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Label Polynomial Discriminant Galois group Class group
8.0.4102893.1 x8 - 3x7 + 3x6 - 3x5 + 5x4 - 6x3 + 6x2 - 3x + 1 \( 3^{4}\cdot 37^{3} \) $D_8$ Trivial
8.2.4286875.1 x8 - x7 + x5 - 2x4 - x3 + 2x2 + 2x - 1 \( -\,5^{4}\cdot 19^{3} \) $D_8$ Trivial
8.0.16290125.1 x8 - x7 - x6 + 4x5 + x4 - 4x3 - x2 + x + 1 \( 5^{3}\cdot 19^{4} \) $D_8$ Trivial
8.0.17643776.1 x8 + 3x6 - 2x3 - x2 + 2x + 1 \( 2^{8}\cdot 41^{3} \) $D_8$ Trivial
8.0.18385461.1 x8 + 5x4 - 9x3 + 6x2 - 3x + 1 \( 3^{4}\cdot 61^{3} \) $D_8$ Trivial
8.0.20123648.2 x8 - 2x7 - 2x6 + 2x5 + 6x4 - 6x3 + 6x2 - 2x + 1 \( 2^{12}\cdot 17^{3} \) $D_8$ Trivial
8.2.50602347.1 x8 - x7 + x6 - 6x5 + 9x4 - 6x3 + x2 - x + 1 \( -\,3^{3}\cdot 37^{4} \) $D_8$ Trivial
8.2.85525504.1 x8 - x4 - 4 \( -\,2^{10}\cdot 17^{4} \) $D_8$ Trivial
8.2.122023936.2 x8 - 2x7 - 3x6 + 6x5 + 6x4 - 6x3 - 5x2 - 2x + 1 \( -\,2^{12}\cdot 31^{3} \) $D_8$ Trivial
8.2.128361875.1 x8 - 3x7 + 7x6 - 10x5 + 7x4 + x3 - 9x2 + 8x - 1 \( -\,5^{4}\cdot 59^{3} \) $D_8$ Trivial
8.0.134217728.1 x8 - 4x6 + 10x4 - 8x2 + 2 \( 2^{27} \) $D_8$ Trivial (GRH)
8.2.180848704.1 x8 - 3x7 + x6 + 4x5 - 4x4 + 4x3 + x2 - 3x + 1 \( -\,2^{6}\cdot 41^{4} \) $D_8$ Trivial
8.0.190563597.3 x8 - x7 + 2x6 - 6x5 + 17x4 + 3x3 - 7x2 - x + 1 \( 3^{4}\cdot 7^{3}\cdot 19^{3} \) $D_8$ Trivial
8.0.190563597.4 x8 - 3x7 + 7x6 - 6x5 + x4 + 6x3 - 3x2 - 9x + 9 \( 3^{4}\cdot 7^{3}\cdot 19^{3} \) $D_8$ Trivial
8.2.268435456.1 x8 - 6x4 - 8x2 - 1 \( -\,2^{28} \) $D_8$ Trivial
8.2.308149375.1 x8 - x7 + 4x6 - 7x5 + 8x4 - 11x3 + 11x2 - 2x - 4 \( -\,5^{4}\cdot 79^{3} \) $D_8$ Trivial
8.0.313461333.1 x8 - 3x7 + 4x6 + x4 + 3x3 - 3x2 + 9x + 9 \( 3^{4}\cdot 157^{3} \) $D_8$ Trivial
8.0.321978368.4 x8 - 4x6 + 11x4 - 20x2 + 17 \( 2^{16}\cdot 17^{3} \) $D_8$ Trivial
8.2.347236875.1 x8 - 3x7 + 9x6 - 19x5 + 19x4 - 3x3 - 14x2 + 10x - 5 \( -\,3^{4}\cdot 5^{4}\cdot 19^{3} \) $D_8$ Trivial
8.2.347501687.1 x8 - x7 - 5x6 + 6x5 + 2x4 - 10x3 - 7x2 - x - 1 \( -\,13^{4}\cdot 23^{3} \) $D_8$ Trivial
8.0.357453677.2 x8 - 3x7 + 4x6 - 6x5 + 8x4 - 2x3 + 9x2 + 3x + 2 \( 7^{4}\cdot 53^{3} \) $D_8$ Trivial
8.0.369381632.1 x8 - 2x7 + 7x6 - 10x5 + 3x2 + 4x + 1 \( 2^{8}\cdot 113^{3} \) $D_8$ Trivial
8.2.373837707.1 x8 - 2x6 - 7x5 + 10x4 + 7x3 - 12x2 - x + 5 \( -\,3^{3}\cdot 61^{4} \) $D_8$ Trivial
8.0.421654016.1 x8 - 3x7 + 7x6 - 14x5 + 21x4 - 21x3 + 21x2 - 10x + 2 \( 2^{9}\cdot 7^{7} \) $D_8$ Trivial
8.2.425259008.1 x8 - 2x7 - x6 + 2x5 + 6x4 - 14x3 + 9x2 - 6x + 1 \( -\,2^{12}\cdot 47^{3} \) $D_8$ Trivial
8.0.472842752.1 x8 - 3x7 + 3x6 - 2x5 + 2x4 + 2x3 + 3x2 + 3x + 1 \( 2^{9}\cdot 31^{4} \) $D_8$ $[3]$
8.0.582313617.2 x8 - 3x7 + 6x6 - 15x5 + 29x4 - 30x3 + 24x2 - 24x + 16 \( 3^{4}\cdot 193^{3} \) $D_8$ Trivial
8.2.606436875.1 x8 + x6 - 3x5 + 9x4 + 6x3 + 16x2 - 5 \( -\,3^{6}\cdot 5^{4}\cdot 11^{3} \) $D_8$ Trivial
8.2.606436875.2 x8 - x7 - x6 + 8x5 - 2x4 - 11x3 + 11x2 + 13x + 1 \( -\,3^{6}\cdot 5^{4}\cdot 11^{3} \) $D_8$ Trivial
8.0.614810677.1 x8 - x7 + x6 - x4 - x3 + 7x2 + 2x + 8 \( 13^{3}\cdot 23^{4} \) $D_8$ $[3]$
8.0.643938125.1 x8 - 2x7 + 8x6 - 9x5 + 18x4 - 17x3 + 6x2 - 5x + 5 \( 5^{4}\cdot 101^{3} \) $D_8$ Trivial
8.0.658266368.1 x8 - 4x7 + 12x6 - 18x5 + 17x4 - 6x3 + 2x2 + 12x + 4 \( 2^{8}\cdot 137^{3} \) $D_8$ Trivial
8.0.741610573.1 x8 - x7 - x6 - x5 + 9x4 - 15x3 + 20x2 - 8x + 1 \( 11^{4}\cdot 37^{3} \) $D_8$ Trivial
8.0.843308032.1 x8 - 4x7 + 7x6 - 14x4 + 14x3 + 7x2 - 18x + 9 \( 2^{10}\cdot 7^{7} \) $D_8$ Trivial
8.0.1050340608.4 x8 + 8x6 + 18x4 + 17x2 + 37 \( 2^{8}\cdot 3^{4}\cdot 37^{3} \) $D_8$ $[2]$
8.0.1096135733.1 x8 - 2x7 + 7x2 - 2x + 4 \( 7^{7}\cdot 11^{3} \) $D_8$ Trivial
8.2.1097440000.5 x8 + 5x6 + 2x4 - 20x2 - 19 \( -\,2^{8}\cdot 5^{4}\cdot 19^{3} \) $D_8$ Trivial
8.0.1124864000.1 x8 - 2x7 - 6x6 + 14x5 + 11x4 - 46x3 + 44x2 - 12x + 1 \( 2^{12}\cdot 5^{3}\cdot 13^{3} \) $D_8$ $[2]$
8.0.1124864000.2 x8 - 4x7 + 12x6 - 18x5 + 19x4 - 10x3 + 6x2 + 6x + 1 \( 2^{12}\cdot 5^{3}\cdot 13^{3} \) $D_8$ $[2]$
8.0.1258815488.2 x8 - 4x6 + 5x4 - 2x2 + 2 \( 2^{19}\cdot 7^{4} \) $D_8$ Trivial
8.0.1258815488.3 x8 + 4x6 + 5x4 + 2x2 + 2 \( 2^{19}\cdot 7^{4} \) $D_8$ Trivial
8.0.1319500125.1 x8 - x7 + 3x5 + 9x4 + 2x3 + 8x2 - 4x + 7 \( 3^{4}\cdot 5^{3}\cdot 19^{4} \) $D_8$ $[2]$
8.0.1334161125.1 x8 - x7 + 3x6 - 7x5 + 10x4 - 6x3 + 15x2 - 9x + 3 \( 3^{6}\cdot 5^{3}\cdot 11^{4} \) $D_8$ $[2]$
8.0.1334161125.2 x8 - 2x7 + 6x6 + x5 + 4x4 + 3x3 + 6x2 + 3x + 3 \( 3^{6}\cdot 5^{3}\cdot 11^{4} \) $D_8$ $[2]$
8.2.1368408064.1 x8 + x4 - 4 \( -\,2^{14}\cdot 17^{4} \) $D_8$ Trivial
8.0.1429145856.1 x8 - 2x7 + 5x6 - 2x5 + 21x4 - 30x3 + 75x2 - 62x + 58 \( 2^{8}\cdot 3^{4}\cdot 41^{3} \) $D_8$ $[2]$
8.2.1438646272.4 x8 - 4x7 + 4x6 - 8x5 + 14x4 - 8x3 + 4x2 - 8x - 2 \( -\,2^{22}\cdot 7^{3} \) $D_8$ Trivial
8.2.1438646272.5 x8 - 4x7 + 8x6 - 22x4 + 48x3 - 44x2 + 16x - 2 \( -\,2^{22}\cdot 7^{3} \) $D_8$ Trivial
8.0.1514670125.1 x8 - 4x7 + 5x6 - x5 + 11x4 - 25x3 + 14x2 - x + 1 \( 5^{3}\cdot 59^{4} \) $D_8$ $[3]$
8.0.1593413632.1 x8 - 8x5 - x4 + 4x3 + 8x2 + 8x + 4 \( 2^{12}\cdot 73^{3} \) $D_8$ Trivial

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