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Label Polynomial Discriminant Galois group Class group
8.0.9453125.1 x8 - 2x7 + 8x6 - 9x5 + 15x4 - 9x3 + 8x2 - 2x + 1 \( 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.20000000.1 x8 - 5x6 + 10x4 - 10x2 + 5 \( 2^{8}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.75078125.1 x8 - 2x7 - 7x6 + 11x5 + 20x4 - 14x3 - 22x2 + 3x + 11 \( 5^{7}\cdot 31^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.320000000.1 x8 - 10x6 + 40x4 - 80x2 + 80 \( 2^{12}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.4.320000000.1 x8 - 2x7 - 2x6 + 6x5 - 10x4 + 6x3 - 2x2 - 2x + 1 \( 2^{12}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.393828125.1 x8 - 2x7 + 3x6 + 11x5 - 30x4 + 36x3 + 13x2 - 142x + 121 \( 5^{7}\cdot 71^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.564736653.1 x8 - 4x7 + 7x6 - 7x5 + 6x4 - 5x3 - 2x2 + 4x + 3 \( 3^{2}\cdot 13^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.765703125.1 x8 - 2x7 - 12x6 + 16x5 + 75x4 - 59x3 - 217x2 + 78x + 241 \( 3^{4}\cdot 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.4.1143828125.1 x8 - x7 - 8x6 + 7x5 + 15x4 - 12x3 - 18x2 - 4x + 1 \( 5^{7}\cdot 11^{4} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.1340703125.1 x8 - 2x7 - 7x6 - 4x5 + 70x4 + 41x3 - 287x2 - 62x + 401 \( 5^{7}\cdot 131^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.1620000000.1 x8 - 15x6 + 90x4 - 270x2 + 405 \( 2^{8}\cdot 3^{4}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.1781328125.1 x8 - 2x7 + 18x6 - 39x5 + 140x4 - 219x3 + 453x2 - 382x + 451 \( 5^{7}\cdot 151^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.4.2147483648.2 x8 - 4x4 + 2 \( 2^{31} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.2147483648.3 x8 + 4x4 + 2 \( 2^{31} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.2420000000.1 x8 - 20x6 + 150x4 - 495x2 + 605 \( 2^{8}\cdot 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.2420000000.2 x8 - 15x6 + 120x4 - 440x2 + 605 \( 2^{8}\cdot 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.2420000000.3 x8 + 5x6 - 40x4 - 110x2 + 605 \( 2^{8}\cdot 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.2420000000.4 x8 + 50x4 + 605 \( 2^{8}\cdot 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.2420000000.5 x8 - 5x6 - 40x4 + 110x2 + 605 \( 2^{8}\cdot 5^{7}\cdot 11^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.2850078125.1 x8 - 2x7 - 7x6 - 9x5 + 95x4 + 46x3 - 372x2 - 232x + 841 \( 5^{7}\cdot 191^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.3412578125.1 x8 - 2x7 + 18x6 - 9x5 + 115x4 + 31x3 + 408x2 + 238x + 671 \( 5^{7}\cdot 11^{2}\cdot 19^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.3412578125.2 x8 - x7 - 18x6 + 7x5 + 130x4 - 52x3 - 378x2 + 431x + 991 \( 5^{7}\cdot 11^{2}\cdot 19^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.3478203125.1 x8 - 3x7 + 23x6 - 36x5 + 185x4 - 141x3 + 633x2 - 188x + 781 \( 5^{7}\cdot 211^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.4921953125.1 x8 - 2x7 - 17x6 + 26x5 + 140x4 - 119x3 - 597x2 + 158x + 1441 \( 5^{7}\cdot 251^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.4.5082629877.1 x8 - 4x7 + 7x6 - 7x5 - 7x4 + 21x3 - 2x2 - 9x + 3 \( 3^{4}\cdot 13^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.4.5120000000.3 x8 - 5x4 + 5 \( 2^{16}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.5737578125.1 x8 - 3x7 - 17x6 + 54x5 + 140x4 - 326x3 - 612x2 + 747x + 1271 \( 5^{7}\cdot 271^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.6081328125.1 x8 - 2x7 + 23x6 - 29x5 + 220x4 - 124x3 + 1013x2 - 142x + 1801 \( 3^{4}\cdot 5^{7}\cdot 31^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.7220000000.1 x8 - 20x6 + 220x4 - 1045x2 + 1805 \( 2^{8}\cdot 5^{7}\cdot 19^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[4]$
8.0.7220000000.2 x8 + 85x4 + 1805 \( 2^{8}\cdot 5^{7}\cdot 19^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.7556328125.1 x8 - 2x7 + 23x6 - 29x5 + 230x4 - 124x3 + 1133x2 - 162x + 2201 \( 5^{7}\cdot 311^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.7950078125.1 x8 - x7 + 27x6 - 23x5 + 275x4 - 172x3 + 1207x2 - 404x + 1891 \( 5^{7}\cdot 11^{2}\cdot 29^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.7950078125.2 x8 - 3x7 + 33x6 - 71x5 + 370x4 - 546x3 + 1653x2 - 1313x + 2131 \( 5^{7}\cdot 11^{2}\cdot 29^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.8559453125.1 x8 - 3x7 - 22x6 + 59x5 + 215x4 - 386x3 - 1042x2 + 842x + 1991 \( 5^{7}\cdot 331^{2} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.9084453125.1 x8 - 2x7 + 28x6 - 39x5 + 305x4 - 239x3 + 1338x2 - 132x + 1721 \( 5^{7}\cdot 11^{2}\cdot 31^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.9084453125.2 x8 - 3x7 + 23x6 - 31x5 + 200x4 - 176x3 + 1073x2 - 373x + 2141 \( 5^{7}\cdot 11^{2}\cdot 31^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.9084453125.3 x8 - x7 - 23x6 + 27x5 + 225x4 - 212x3 - 1048x2 + 701x + 2321 \( 5^{7}\cdot 11^{2}\cdot 31^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.9084453125.4 x8 - x7 - 8x6 + 27x5 - 80x4 - 12x3 + 622x2 - 789x + 2441 \( 5^{7}\cdot 11^{2}\cdot 31^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.14512578125.1 x8 - 3x7 + 33x6 - 56x5 + 350x4 - 306x3 + 1678x2 - 633x + 3641 \( 5^{7}\cdot 431^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[3]$
8.4.14580000000.3 x8 - 60x4 - 45x2 + 45 \( 2^{8}\cdot 3^{6}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.4.14580000000.4 x8 - 15x4 + 45 \( 2^{8}\cdot 3^{6}\cdot 5^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.15890703125.1 x8 - 2x7 - 32x6 + 41x5 + 380x4 - 249x3 - 1892x2 + 483x + 3371 \( 5^{7}\cdot 11^{2}\cdot 41^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.15890703125.2 x8 - 3x7 - 27x6 + 64x5 + 310x4 - 486x3 - 1722x2 + 1237x + 3931 \( 5^{7}\cdot 11^{2}\cdot 41^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.15890703125.3 x8 - x7 - 33x6 + 37x5 + 395x4 - 382x3 - 2018x2 + 1081x + 4051 \( 5^{7}\cdot 11^{2}\cdot 41^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.15890703125.4 x8 - 3x7 - 27x6 + 59x5 + 315x4 - 421x3 - 1772x2 + 1142x + 4061 \( 5^{7}\cdot 11^{2}\cdot 41^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.15890703125.5 x8 - 2x7 - 27x6 + 56x5 + 310x4 - 499x3 - 1787x2 + 1438x + 4201 \( 5^{7}\cdot 11^{2}\cdot 41^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.15890703125.6 x8 - 2x7 - 27x6 + 41x5 + 315x4 - 344x3 - 1747x2 + 1073x + 4331 \( 5^{7}\cdot 11^{2}\cdot 41^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2, 2]$
8.0.16063620352.1 x8 + 13x4 + 13 \( 2^{8}\cdot 13^{7} \) $(C_8:C_2):C_2$ (as 8T16) Trivial
8.0.16820000000.1 x8 - 30x6 + 330x4 - 1595x2 + 4205 \( 2^{8}\cdot 5^{7}\cdot 29^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$
8.0.16820000000.2 x8 + 130x4 + 4205 \( 2^{8}\cdot 5^{7}\cdot 29^{2} \) $(C_8:C_2):C_2$ (as 8T16) $[2]$

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