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Label Polynomial Discriminant Galois group Class group
8.0.17850625.1 x8 - x7 + 3x6 - x5 + 3x4 + x3 + 3x2 + x + 1 \( 5^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.39337984.2 x8 - 2x7 + 4x6 - 4x5 + 4x4 - 8x3 + 12x2 - 8x + 2 \( 2^{14}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.68574961.1 x8 - x7 + x6 - x5 - x4 + x3 + x2 + x + 1 \( 7^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.107495424.1 x8 - 2x7 + 2x6 + 2x5 - 4x4 - 2x3 + 2x2 + 2x + 1 \( 2^{14}\cdot 3^{8} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.236421376.1 x8 - 2x7 + x6 - 2x5 + 16x4 + 2x3 + x2 + 2x + 1 \( 2^{8}\cdot 31^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.241864704.1 x8 - 4x7 + 4x6 + 2x5 + x4 - 10x3 + 4x2 + 2x + 7 \( 2^{12}\cdot 3^{10} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.312900721.1 x8 - x7 + 4x6 + 6x4 + 4x2 + x + 1 \( 7^{4}\cdot 19^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.467943424.1 x8 - 2x7 - 2x6 + 10x5 + 4x4 - 10x3 - 2x2 + 2x + 1 \( 2^{14}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.481890304.5 x8 - 2x7 + 2x6 - 8x5 + 18x4 - 16x3 + 8x2 + 8 \( 2^{12}\cdot 7^{6} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.547981281.1 x8 - x7 + 2x6 - 2x5 + 2x4 + 2x3 + 2x2 + x + 1 \( 3^{8}\cdot 17^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.629407744.3 x8 + 2x6 + 10x4 - 4x3 + 10x2 - 4x + 3 \( 2^{18}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.629407744.4 x8 + 2x6 - 4x5 - 2x4 - 4x3 + 6x2 + 8x + 7 \( 2^{18}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.796594176.15 x8 - 2x7 + 2x6 - 4x5 + 2x4 + 8x3 - 4x2 + 4 \( 2^{12}\cdot 3^{4}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.855036081.1 x8 - x7 + 5x6 + x5 + 11x4 - x3 + 5x2 + x + 1 \( 3^{8}\cdot 19^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.875213056.3 x8 - 2x7 + 2x6 + 4x5 - 9x4 + 4x3 + 18x2 - 30x + 25 \( 2^{8}\cdot 43^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.967458816.1 x8 - 2x7 - 2x6 + 2x5 + 8x4 + 2x3 - 2x2 - 2x + 1 \( 2^{14}\cdot 3^{10} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.1121513121.1 x8 - 3x7 + 4x6 - 4x5 + 8x4 + 16x3 + 18x2 + 28x + 13 \( 3^{4}\cdot 61^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.1445900625.6 x8 - x7 + x6 + 6x5 - 7x4 + 8x3 + 9x2 - 12x + 16 \( 3^{4}\cdot 5^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.1445900625.7 x8 - x7 + 6x6 - 8x5 + 13x4 - 15x3 + 17x2 - 11x + 4 \( 3^{4}\cdot 5^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.1632240801.1 x8 - 3x7 + 5x6 - 6x5 + x4 - 6x3 + 15x2 - 18x + 36 \( 3^{4}\cdot 67^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.1698181681.2 x8 - x7 + x6 - 3x5 + 3x4 + 3x3 + x2 + x + 1 \( 7^{4}\cdot 29^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.1719926784.3 x8 + 6x4 - 8x2 + 9 \( 2^{18}\cdot 3^{8} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.1719926784.4 x8 + 6x4 + 8x2 + 9 \( 2^{18}\cdot 3^{8} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.1908029761.1 x8 - x7 - 5x6 + 3x5 + 13x4 + 3x3 - 5x2 - x + 1 \( 11^{4}\cdot 19^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.1927561216.9 x8 - 2x7 + 4x6 - 4x5 + 4x4 - 4x3 + 4x2 + 4x + 2 \( 2^{14}\cdot 7^{6} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.2135179264.1 x8 - 4x5 - 8x4 - 8x3 + 8x2 + 24x + 36 \( 2^{14}\cdot 19^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.2300257521.2 x8 + 2x6 + 13x4 + 15x2 + 36 \( 3^{4}\cdot 73^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.3016755625.2 x8 - x7 - 3x6 + 9x5 - 4x4 - 10x3 + 17x2 - 14x + 9 \( 5^{4}\cdot 13^{6} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.3016755625.3 x8 - x7 - 2x6 - 6x5 + 18x4 + 6x3 - 2x2 + x + 1 \( 5^{4}\cdot 13^{6} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.3186376704.9 x8 - 2x7 + 8x4 + 20x3 + 16x2 + 12x + 6 \( 2^{14}\cdot 3^{4}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.3360173089.1 x8 - 2x7 + 2x6 - 8x5 + 32x4 - 51x3 + 36x2 - 7x + 1 \( 7^{6}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.3360173089.2 x8 - x7 + 8x6 + 3x5 + 9x4 + 13x3 + 18x2 + 9x + 4 \( 7^{6}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.3782742016.1 x8 - 2x7 + x6 - 2x5 + 5x4 - 4x3 + 4x2 - 16x + 16 \( 2^{12}\cdot 31^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.3782742016.5 x8 - 2x7 + 11x6 - 14x5 + 39x4 - 28x3 + 54x2 - 16x + 28 \( 2^{12}\cdot 31^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.4032758016.4 x8 - 2x7 + 2x6 - 4x5 - x4 + 4x3 + 2x2 - 10x + 25 \( 2^{8}\cdot 3^{8}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.4569760000.9 x8 + x6 + 2x4 + 9x2 + 16 \( 2^{8}\cdot 5^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.4569760000.11 x8 - 2x6 + 3x4 + 3x2 + 1 \( 2^{8}\cdot 5^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.4931831529.1 x8 - x7 + x6 + 5x5 + 13x4 + 5x3 + x2 - x + 1 \( 3^{10}\cdot 17^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.4931831529.2 x8 - x7 - 5x6 + 4x5 + 23x4 - 14x3 - 23x2 - 40x + 64 \( 3^{10}\cdot 17^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.5554571841.4 x8 - x7 - 4x6 + 3x5 + 18x4 - 14x3 + x2 - 12x + 9 \( 3^{4}\cdot 7^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2, 2]$
8.0.5554571841.5 x8 - x7 + 8x6 - 6x5 + 21x4 - 11x3 + 25x2 - 9x + 12 \( 3^{4}\cdot 7^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[4]$
8.0.5554571841.6 x8 - 13x6 + 46x4 - 21x2 + 36 \( 3^{4}\cdot 7^{4}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.6146560000.15 x8 - 2x7 + 2x6 + 4x5 + 18x4 + 16x3 + 12x2 + 4 \( 2^{12}\cdot 5^{4}\cdot 7^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.6784652161.1 x8 - x7 - 4x5 + 6x4 + 4x3 + x + 1 \( 7^{4}\cdot 41^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.7487094784.2 x8 - 8x6 + 22x4 - 16x2 + 9 \( 2^{18}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.7487094784.3 x8 + 8x6 + 22x4 + 16x2 + 9 \( 2^{18}\cdot 13^{4} \) $A_4\times C_2$ (as 8T13) Trivial
8.0.7695324729.2 x8 - 9x6 + 18x4 + 3x2 + 36 \( 3^{10}\cdot 19^{4} \) $A_4\times C_2$ (as 8T13) $[4]$
8.0.7695324729.3 x8 - x7 - 8x6 - 4x5 + 40x4 - 4x3 - 8x2 - x + 1 \( 3^{10}\cdot 19^{4} \) $A_4\times C_2$ (as 8T13) $[4]$
8.0.8208541201.1 x8 - x7 + 7x6 + 3x5 + 27x4 - 3x3 + 7x2 + x + 1 \( 7^{4}\cdot 43^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
8.0.9116621361.1 x8 - 3x7 + 2x6 + 3x5 - 12x4 - 6x3 + 5x2 + 42x + 49 \( 3^{4}\cdot 103^{4} \) $A_4\times C_2$ (as 8T13) $[2]$
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