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Label Polynomial Discriminant Galois group Class group
12.0.41223887921.1 x12 - 2x11 + 2x10 - x9 + 2x8 - 5x7 + 8x6 - 7x5 + 4x4 - 3x3 + 4x2 - 3x + 1 \( 37^{2}\cdot 41\cdot 857^{2} \) 12T293 Trivial
12.0.41479432225.1 x12 - 4x11 + 8x10 - 11x9 + 12x8 - 9x7 + 3x6 + 2x5 - 3x4 + 2x3 - x + 1 \( 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 23^{4} \) 12T139 Trivial
12.0.42058512657.1 x12 + 2x10 - x9 + x8 - 5x7 + 6x6 - 10x5 + 13x4 - 10x3 + 7x2 - 4x + 1 \( 3^{6}\cdot 7^{2}\cdot 73\cdot 127^{2} \) 12T260 Trivial
12.0.42194001221.1 x12 - 3x11 + 7x10 - 12x9 + 17x8 - 21x7 + 24x6 - 24x5 + 22x4 - 17x3 + 10x2 - 4x + 1 \( 41\cdot 1029121981 \) $S_{12}$ Trivial
12.0.42553255797.1 x12 - x9 + 5x8 - 2x7 - x6 - 7x5 + 8x4 - 4x3 + 5x2 - 4x + 1 \( 3^{6}\cdot 13^{3}\cdot 163^{2} \) 12T167 Trivial
12.0.42925852301.1 x12 - x11 - 2x10 + 3x9 + x8 - x7 - x6 - 2x5 + 3x4 + 2x3 - 2x2 - x + 1 \( 79\cdot 543365219 \) $S_{12}$ Trivial
12.0.44223092609.1 x12 - x11 + x9 - 2x8 + x7 + 3x4 - x3 - 2x2 + 1 \( 89\cdot 22291^{2} \) 12T293 Trivial
12.0.44533203125.1 x12 - 2x11 + 7x10 - 7x9 + 14x8 - 6x7 + 13x6 - 2x5 + 10x4 - 2x3 + 5x2 - x + 1 \( 5^{9}\cdot 151^{2} \) 12T131 Trivial
12.0.45425463296.1 x12 - 2x11 + 2x9 - 2x8 + 3x6 - 2x4 - 2x3 + 2x + 1 \( 2^{12}\cdot 89\cdot 353^{2} \) 12T260 Trivial
12.0.45539379833.1 x12 - x11 - x9 + 3x8 - 2x7 + x6 - 2x5 + 3x4 - x3 - x + 1 \( 17\cdot 73^{2}\cdot 709^{2} \) 12T293 Trivial
12.0.46060985097.1 x12 - 5x11 + 12x10 - 19x9 + 24x8 - 27x7 + 28x6 - 24x5 + 15x4 - 5x3 + x2 - x + 1 \( 3^{6}\cdot 337\cdot 433^{2} \) 12T260 Trivial
12.0.46110822453.1 x12 - 2x11 + x10 + x9 + x8 - 5x7 + 6x6 - 4x5 + 4x4 - 5x3 + 5x2 - 3x + 1 \( 3^{6}\cdot 63252157 \) $S_6\wr C_2$ Trivial
12.0.46574387721.1 x12 - x11 - x10 + x9 + 2x8 - 3x6 + 2x4 + x3 - x2 - x + 1 \( 3^{6}\cdot 7993^{2} \) $S_6\times C_2$ Trivial
12.0.46580196393.1 x12 - 3x10 - x9 + 5x8 + x7 - 7x6 - x5 + 8x4 + 2x3 - 4x2 - x + 1 \( 3^{6}\cdot 157\cdot 406981 \) $S_6\wr C_2$ Trivial
12.0.46716936381.1 x12 - 4x11 + 9x10 - 15x9 + 23x8 - 33x7 + 44x6 - 50x5 + 45x4 - 29x3 + 13x2 - 4x + 1 \( 3^{6}\cdot 23^{4}\cdot 229 \) 12T193 Trivial
12.0.46779109213.1 x12 - 4x11 + 8x10 - 10x9 + 8x8 - 3x7 - 2x6 + 4x5 - 2x4 - x3 + 2x2 - x + 1 \( 31^{4}\cdot 37^{3} \) 12T150 Trivial
12.0.46911328256.1 x12 - 2x9 + 4x8 - 4x7 + x6 + 4x4 - 8x3 + 8x2 - 4x + 1 \( 2^{12}\cdot 13^{4}\cdot 401 \) 12T208 Trivial
12.0.47724987301.1 x12 - 3x11 + 7x10 - 11x9 + 16x8 - 19x7 + 20x6 - 18x5 + 15x4 - 11x3 + 6x2 - 3x + 1 \( 61\cdot 83^{2}\cdot 337^{2} \) 12T293 Trivial
12.0.47738317081.1 x12 - 3x11 + x10 + 7x9 - 8x8 - 4x7 + 13x6 - 4x5 - 8x4 + 7x3 + x2 - 3x + 1 \( 7^{10}\cdot 13^{2} \) 12T25 Trivial
12.0.48737056617.1 x12 - 2x11 + 5x10 - 10x9 + 16x8 - 22x7 + 30x6 - 31x5 + 28x4 - 27x3 + 19x2 - 7x + 1 \( 3^{9}\cdot 19^{5} \) 12T42 Trivial
12.0.50551744653.1 x12 - 4x11 + 11x10 - 21x9 + 32x8 - 40x7 + 45x6 - 46x5 + 40x4 - 26x3 + 12x2 - 4x + 1 \( 3^{6}\cdot 37^{5} \) 12T42 Trivial
12.0.51067940737.1 x12 - 3x11 + 6x10 - 10x9 + 15x8 - 18x7 + 20x6 - 19x5 + 16x4 - 12x3 + 7x2 - 3x + 1 \( 11^{2}\cdot 31^{4}\cdot 457 \) 12T250 Trivial
12.0.51514924901.1 x12 - 2x11 - x10 + 2x9 + 4x8 - x7 - 7x6 + x5 + 4x4 - 2x3 - x2 + 2x + 1 \( 11^{2}\cdot 31^{4}\cdot 461 \) 12T250 Trivial
12.0.53440955929.1 x12 - x11 + x10 - 3x9 + 4x8 - 2x7 + x6 - 2x5 + 4x4 - 3x3 + x2 - x + 1 \( 19^{2}\cdot 23^{6} \) $C_2\times S_4$ Trivial
12.0.54507773961.1 x12 - x11 - 2x10 + 5x9 - x8 - 4x7 + 5x6 - 4x5 - x4 + 5x3 - 2x2 - x + 1 \( 3^{6}\cdot 8647^{2} \) $S_6\times C_2$ Trivial
12.0.55358453125.1 x12 - 4x11 + 11x10 - 22x9 + 35x8 - 45x7 + 49x6 - 44x5 + 33x4 - 21x3 + 11x2 - 4x + 1 \( 5^{6}\cdot 61\cdot 241^{2} \) 12T260 Trivial
12.0.56689952000.1 x12 - 5x11 + 13x10 - 25x9 + 39x8 - 50x7 + 53x6 - 48x5 + 37x4 - 23x3 + 12x2 - 4x + 1 \( 2^{8}\cdot 5^{3}\cdot 11^{6} \) $(C_6\times C_2):C_2$ Trivial
12.0.58300115053.1 x12 - x11 + 4x10 - 4x9 + 9x8 - 6x7 + 11x6 - 6x5 + 8x4 - 3x3 + 4x2 - x + 1 \( 23^{4}\cdot 208333 \) 12T294 Trivial
12.0.59081901957.1 x12 - 3x11 + 5x10 - 6x9 + 5x8 - 2x7 - x6 + 4x5 - 4x4 + 2x3 - x + 1 \( 3^{6}\cdot 13^{3}\cdot 37\cdot 997 \) 12T274 Trivial
12.0.59182215273.1 x12 - 5x11 + 14x10 - 31x9 + 53x8 - 72x7 + 81x6 - 72x5 + 53x4 - 31x3 + 14x2 - 5x + 1 \( 3^{6}\cdot 433^{3} \) 12T35 Trivial
12.0.59767578125.1 x12 - 5x11 + 13x10 - 21x9 + 24x8 - 21x7 + 18x6 - 17x5 + 15x4 - 9x3 + 4x2 - 2x + 1 \( 5^{9}\cdot 71\cdot 431 \) 12T264 Trivial
12.0.60454515625.1 x12 - x11 - 2x10 + 2x9 + 4x8 - 3x7 - 5x6 + 3x5 + 5x4 - x3 - 3x2 + 1 \( 5^{6}\cdot 7^{2}\cdot 281^{2} \) 12T236 Trivial
12.0.63518590021.1 x12 - 2x11 + 3x10 - 2x9 + 2x8 - 4x7 + 4x6 - 2x5 - x4 + 2x2 - x + 1 \( 23^{4}\cdot 61^{3} \) 12T150 Trivial
12.0.63568613376.1 x12 - 4x11 + 9x10 - 14x9 + 16x8 - 14x7 + 10x6 - 6x5 + 6x4 - 6x3 + 6x2 - 4x + 1 \( 2^{12}\cdot 3^{6}\cdot 61\cdot 349 \) 12T261 Trivial
12.0.63853279857.1 x12 - 4x11 + 9x10 - 13x9 + 17x8 - 21x7 + 25x6 - 27x5 + 26x4 - 20x3 + 12x2 - 5x + 1 \( 3^{6}\cdot 23^{4}\cdot 313 \) 12T193 Trivial
12.0.63995902381.1 x12 - x11 + 2x9 - x8 - 4x7 + 5x6 - x5 - x4 - x3 + 4x2 - 3x + 1 \( 73^{2}\cdot 229^{3} \) 12T231 Trivial
12.0.66468114161.1 x12 - x11 - 2x10 + 4x9 + x8 - 5x7 + x6 + 5x5 + x4 - 4x3 - 2x2 + x + 1 \( 23^{6}\cdot 449 \) 12T135 Trivial
12.0.66699927001.1 x12 - x9 + x7 - x4 - x3 + x + 1 \( 47\cdot 1117\cdot 1270499 \) $S_{12}$ Trivial
12.0.67030763409.1 x12 - x11 - 2x10 + 6x8 - x7 - 5x6 - x5 + 6x4 - 2x2 - x + 1 \( 3^{6}\cdot 43^{2}\cdot 223^{2} \) $S_6\times C_2$ Trivial
12.0.69637938597.1 x12 - 2x11 + 3x10 - 2x9 + 4x6 - 11x5 + 17x4 - 16x3 + 11x2 - 5x + 1 \( 3^{6}\cdot 19^{4}\cdot 733 \) 12T208 Trivial
12.0.70127513856.1 x12 + x10 - 3x8 - 3x6 + 2x4 + 2x2 + 1 \( 2^{8}\cdot 3^{6}\cdot 613^{2} \) 12T236 Trivial
12.0.70516271401.1 x12 - 3x11 + 4x10 - x9 - 3x8 + 4x7 - 3x6 + 4x5 - 3x4 - x3 + 4x2 - 3x + 1 \( 37^{2}\cdot 7177^{2} \) 12T285 Trivial
12.0.71939651121.1 x12 - x11 - 3x10 + x9 + 5x8 + 3x7 - 3x6 - 7x5 - 2x4 + 3x3 + 2x2 + x + 1 \( 3^{6}\cdot 13^{3}\cdot 44917 \) 12T274 Trivial
12.0.72509192309.1 x12 - x10 - x9 + x7 + x6 + x5 - 2x3 - x2 + x + 1 \( 72509192309 \) $S_{12}$ Trivial
12.0.73358639104.1 x12 - 2x11 + 2x10 - 2x9 + 6x8 - 10x7 + 10x6 - 12x5 + 17x4 - 14x3 + 8x2 - 4x + 1 \( 2^{18}\cdot 23^{4} \) 12T23 Trivial
12.0.73645476129.1 x12 - x11 - x10 + 2x9 - 2x7 + 3x5 - 2x4 + 2x2 - 2x + 1 \( 3^{6}\cdot 19^{2}\cdot 23^{4} \) 12T48 Trivial
12.0.74733890625.1 x12 - 6x11 + 21x10 - 50x9 + 93x8 - 138x7 + 164x6 - 153x5 + 111x4 - 61x3 + 24x2 - 6x + 1 \( 3^{14}\cdot 5^{6} \) $D_6$ Trivial
12.0.74880094208.1 x12 - 2x11 + 2x10 - 2x9 + 5x8 - 10x7 + 14x6 - 16x5 + 17x4 - 14x3 + 9x2 - 4x + 1 \( 2^{12}\cdot 17^{3}\cdot 61^{2} \) 12T167 Trivial
12.0.74948100349.1 x12 - x11 - x10 + 2x9 + 2x8 - 5x7 + 3x6 + 2x4 - 6x3 + 7x2 - 4x + 1 \( 79^{2}\cdot 229^{3} \) 12T231 Trivial
12.0.75794375168.1 x12 - 4x11 + 9x10 - 12x9 + 14x8 - 19x7 + 30x6 - 39x5 + 37x4 - 26x3 + 14x2 - 5x + 1 \( 2^{9}\cdot 23^{6} \) $(C_6\times C_2):C_2$ Trivial

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