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Label Polynomial Discriminant Galois group Class group
8.0.12230590464.1 x8 + 12x6 + 36x4 + 36x2 + 9 \( 2^{24}\cdot 3^{6} \) $Q_8$ (as 8T5) $[2]$
8.8.12230590464.1 x8 - 12x6 + 36x4 - 36x2 + 9 \( 2^{24}\cdot 3^{6} \) $Q_8$ (as 8T5) Trivial
8.0.1340095640625.1 x8 - 3x7 + 22x6 - 60x5 + 201x4 - 450x3 + 1528x2 - 3069x + 4561 \( 3^{6}\cdot 5^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 2, 2]$
8.8.1340095640625.1 x8 - x7 - 34x6 + 29x5 + 361x4 - 305x3 - 1090x2 + 1345x - 395 \( 3^{6}\cdot 5^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.7644119040000.1 x8 + 60x6 + 900x4 + 4500x2 + 5625 \( 2^{24}\cdot 3^{6}\cdot 5^{4} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.8.7644119040000.1 x8 - 60x6 + 900x4 - 4500x2 + 5625 \( 2^{24}\cdot 3^{6}\cdot 5^{4} \) $Q_8$ (as 8T5) $[2]$
8.8.9294114390625.1 x8 - x7 - 47x6 + 40x5 + 581x4 - 220x3 - 2038x2 - 932x - 109 \( 5^{6}\cdot 29^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.29365647704064.1 x8 + 84x6 + 1764x4 + 12348x2 + 21609 \( 2^{24}\cdot 3^{6}\cdot 7^{4} \) $Q_8$ (as 8T5) $[2, 10, 10]$
8.8.29365647704064.1 x8 - 84x6 + 1764x4 - 12348x2 + 21609 \( 2^{24}\cdot 3^{6}\cdot 7^{4} \) $Q_8$ (as 8T5) $[2]$
8.0.29721861554176.1 x8 + 44x6 + 308x4 + 484x2 + 121 \( 2^{24}\cdot 11^{6} \) $Q_8$ (as 8T5) $[3, 6]$
8.8.29721861554176.1 x8 - 44x6 + 308x4 - 484x2 + 121 \( 2^{24}\cdot 11^{6} \) $Q_8$ (as 8T5) Trivial
8.0.47775744000000.1 x8 + 60x6 + 810x4 + 1800x2 + 900 \( 2^{22}\cdot 3^{6}\cdot 5^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.0.47775744000000.2 x8 + 60x6 + 1170x4 + 9000x2 + 22500 \( 2^{22}\cdot 3^{6}\cdot 5^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.8.47775744000000.2 x8 - 60x6 + 810x4 - 1800x2 + 900 \( 2^{22}\cdot 3^{6}\cdot 5^{6} \) $Q_8$ (as 8T5) $[2]$
8.8.47775744000000.3 x8 - 60x6 + 1170x4 - 9000x2 + 22500 \( 2^{22}\cdot 3^{6}\cdot 5^{6} \) $Q_8$ (as 8T5) $[2]$
8.8.74220378765625.1 x8 - 3x7 - 63x6 + 90x5 + 1311x4 - 20x3 - 7702x2 - 5524x - 1009 \( 5^{6}\cdot 41^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.101240302206976.2 x8 + 68x6 + 986x4 + 4624x2 + 4624 \( 2^{22}\cdot 17^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.8.101240302206976.2 x8 - 68x6 + 986x4 - 4624x2 + 4624 \( 2^{22}\cdot 17^{6} \) $Q_8$ (as 8T5) $[2]$
8.8.116507435287321.1 x8 - 3x7 - 67x6 - 16x5 + 863x4 + 1276x3 + 392x2 - 54x + 1 \( 13^{6}\cdot 17^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.151939915084881.1 x8 - x7 + 50x6 + 71x5 + 529x4 + 2173x3 + 842x2 + 5545x + 17623 \( 3^{6}\cdot 7^{6}\cdot 11^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.8.151939915084881.1 x8 - 3x7 - 62x6 + 66x5 + 1125x4 + 264x3 - 4982x2 - 4245x + 823 \( 3^{6}\cdot 7^{6}\cdot 11^{6} \) $Q_8$ (as 8T5) Trivial
8.0.179068074983424.1 x8 + 132x6 + 4356x4 + 47916x2 + 131769 \( 2^{24}\cdot 3^{6}\cdot 11^{4} \) $Q_8$ (as 8T5) $[2, 14, 14]$
8.8.179068074983424.2 x8 - 132x6 + 4356x4 - 47916x2 + 131769 \( 2^{24}\cdot 3^{6}\cdot 11^{4} \) $Q_8$ (as 8T5) $[2, 2]$
8.0.343064484000000.1 x8 + 105x6 + 3780x4 + 55125x2 + 275625 \( 2^{8}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 2, 2, 6, 6]$
8.8.343064484000000.1 x8 - 105x6 + 3465x4 - 44100x2 + 176400 \( 2^{8}\cdot 3^{6}\cdot 5^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 2]$
8.0.349317894242304.1 x8 + 156x6 + 6084x4 + 79092x2 + 257049 \( 2^{24}\cdot 3^{6}\cdot 13^{4} \) $Q_8$ (as 8T5) $[2, 14, 14]$
8.8.349317894242304.3 x8 - 156x6 + 6084x4 - 79092x2 + 257049 \( 2^{24}\cdot 3^{6}\cdot 13^{4} \) $Q_8$ (as 8T5) $[2]$
8.0.359729184374784.1 x8 + 84x6 + 1890x4 + 10584x2 + 1764 \( 2^{22}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.0.359729184374784.2 x8 + 84x6 + 2394x4 + 24696x2 + 44100 \( 2^{22}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 14, 14]$
8.8.359729184374784.2 x8 - 84x6 + 1890x4 - 10584x2 + 1764 \( 2^{22}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) Trivial
8.8.359729184374784.3 x8 - 84x6 + 2394x4 - 24696x2 + 44100 \( 2^{22}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) Trivial
8.0.752823265640625.1 x8 - x7 + 98x6 - 105x5 + 3191x4 + 1665x3 + 44072x2 + 47933x + 328171 \( 3^{4}\cdot 5^{6}\cdot 29^{6} \) $Q_8$ (as 8T5) $[2, 2, 4, 4, 4]$
8.0.789298907447296.1 x8 + 76x6 + 1748x4 + 12996x2 + 29241 \( 2^{24}\cdot 19^{6} \) $Q_8$ (as 8T5) $[7, 14]$
8.8.789298907447296.1 x8 - 76x6 + 1748x4 - 12996x2 + 29241 \( 2^{24}\cdot 19^{6} \) $Q_8$ (as 8T5) Trivial
8.0.805005849390625.1 x8 - 3x7 + 57x6 + 135x5 + 306x4 + 5365x3 + 23383x2 + 40951x + 75421 \( 5^{6}\cdot 61^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.0.1021511146143744.1 x8 + 204x6 + 10404x4 + 176868x2 + 751689 \( 2^{24}\cdot 3^{6}\cdot 17^{4} \) $Q_8$ (as 8T5) $[2, 22, 22]$
8.8.1021511146143744.3 x8 - 204x6 + 10404x4 - 176868x2 + 751689 \( 2^{24}\cdot 3^{6}\cdot 17^{4} \) $Q_8$ (as 8T5) $[2, 2]$
8.0.1438916737499136.1 x8 + 84x6 + 1260x4 + 5292x2 + 441 \( 2^{24}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 6, 12]$
8.8.1438916737499136.1 x8 - 84x6 + 2268x4 - 19404x2 + 441 \( 2^{24}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.1438916737499136.2 x8 + 84x6 + 2268x4 + 19404x2 + 441 \( 2^{24}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2, 10, 20]$
8.8.1438916737499136.2 x8 - 84x6 + 1260x4 - 5292x2 + 441 \( 2^{24}\cdot 3^{6}\cdot 7^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.1593902779858944.1 x8 + 228x6 + 12996x4 + 246924x2 + 1172889 \( 2^{24}\cdot 3^{6}\cdot 19^{4} \) $Q_8$ (as 8T5) $[2, 22, 22]$
8.8.1593902779858944.2 x8 - 228x6 + 12996x4 - 246924x2 + 1172889 \( 2^{24}\cdot 3^{6}\cdot 19^{4} \) $Q_8$ (as 8T5) $[2, 2]$
8.0.1686221298140625.1 x8 - 3x7 + 64x6 - 192x5 + 1836x4 - 4635x3 + 39520x2 - 110850x + 565795 \( 3^{6}\cdot 5^{6}\cdot 23^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.8.1686221298140625.1 x8 - x7 - 112x6 + 95x5 + 2881x4 + 835x3 - 16858x2 - 25817x - 10769 \( 3^{6}\cdot 5^{6}\cdot 23^{6} \) $Q_8$ (as 8T5) $[2]$ (GRH)
8.0.2070185663499849.1 x8 - x7 + 65x6 - 439x5 + 1876x4 - 12191x3 + 60887x2 - 124718x + 121291 \( 3^{6}\cdot 7^{6}\cdot 17^{6} \) $Q_8$ (as 8T5) $[2, 6, 6]$
8.8.2070185663499849.1 x8 - 3x7 - 110x6 + 153x5 + 3789x4 + 1989x3 - 44000x2 - 97899x - 46703 \( 3^{6}\cdot 7^{6}\cdot 17^{6} \) $Q_8$ (as 8T5) $[2]$
8.0.2379293284000000.1 x8 + 145x6 + 6380x4 + 105125x2 + 525625 \( 2^{8}\cdot 5^{6}\cdot 29^{6} \) $Q_8$ (as 8T5) $[2, 2, 2, 6, 12]$
8.0.2407470785888256.1 x8 + 132x6 + 2772x4 + 13068x2 + 9801 \( 2^{24}\cdot 3^{4}\cdot 11^{6} \) $Q_8$ (as 8T5) $[2, 18, 18]$
8.8.2407470785888256.1 x8 - 132x6 + 2772x4 - 13068x2 + 9801 \( 2^{24}\cdot 3^{4}\cdot 11^{6} \) $Q_8$ (as 8T5) $[2, 2]$

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