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Label Polynomial Discriminant Galois group Class group
8.0.1601613.1 x8 - 2x6 - 3x5 + 3x4 + 3x3 - 2x2 + 1 \( 3^{6}\cdot 13^{3} \) $C_4\wr C_2$ (as 8T17) trivial
8.0.4243509.1 x8 - 3x7 + 4x6 - 3x5 + 3x3 - 2x2 + 1 \( 3^{6}\cdot 5821 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.4665600.1 x8 - 2x7 + 2x6 + 4x5 - 8x4 + 2x3 + 5x2 - 4x + 1 \( 2^{8}\cdot 3^{6}\cdot 5^{2} \) $Q_8:C_2$ (as 8T11) trivial
8.0.4987089.1 x8 - x7 - x6 + 2x5 - 2x4 + x3 + 2x2 - 2x + 1 \( 3^{6}\cdot 6841 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.7290000.1 x8 - 3x7 + x6 + 3x5 - 3x3 + x2 + 3x + 1 \( 2^{4}\cdot 3^{6}\cdot 5^{4} \) $Q_8:C_2$ (as 8T11) trivial
8.0.7559001.1 x8 - 2x7 - x6 + 4x5 + x4 - 7x3 + 8x2 - 4x + 1 \( 3^{6}\cdot 10369 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.7637733.1 x8 - 3x7 + 4x6 - 6x4 + 6x3 + x2 - 3x + 1 \( 3^{6}\cdot 10477 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.8993673.1 x8 - 2x7 - x6 + 7x5 - 2x4 - 7x3 + 5x2 + 5x + 1 \( 3^{6}\cdot 13^{2}\cdot 73 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.10404288.1 x8 - x7 - x6 - x5 + 4x4 + x3 - x2 - 2x + 1 \( 2^{6}\cdot 3^{6}\cdot 223 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.16385733.1 x8 - x7 - 4x6 - x5 + 10x4 + 7x3 - 10x2 - 8x + 7 \( 3^{6}\cdot 7\cdot 13^{2}\cdot 19 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.16560693.1 x8 - x7 - x6 + 2x5 - 2x4 - 2x3 + 2x2 + x + 1 \( 3^{6}\cdot 22717 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.17417997.1 x8 - 2x7 - x6 + 4x5 - 2x4 - x3 + 5x2 - 4x + 1 \( 3^{6}\cdot 23893 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.18102528.1 x8 + 4x6 - 6x5 + 9x4 - 6x3 + 10x2 - 12x + 4 \( 2^{8}\cdot 3^{6}\cdot 97 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial
8.0.22203153.1 x8 - 2x6 + 4x2 - 3x + 1 \( 3^{6}\cdot 7\cdot 19\cdot 229 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.22299381.1 x8 - 2x7 + x6 + x5 - 2x4 + 10x3 - 2x2 - 5x + 7 \( 3^{6}\cdot 13^{2}\cdot 181 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.24057729.1 x8 - x7 - 4x6 + 5x5 + x4 - 5x3 + 8x2 - 5x + 1 \( 3^{6}\cdot 61\cdot 541 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.24565113.1 x8 - 2x6 - 3x5 + 6x4 + x2 - 3x + 1 \( 3^{6}\cdot 31\cdot 1087 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.25326189.1 x8 - 3x7 + 4x6 - 6x5 + 6x4 + 3x3 - 5x2 + 1 \( 3^{6}\cdot 7^{2}\cdot 709 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.26734617.1 x8 - 3x7 + 10x6 - 18x5 + 33x4 - 36x3 + 40x2 - 24x + 16 \( 3^{6}\cdot 7\cdot 13^{2}\cdot 31 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.27023301.1 x8 - 3x7 + 7x6 - 15x5 + 21x4 - 21x3 + 16x2 - 6x + 1 \( 3^{6}\cdot 19\cdot 1951 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.28213029.1 x8 - 4x7 + 7x6 - 7x5 + x4 + 5x3 - 8x2 + 5x + 7 \( 3^{6}\cdot 13^{2}\cdot 229 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.29254041.1 x8 - 5x6 + 9x4 - 3x3 - 2x2 + 1 \( 3^{6}\cdot 40129 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.30819933.1 x8 - 3x7 + x6 + 3x5 - 5x2 + 4 \( 3^{6}\cdot 67\cdot 631 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.30874608.1 x8 - 3x7 + 7x6 - 9x5 + 12x4 - 9x3 + 7x2 + 1 \( 2^{4}\cdot 3^{6}\cdot 2647 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.31108617.1 x8 - x7 - x6 - x5 + 7x4 - 5x3 - x2 + x + 1 \( 3^{6}\cdot 139\cdot 307 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.32569533.1 x8 - x7 + 2x6 + 2x5 + x4 + x3 + 5x2 + 4x + 1 \( 3^{6}\cdot 43\cdot 1039 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.35605089.1 x8 - x7 + 2x6 + 5x5 + x4 + 7x3 + 8x2 + 13x + 13 \( 3^{6}\cdot 13^{2}\cdot 17^{2} \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial
8.0.36403344.1 x8 - 2x7 + 2x6 - 2x5 + 7x4 - 4x3 - 4x2 + 2x + 1 \( 2^{4}\cdot 3^{6}\cdot 3121 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.36768573.1 x8 - 4x7 + 11x6 - 19x5 + 25x4 - 20x3 + 14x2 - 5x + 1 \( 3^{6}\cdot 31\cdot 1627 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.36812313.1 x8 + 4x6 + 3x4 + x2 - 3x + 1 \( 3^{6}\cdot 50497 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.37083501.1 x8 - x7 - x6 - 4x5 + x4 - 2x3 + 11x2 + 13x + 13 \( 3^{6}\cdot 7\cdot 13^{2}\cdot 43 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.37258461.1 x8 - x7 - x6 + 5x5 + x4 - 5x3 + 2x2 + 4x + 1 \( 3^{6}\cdot 51109 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.38817792.1 x8 - 2x7 - 4x6 + 4x5 + 22x4 - 28x3 - 4x2 + 8x + 4 \( 2^{12}\cdot 3^{6}\cdot 13 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial
8.0.39762576.1 x8 - x7 + 2x6 - x5 + 4x4 - 5x3 + 8x2 - 5x + 1 \( 2^{4}\cdot 3^{6}\cdot 7\cdot 487 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.39891609.1 x8 - 2x7 + 8x6 - 8x5 + 16x4 - 7x3 + 8x2 - x + 1 \( 3^{6}\cdot 54721 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.40206537.1 x8 - x7 + 2x6 - x5 + 4x4 + 4x3 + 5x2 + 4x + 1 \( 3^{6}\cdot 7\cdot 7879 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.42551001.1 x8 - 3x7 + x6 + 6x5 - 6x4 - 3x3 + 7x2 - 6x + 4 \( 3^{6}\cdot 58369 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.42935913.1 x8 - 2x7 - x6 + 4x5 - 5x4 - x3 + 8x2 + 2x + 1 \( 3^{6}\cdot 58897 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.43075881.1 x8 + x6 - 6x4 - 3x3 + 4x2 + 3x + 1 \( 3^{6}\cdot 37\cdot 1597 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.43259589.1 x8 - x7 + 5x6 - 7x5 + 10x4 - 11x3 + 5x2 - 2x + 1 \( 3^{6}\cdot 59341 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.44976384.1 x8 - 2x7 + 2x6 - 2x5 - 5x4 + 8x3 + 2x2 - 4x + 1 \( 2^{8}\cdot 3^{6}\cdot 241 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.47810736.1 x8 - x7 + 5x6 - 7x5 + 13x4 - 14x3 + 14x2 - 8x + 4 \( 2^{4}\cdot 3^{6}\cdot 4099 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.49251969.1 x8 - 2x7 + 2x6 + x5 - 2x4 - 4x3 + 5x2 + 5x + 1 \( 3^{6}\cdot 13\cdot 5197 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.49663125.1 x8 - 2x7 + 2x6 - 5x5 + 7x4 - x3 + 11x2 + 2x + 4 \( 3^{6}\cdot 5^{4}\cdot 109 \) $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial
8.0.50389209.1 x8 - x7 - 7x6 + 8x5 + 19x4 - 20x3 - 16x2 + 10x + 7 \( 3^{6}\cdot 13^{2}\cdot 409 \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.50502933.1 x8 - 3x7 + 4x6 - 3x4 + 4x2 + 3x + 1 \( 3^{6}\cdot 13\cdot 73^{2} \) $C_2 \wr C_2\wr C_2$ (as 8T35) trivial
8.0.51229017.1 x8 - x7 - x6 - x5 + 4x4 + 4x3 + 5x2 + 4x + 1 \( 3^{6}\cdot 7\cdot 10039 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.51482709.1 x8 - 2x7 - 4x6 + 10x5 + x4 - 13x3 + 8x2 - x + 1 \( 3^{6}\cdot 70621 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.53269488.1 x8 - x7 + 2x6 + 5x5 - 8x4 + x3 + 5x2 - 8x + 4 \( 2^{4}\cdot 3^{6}\cdot 4567 \) $S_4\wr C_2$ (as 8T47) trivial
8.0.53625969.1 x8 - 4x7 + 11x6 - 16x5 + 16x4 - 5x3 - x2 + x + 1 \( 3^{6}\cdot 73561 \) $S_4\wr C_2$ (as 8T47) trivial
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