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Label Polynomial Discriminant Galois group Class group
12.2.419159399791.1 x12 - 2x11 + 3x9 - 2x8 - x7 + x6 - x5 + x4 + 2x3 - 2x2 + 1 \( -\,11^{4}\cdot 31^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.838790656103.1 x12 - 2x11 + x10 + 2x9 - 4x8 + 4x7 - 2x6 - 3x5 + 6x4 - 7x3 + 5x2 - 3x + 1 \( -\,19^{4}\cdot 23^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.1008394404608.1 x12 - 3x11 + 4x10 - 11x8 + 24x7 - 29x6 + 24x5 - 11x4 + 4x2 - 3x + 1 \( -\,2^{8}\cdot 83^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.1687248699392.2 x12 - 4x11 + 2x10 + 10x9 - 11x8 - 4x7 - 2x6 + 14x5 + 12x4 - 30x3 + 10x2 + 2x - 1 \( -\,2^{18}\cdot 23^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.2928329928704.1 x12 - x11 + x10 - x9 + x8 - 4x7 + 7x6 - x5 - 8x4 + 8x3 - 2x2 - x + 1 \( -\,2^{12}\cdot 59^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.3286040887296.1 x12 - 2x11 + 2x10 + 2x9 - 9x8 + 20x7 - 24x6 + 20x5 - 9x4 + 2x3 + 2x2 - 2x + 1 \( -\,2^{14}\cdot 3^{4}\cdot 19^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.6335421661184.1 x12 - 2x11 + 2x10 - 3x8 + 8x7 - 10x6 + 8x5 - 3x4 + 2x2 - 2x + 1 \( -\,2^{14}\cdot 7^{4}\cdot 11^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.7504960159744.1 x12 - 6x11 + 16x10 - 16x9 - 16x8 + 64x7 - 70x6 + 22x5 + 15x4 - 6x3 - 6x2 + 2x - 1 \( -\,2^{18}\cdot 31^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.10807949656064.1 x12 - 4x11 + 2x10 + 4x9 + 3x8 - 8x6 - 12x5 + 11x4 + 8x3 - 10x2 + 4x - 1 \( -\,2^{26}\cdot 11^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.0.11095033120000.1 x12 - 3x11 + 7x10 - 12x9 + 19x8 - 21x7 + 22x6 - 21x5 + 19x4 - 12x3 + 7x2 - 3x + 1 \( 2^{8}\cdot 5^{4}\cdot 37^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.11713319714816.1 x12 - 2x11 + 8x9 - 28x8 + 54x7 - 62x6 + 54x5 - 28x4 + 8x3 - 2x + 1 \( -\,2^{14}\cdot 59^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.16325867520000.1 x12 - 3x8 - 6x7 - 2x6 - 6x5 - 3x4 + 1 \( -\,2^{14}\cdot 3^{13}\cdot 5^{4} \) $C_2 \times S_4$ (as 12T22) Trivial
12.4.18178102263808.1 x12 - 2x11 - 4x10 + 4x9 + 2x8 + 6x7 + 18x6 + 2x4 + 12x3 - 6x2 - 4x + 2 \( 2^{18}\cdot 37^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.27406859829248.1 x12 - 3x10 - 4x9 + 10x8 + 8x7 + 5x6 - 28x5 - x4 + 8x3 - 8x - 4 \( -\,2^{16}\cdot 53^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.38537381281792.1 x12 - 8x9 + 6x7 + 34x6 + 16x5 + 6x4 - 20x3 - 10x2 - 8x + 2 \( -\,2^{18}\cdot 43^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.42845606719488.1 x12 - 3x11 + 8x9 - 9x8 - 6x7 + 17x6 - 6x5 - 9x4 + 8x3 - 3x + 1 \( -\,2^{12}\cdot 3^{21} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.43231798624256.1 x12 - 6x10 + 11x8 - 4x6 - x4 - 6x2 - 11 \( -\,2^{28}\cdot 11^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.43231798624256.2 x12 + 6x10 + 11x8 + 4x6 - x4 + 6x2 - 11 \( -\,2^{28}\cdot 11^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.55351463182336.1 x12 - 4x11 + 4x10 + 4x9 - 12x8 + 12x7 - 8x5 + 7x4 - 12x3 + 4x2 - 4 \( -\,2^{16}\cdot 61^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.56192894500864.1 x12 - 3x11 + 2x10 + 9x9 - 32x8 + 55x7 - 62x6 + 55x5 - 32x4 + 9x3 + 2x2 - 3x + 1 \( -\,2^{18}\cdot 11^{8} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.86029994295296.1 x12 - 4x10 + 4x8 - 12x7 + 12x6 - 25x4 + 12x3 + 16x2 - 8x - 4 \( -\,2^{22}\cdot 29^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.86029994295296.2 x12 - 6x11 + 17x10 - 28x9 + 23x8 + 4x7 - 34x6 + 32x5 + 2x4 - 16x3 + 6x2 - 2 \( -\,2^{22}\cdot 29^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.86029994295296.3 x12 + 5x10 - 2x9 + x8 + 4x7 - 26x6 + 24x5 - 17x4 + 44x3 - 35x2 + 10x - 1 \( -\,2^{22}\cdot 29^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.102241426653184.2 x12 - 2x11 + 6x9 - 23x8 + 42x7 - 46x6 + 42x5 - 23x4 + 6x3 - 2x + 1 \( -\,2^{14}\cdot 7^{5}\cdot 13^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.106993205379072.1 x12 - 8x9 + 12x7 + 20x6 - 54x4 + 12x3 + 24x2 - 6 \( -\,2^{26}\cdot 3^{13} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.107983916761088.2 x12 + 6x10 + 10x8 - 6x6 - 39x4 - 50x2 - 23 \( -\,2^{24}\cdot 23^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.107983916761088.5 x12 - 6x10 + 10x8 + 6x6 - 39x4 + 50x2 - 23 \( -\,2^{24}\cdot 23^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.0.164499237983257.1 x12 - 3x11 + 8x10 - 16x9 + 21x8 - 17x7 + 9x6 + 11x5 - 19x4 + 5x3 + 20x2 - 20x + 8 \( 17^{5}\cdot 41^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.166168191041536.1 x12 - 12x9 - 6x8 + 20x6 + 16x5 - 16x4 - 16x3 + 16x2 - 4 \( -\,2^{26}\cdot 19^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.171382426877952.2 x12 - 6x11 + 18x10 - 32x9 + 45x8 - 78x7 + 146x6 - 180x5 + 99x4 + 30x3 - 72x2 + 36x - 6 \( -\,2^{14}\cdot 3^{21} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.180551034077184.5 x12 - 6x11 + 9x10 + 4x9 - 9x8 - 12x7 + 10x6 + 6x4 - 6x2 + 2 \( -\,2^{22}\cdot 3^{16} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.199336411529216.1 x12 - 2x10 - 8x9 - 18x8 - 20x7 - 10x6 + 8x5 + 11x4 + 4x3 - 8x2 - 8x - 2 \( -\,2^{29}\cdot 13^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.199336411529216.2 x12 - 2x10 + 12x8 - 24x7 + 4x6 + 20x5 - 4x4 - 12x3 + 6x2 - 4x + 1 \( -\,2^{29}\cdot 13^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.4.201657968164864.1 x12 - 2x11 - 7x10 + 10x9 + 18x8 - 6x7 - 21x6 - 30x5 - 24x4 + 2x3 + 11x2 + 6x + 1 \( 2^{16}\cdot 79^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.209715200000000.2 x12 + 2x10 + 2x8 - 24x6 - 4x4 + 8x2 - 8 \( -\,2^{29}\cdot 5^{8} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.427972821516288.3 x12 - 4x9 - 3x8 + 12x7 - 16x6 + 24x5 - 45x4 + 52x3 - 24x2 + 12x - 3 \( -\,2^{28}\cdot 3^{13} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.427972821516288.4 x12 - 8x9 - 3x8 - 12x7 - 20x6 - 24x5 - 27x4 - 12x3 - 1 \( -\,2^{28}\cdot 3^{13} \) $C_2 \times S_4$ (as 12T22) Trivial
12.4.439022168653824.1 x12 - 6x10 - 6x9 + 9x8 + 12x7 + 20x6 - 21x4 + 8x3 - 6x2 - 6x - 1 \( 2^{14}\cdot 3^{13}\cdot 7^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.457884390703104.2 x12 - 2x11 - 2x10 + 4x9 + 7x8 - 2x7 - 26x6 + 4x5 + 31x4 + 30x3 - 54x2 - 54x + 81 \( -\,2^{14}\cdot 3^{9}\cdot 17^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.480317450223616.2 x12 - 2x10 + 2x8 - 30x6 + 13x4 - 20x2 - 31 \( -\,2^{24}\cdot 31^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.480317450223616.5 x12 + 2x10 + 2x8 + 30x6 + 13x4 + 20x2 - 31 \( -\,2^{24}\cdot 31^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.537824000000000.2 x12 - 2x11 + 2x10 - 6x9 + 15x8 - 28x7 + 32x6 - 28x5 + 15x4 - 6x3 + 2x2 - 2x + 1 \( -\,2^{14}\cdot 5^{9}\cdot 7^{5} \) $C_2 \times S_4$ (as 12T22) $[2]$
12.2.618121839509504.1 x12 - 4x10 - 2x9 + 17x8 + 6x7 - 30x6 - 6x5 + 31x4 - 26x3 - 4x2 + 28x - 13 \( -\,2^{18}\cdot 11^{9} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.664672764166144.1 x12 + 2x10 + 7x8 + 16x6 - 17x4 - 42x2 - 19 \( -\,2^{28}\cdot 19^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.664672764166144.2 x12 - 2x10 + 7x8 - 16x6 - 17x4 + 42x2 - 19 \( -\,2^{28}\cdot 19^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.797345646116864.3 x12 - 2x10 + 16x8 - 24x7 - 8x6 + 16x5 - 18x4 - 8x3 + 12x2 - 4 \( -\,2^{31}\cdot 13^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.855945643032576.1 x12 - 8x9 + 3x8 + 12x7 - 12x6 - 48x5 + 6x4 + 32x3 - 4 \( -\,2^{29}\cdot 3^{13} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.855945643032576.2 x12 - 6x10 - 12x9 - 12x8 + 14x6 + 12x5 - 9x4 - 8x3 + 12x2 - 4 \( -\,2^{29}\cdot 3^{13} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.1276813346484375.1 x12 - 5x11 + 8x10 - x9 - 9x8 - 2x7 + 44x6 - 93x5 + 118x4 - 105x3 + 40x2 + 24x - 19 \( -\,3^{4}\cdot 5^{8}\cdot 7^{9} \) $C_2 \times S_4$ (as 12T22) Trivial
12.2.1329345528332288.1 x12 + 4x10 - 4x9 + 2x8 - 4x7 - 48x6 + 4x5 + 43x4 - 4x3 - 16x2 + 8x - 2 \( -\,2^{29}\cdot 19^{5} \) $C_2 \times S_4$ (as 12T22) Trivial
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