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Label Polynomial Discriminant Galois group Class group
6.2.525625.1 x6 - x5 + x4 - x3 - 4x2 + 5 \( 5^{4}\cdot 29^{2} \) $C_3^2:C_4$ Trivial
6.2.600625.1 x6 - x5 + 4x4 - 2x3 + 6x2 - 5x + 1 \( 5^{4}\cdot 31^{2} \) $C_3^2:C_4$ Trivial
6.2.802816.1 x6 - 2x5 - x4 + 6x2 - 4x + 2 \( 2^{14}\cdot 7^{2} \) $C_3^2:C_4$ Trivial
6.2.2175625.1 x6 - x5 + x4 - 7x3 - 6x2 - 6x - 1 \( 5^{4}\cdot 59^{2} \) $C_3^2:C_4$ Trivial
6.2.2313441.1 x6 - x5 - 3x4 + x3 + 6x2 - 3 \( 3^{4}\cdot 13^{4} \) $C_3^2:C_4$ Trivial
6.2.2325625.1 x6 - x5 + 6x4 - 2x3 + 4x2 + 9x - 1 \( 5^{4}\cdot 61^{2} \) $C_3^2:C_4$ Trivial
6.2.4100625.1 x6 - 6x4 - x3 + 9x2 + 3x - 11 \( 3^{8}\cdot 5^{4} \) $C_3^2:C_4$ Trivial
6.2.4100625.2 x6 + 6x4 - 3x3 + 9x2 - 9x + 1 \( 3^{8}\cdot 5^{4} \) $C_3^2:C_4$ Trivial
6.2.4840000.2 x6 - x5 + x4 - 12x3 - 21x2 - 11x - 1 \( 2^{6}\cdot 5^{4}\cdot 11^{2} \) $C_3^2:C_4$ Trivial
6.2.4950625.1 x6 - x5 + 4x4 - 10x3 + 15x - 5 \( 5^{4}\cdot 89^{2} \) $C_3^2:C_4$ Trivial
6.2.7290000.1 x6 - 6x4 - 4x3 + 9x2 + 12x - 16 \( 2^{4}\cdot 3^{6}\cdot 5^{4} \) $C_3^2:C_4$ Trivial
6.2.7290000.2 x6 + 6x4 - 2x3 + 9x2 - 6x - 4 \( 2^{4}\cdot 3^{6}\cdot 5^{4} \) $C_3^2:C_4$ Trivial
6.2.8254129.1 x6 - 2x5 + 4x4 - 9x3 + 5x2 + 4x - 4 \( 13^{4}\cdot 17^{2} \) $C_3^2:C_4$ Trivial
6.2.11560000.1 x6 - x5 - 4x4 - 7x3 - 16x2 - 21x - 11 \( 2^{6}\cdot 5^{4}\cdot 17^{2} \) $C_3^2:C_4$ $[3]$
6.2.11560000.3 x6 - 2x5 + 4x4 + 4x3 - 6x2 + 18x + 1 \( 2^{6}\cdot 5^{4}\cdot 17^{2} \) $C_3^2:C_4$ $[3]$
6.2.11943936.1 x6 + 6x4 - 4x3 + 9x2 - 12x - 4 \( 2^{14}\cdot 3^{6} \) $C_3^2:C_4$ Trivial
6.2.11943936.2 x6 + 6x4 - 4x3 - 9x2 + 12x - 4 \( 2^{14}\cdot 3^{6} \) $C_3^2:C_4$ Trivial
6.2.12425625.1 x6 - 3x5 + 6x4 - 15x2 + 30x - 20 \( 3^{2}\cdot 5^{4}\cdot 47^{2} \) $C_3^2:C_4$ $[3]$
6.2.12425625.2 x6 - 3x5 + 9x4 - 9x3 + 9x2 + 12x + 1 \( 3^{2}\cdot 5^{4}\cdot 47^{2} \) $C_3^2:C_4$ $[3]$
6.2.12780625.1 x6 - 2x5 - 6x4 + 19x3 - x2 - 37x + 31 \( 5^{4}\cdot 11^{2}\cdot 13^{2} \) $C_3^2:C_4$ Trivial
6.2.13875625.1 x6 - x5 - x4 + 5x3 - 10x2 - 30x - 5 \( 5^{4}\cdot 149^{2} \) $C_3^2:C_4$ Trivial
6.2.14250625.1 x6 - x5 + 9x4 - 7x3 + 16x2 - 20x + 1 \( 5^{4}\cdot 151^{2} \) $C_3^2:C_4$ $[3]$
6.2.14440000.2 x6 - x5 - x4 - 12x3 - 24x2 - 20x - 4 \( 2^{6}\cdot 5^{4}\cdot 19^{2} \) $C_3^2:C_4$ Trivial
6.2.15108769.1 x6 - 3x5 + x4 - x3 + 11x2 - 24x + 27 \( 13^{4}\cdot 23^{2} \) $C_3^2:C_4$ Trivial
6.2.16370116.1 x6 - 2x5 + 7x4 + 2x3 + x2 + 24x - 1 \( 2^{2}\cdot 7^{2}\cdot 17^{4} \) $C_3^2:C_4$ Trivial
6.2.17682025.1 x6 - 2x5 + 5x4 - 3x3 + 3x2 + 2x - 7 \( 5^{2}\cdot 29^{4} \) $C_3^2:C_4$ Trivial
6.2.18490000.1 x6 - 2x5 + 4x4 - 6x3 + 4x2 - 12x - 9 \( 2^{4}\cdot 5^{4}\cdot 43^{2} \) $C_3^2:C_4$ $[3]$
6.2.18490000.2 x6 - 3x5 + 11x4 - 14x3 + 21x2 + 5x - 1 \( 2^{4}\cdot 5^{4}\cdot 43^{2} \) $C_3^2:C_4$ $[3]$
6.2.20025625.1 x6 - 3x5 + 4x4 - 2x3 - 19x2 + 30x + 20 \( 5^{4}\cdot 179^{2} \) $C_3^2:C_4$ Trivial
6.2.20475625.1 x6 - x5 - 9x4 - 7x3 + 29x2 + 44x + 19 \( 5^{4}\cdot 181^{2} \) $C_3^2:C_4$ Trivial
6.2.21160000.3 x6 - 2x5 + x4 - 20x3 + 15x2 + 30x + 55 \( 2^{6}\cdot 5^{4}\cdot 23^{2} \) $C_3^2:C_4$ $[3]$
6.2.21160000.4 x6 - x5 + 5x4 + 10x3 - 10x2 + 44x + 76 \( 2^{6}\cdot 5^{4}\cdot 23^{2} \) $C_3^2:C_4$ $[3]$
6.2.21855625.2 x6 - x5 + 5x4 + 15x3 - 10x2 + 54x + 61 \( 5^{4}\cdot 11^{2}\cdot 17^{2} \) $C_3^2:C_4$ Trivial
6.2.22325625.3 x6 + 6x4 - 7x3 + 9x2 - 21x + 11 \( 3^{6}\cdot 5^{4}\cdot 7^{2} \) $C_3^2:C_4$ Trivial
6.2.22325625.4 x6 - 9x4 - 13x3 + 9x2 + 36x + 31 \( 3^{6}\cdot 5^{4}\cdot 7^{2} \) $C_3^2:C_4$ Trivial
6.2.24920064.1 x6 - 2x5 + 11x4 - 12x3 + 25x2 - 14x - 1 \( 2^{14}\cdot 3^{2}\cdot 13^{2} \) $C_3^2:C_4$ $[3]$
6.2.24920064.2 x6 - 2x5 + 9x4 - 4x3 + 21x2 + 10x + 1 \( 2^{14}\cdot 3^{2}\cdot 13^{2} \) $C_3^2:C_4$ $[3]$
6.2.27541504.1 x6 + 6x4 - 8x3 - 2x2 - 32x + 4 \( 2^{14}\cdot 41^{2} \) $C_3^2:C_4$ Trivial
6.2.27825625.1 x6 - x5 + 11x4 - 11x3 + 26x2 - 10x - 5 \( 5^{4}\cdot 211^{2} \) $C_3^2:C_4$ Trivial
6.2.29160000.2 x6 - 6x4 - 4x3 + 9x2 + 12x - 76 \( 2^{6}\cdot 3^{6}\cdot 5^{4} \) $C_3^2:C_4$ Trivial
6.2.29160000.5 x6 + 6x4 - 8x3 + 9x2 - 24x - 4 \( 2^{6}\cdot 3^{6}\cdot 5^{4} \) $C_3^2:C_4$ Trivial
6.2.32490000.1 x6 - 2x5 + 10x3 - 20x2 - 72x - 81 \( 2^{4}\cdot 3^{2}\cdot 5^{4}\cdot 19^{2} \) $C_3^2:C_4$ Trivial
6.2.33350625.1 x6 - 3x5 - 4x4 + 10x3 - 5x2 + 10x - 20 \( 3^{2}\cdot 5^{4}\cdot 7^{2}\cdot 11^{2} \) $C_3^2:C_4$ Trivial
6.2.34656769.1 x6 + x4 - x3 - 7x2 + 14x - 7 \( 7^{2}\cdot 29^{4} \) $C_3^2:C_4$ Trivial
6.2.35700625.1 x6 - 2x5 + 6x4 - 5x3 - 25x2 + 50x - 20 \( 5^{4}\cdot 239^{2} \) $C_3^2:C_4$ Trivial
6.2.36192256.1 x6 - 2x5 - 5x4 - 16x3 + 8x + 28 \( 2^{14}\cdot 47^{2} \) $C_3^2:C_4$ Trivial
6.2.36300625.1 x6 - x5 + 11x4 - 21x3 + 36x2 - 110x + 95 \( 5^{4}\cdot 241^{2} \) $C_3^2:C_4$ Trivial
6.2.37015056.2 x6 + 6x4 - 6x3 + 9x2 - 18x - 4 \( 2^{4}\cdot 3^{4}\cdot 13^{4} \) $C_3^2:C_4$ Trivial
6.2.38130625.1 x6 - x5 - 4x4 - 2x3 - 16x2 - x + 59 \( 5^{4}\cdot 13^{2}\cdot 19^{2} \) $C_3^2:C_4$ Trivial
6.2.38440000.1 x6 - 2x5 - 6x4 + 12x3 - 4x2 - 70x - 55 \( 2^{6}\cdot 5^{4}\cdot 31^{2} \) $C_3^2:C_4$ Trivial

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