2 x^{6} + 2 x^{5} + x^{3} + x^{2} - 2 x + 1$ | $3^{4}\cdot 13^{2}\cdot 157$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.2178981.1 | $x^{8} - x^{7} - x^{6} + 2 x^{5} + x^{4} - 2 x^{3} - x^{2} + x + 1$ | $3^{6}\cdot 7^{2}\cdot 61$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.2193125.1 | $x^{8} - 2 x^{7} + 4 x^{6} - 5 x^{5} + 5 x^{4} - 5 x^{3} + 4 x^{2} - 2 x + 1$ | $5^{4}\cdot 11^{2}\cdot 29$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.2217213.1 | $x^{8} - x^{7} - x^{6} - x^{5} + 3 x^{4} - x + 1$ | $3^{4}\cdot 31\cdot 883$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.2313441.1 | $x^{8} - x^{7} + 2 x^{6} + 3 x^{5} - x^{4} + 3 x^{3} + 2 x^{2} - x + 1$ | $3^{4}\cdot 13^{4}$ | $D_4$ (as 8T4) | trivial |
8.0.2314413.1 | $x^{8} - x^{6} - x^{5} - x^{3} + 2 x + 1$ | $3^{4}\cdot 28573$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.2477709.1 | $x^{8} - x^{7} + 3 x^{5} - x^{3} + 2 x^{2} + 2 x + 1$ | $3^{4}\cdot 13^{2}\cdot 181$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.2560000.1 | $x^{8} - 2 x^{7} + 2 x^{6} + 2 x^{5} - 2 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ | $2^{12}\cdot 5^{4}$ | $D_4$ (as 8T4) | trivial |
8.0.2671805.1 | $x^{8} - x^{5} + x^{4} - x^{3} + 1$ | $5\cdot 17^{2}\cdot 43^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.2708009.1 | $x^{8} - x^{7} - x^{6} + x^{5} + x^{4} - x^{3} - x^{2} + x + 1$ | $41\cdot 257^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.2712933.1 | $x^{8} - 3 x^{7} + 3 x^{6} - x^{5} + x^{4} - 2 x^{2} + x + 1$ | $3^{4}\cdot 33493$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.2824713.1 | $x^{8} - 3 x^{7} + 2 x^{6} + 3 x^{5} - 4 x^{4} + x^{2} + 1$ | $3^{4}\cdot 43\cdot 811$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.2828125.1 | $x^{8} - x^{7} - x^{6} - 2 x^{5} + 4 x^{4} + x^{3} + x^{2} - 3 x + 1$ | $5^{6}\cdot 181$ | $((C_8 : C_2):C_2):C_2$ (as 8T27) | trivial |
8.0.2844928.1 | $x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ | $2^{8}\cdot 11113$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.2963293.1 | $x^{8} - 3 x^{7} + 5 x^{6} - 6 x^{5} + 7 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$ | $37\cdot 283^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.2970513.1 | $x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 3 x^{4} - 3 x^{2} + x + 1$ | $3^{4}\cdot 7\cdot 13^{2}\cdot 31$ | $C_2 \wr C_2\wr C_2$ (as 8T35) | trivial |
8.0.2985984.1 | $x^{8} - 2 x^{7} + 2 x^{6} - 2 x^{5} + 7 x^{4} - 10 x^{3} + 8 x^{2} - 4 x + 1$ | $2^{12}\cdot 3^{6}$ | $D_4$ (as 8T4) | trivial |
8.0.3057993.1 | $x^{8} - 2 x^{7} + 3 x^{6} - 2 x^{5} + x^{3} + 2 x^{2} - 3 x + 1$ | $3^{4}\cdot 19\cdot 1987$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.3134053.1 | $x^{8} - x^{7} + x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + x^{2} - x + 1$ | $13\cdot 491^{2}$ | $C_2 \wr S_4$ (as 8T44) | trivial |
8.0.3167829.1 | $x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{4} + 3 x^{3} + 2 x^{2} - 3 x + 1$ | $3^{4}\cdot 7\cdot 37\cdot 151$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.3198933.1 | $x^{8} - x^{7} - x^{6} + 4 x^{4} - x^{3} - 3 x^{2} + x + 1$ | $3^{4}\cdot 73\cdot 541$ | $S_4\wr C_2$ (as 8T47) | trivial |
8.0.3203125.1 | $x^{8} - x^{7} + 2 x^{6} + 2 x^{5} + 3 x^{3} + 2 x^{2} + x + 1$ | $5^{7}\cdot 41$ | $((C_8 : C_2):C_2):C_2$ (as 8T27) | trivial |
8.0.3207681.1 | $x^{8} - 3 x^{7} + 4 x^{6} - 3 x^{5} + 2 x^{4} - x^{2} + 1$ | $3^{4}\cdot 199^{2}$ | $S_4\times C_2$ (as 8T24) | trivial |
8.0.3211264.1 | $x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 7 x^{4} - 8 x^{3} + 8 x^{2} - 4 x + 1$ | $2^{16}\cdot 7^{2}$ | $D_4\times C_2$ (as 8T9) | trivial |
8.0.3240000.1 | $x^{8} - 3 x^{7} + 3 x^{6} + x^{5} - 2 x^{4} - 3 x^{3} + 7 x^{2} - 4 x + 1$ | $2^{6}\cdot 3^{4}\cdot 5^{4}$ | $Q_8:C_2$ (as 8T11) | trivial |