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Results: (displaying matches 1-20 of 3078042)

Label Polynomial Discriminant Galois group Class group
8.0.1257728.1 x8 - 2x7 + 4x5 - 4x4 + 3x2 - 2x + 1 \( 2^{8}\cdot 17^{3} \) $C_4\wr C_2$ Trivial
8.0.1265625.1 x8 - x7 + x5 - x4 + x3 - x + 1 \( 3^{4}\cdot 5^{6} \) $C_4\times C_2$ Trivial
8.0.1282789.1 x8 - x7 + 2x6 - 3x5 + 3x4 - 3x3 + 3x2 - 2x + 1 \( 1103\cdot 1163 \) $S_8$ Trivial
8.0.1327833.1 x8 - x7 + x6 - 2x5 + 3x4 - 4x3 + 4x2 - 2x + 1 \( 3^{4}\cdot 13^{2}\cdot 97 \) $C_2 \wr C_2\wr C_2$ Trivial
8.0.1342413.1 x8 - x7 + x6 + x4 - 2x3 + 3x2 - 3x + 1 \( 3^{4}\cdot 16573 \) $S_4\wr C_2$ Trivial
8.0.1361513.1 x8 - x7 + 2x6 - 3x5 + 3x4 - 3x3 + 2x2 - x + 1 \( 17\cdot 283^{2} \) $C_2 \wr S_4$ Trivial
8.0.1385533.1 x8 - 2x7 + 3x6 - 3x5 + x4 + 1 \( 29\cdot 47777 \) $S_8$ Trivial
8.0.1424293.1 x8 - 2x7 + 2x6 - x5 + x4 - x3 + 2x2 - 2x + 1 \( 13\cdot 331^{2} \) $C_2 \wr S_4$ Trivial
8.0.1492101.1 x8 - x7 + x6 - 3x5 + x4 - 2x3 + 3x2 + 1 \( 3^{4}\cdot 13^{2}\cdot 109 \) $C_2 \wr C_2\wr C_2$ Trivial
8.0.1513728.1 x8 - 2x7 + x6 + 2x5 - 3x4 - 2x3 + x2 + 2x + 1 \( 2^{8}\cdot 3^{4}\cdot 73 \) 8T31 Trivial
8.0.1520789.1 x8 - x7 - x6 + x4 - x2 + x + 1 \( 29\cdot 229^{2} \) $C_2 \wr S_4$ Trivial
8.0.1578125.1 x8 - 2x7 + 3x5 - x4 - 3x3 + 2x + 1 \( 5^{6}\cdot 101 \) 8T27 Trivial
8.0.1601613.1 x8 - 2x6 - 3x5 + 3x4 + 3x3 - 2x2 + 1 \( 3^{6}\cdot 13^{3} \) $C_4\wr C_2$ Trivial
8.0.1750329.1 x8 - 3x7 + 4x6 - 3x5 + 3x4 - 3x3 + 4x2 - 3x + 1 \( 3^{6}\cdot 7^{4} \) $D_4$ Trivial
8.0.1763584.1 x8 - 2x7 + x6 + 2x5 - 3x4 + 2x3 + x2 - 2x + 1 \( 2^{8}\cdot 83^{2} \) $S_4\times C_2$ Trivial
8.0.1797309.1 x8 - 3x7 + 6x6 - 8x5 + 10x4 - 9x3 + 7x2 - 4x + 1 \( 3^{4}\cdot 22189 \) $S_4\wr C_2$ Trivial
8.0.1820637.1 x8 - x7 + x5 - x4 - 2x3 + 2x + 1 \( 3^{4}\cdot 7\cdot 13^{2}\cdot 19 \) $C_2 \wr C_2\wr C_2$ Trivial
8.0.1890625.1 x8 - 3x7 + 6x6 - 9x5 + 9x4 - 7x3 + 4x2 - x + 1 \( 5^{6}\cdot 11^{2} \) $C_2^2:C_4$ Trivial
8.0.2067245.1 x8 - x7 + x6 - x4 + x2 - x + 1 \( 5\cdot 643^{2} \) $C_2 \wr S_4$ Trivial
8.0.2118069.1 x8 - x7 - x3 + 2x2 - x + 1 \( 3^{4}\cdot 79\cdot 331 \) $S_4\wr C_2$ Trivial

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