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Label Polynomial Discriminant Galois group Class group
24.0.304383340063522342681884765625.1 x24 - x23 + x19 - x18 + x17 - x16 + x14 - x13 + x12 - x11 + x10 - x8 + x7 - x6 + x5 - x + 1 \( 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) Trivial (GRH)
24.0.572565594852444156646728515625.1 x24 - x21 + x15 - x12 + x9 - x3 + 1 \( 3^{36}\cdot 5^{18} \) $C_2\times C_{12}$ (as 24T2) Trivial (GRH)
24.0.711435861303500483618465120256.1 x24 + x22 - x18 - x16 + x12 - x8 - x6 + x2 + 1 \( 2^{24}\cdot 3^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) Trivial (GRH)
24.0.1706902865139206151939937338729.1 x24 - x23 + x21 - x20 + x18 - x17 + x15 - x14 + x12 - x10 + x9 - x7 + x6 - x4 + x3 - x + 1 \( 3^{12}\cdot 13^{22} \) $C_2\times C_{12}$ (as 24T2) $[2]$ (GRH)
24.0.10352754344108696148301025390625.1 x24 - x23 - x22 + 4x21 - 4x20 - 4x19 + 17x18 + 12x17 - 46x16 + 43x15 + 44x14 - 188x13 + 189x12 + 188x11 + 44x10 - 43x9 - 46x8 - 12x7 + 17x6 + 4x5 - 4x4 - 4x3 - x2 + x + 1 \( 3^{12}\cdot 5^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) Trivial (GRH)
24.0.22459526297810799636782730182656.1 x24 - x20 + x16 - x12 + x8 - x4 + 1 \( 2^{48}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[2]$ (GRH)
24.0.32982361051400240694294150960561.1 x24 - 3x23 + 9x22 - 26x21 + 57x20 - 122x19 + 241x18 - 433x17 + 746x16 - 1222x15 + 1898x14 - 2838x13 + 4105x12 - 5676x11 + 7592x10 - 9776x9 + 11936x8 - 13856x7 + 15424x6 - 15616x5 + 14592x4 - 13312x3 + 9216x2 - 6144x + 4096 \( 3^{12}\cdot 7^{20}\cdot 167^{4} \) $C_2^3\times A_4$ (as 24T135) $[2]$ (GRH)
24.0.42247883974617233597120303333376.1 x24 - x12 + 1 \( 2^{48}\cdot 3^{36} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.53885714612646242347927893704704.1 x24 - x22 + x20 - x18 + x16 - x14 + x12 - x10 + x8 - x6 + x4 - x2 + 1 \( 2^{24}\cdot 13^{22} \) $C_2\times C_{12}$ (as 24T2) $[3]$ (GRH)
24.0.63990935712336613969356040175616.1 x24 + 12x22 + 96x20 + 412x18 + 1260x16 + 2511x14 + 3666x12 + 3492x10 + 2322x8 + 736x6 + 165x4 + 15x2 + 1 \( 2^{24}\cdot 3^{36}\cdot 71^{4} \) $C_2^3\times A_4$ (as 24T135) $[2]$ (GRH)
24.0.67372672480923938907623291015625.1 x24 - x23 - 2x22 + 5x21 - 4x20 + 8x19 + 15x18 - 59x17 + 26x16 + 114x15 + 34x14 - 119x13 - 10x12 - 196x11 - 198x10 + 289x9 + 559x8 - 307x7 + 22x6 + 46x5 - 22x4 + 12x3 - x2 - 2x + 1 \( 3^{12}\cdot 5^{18}\cdot 7^{16} \) $C_2\times C_{12}$ (as 24T2) Trivial (GRH)
24.0.138359014736314946502328332753681.1 x24 - 2x23 + 2x22 + 10x21 - 20x20 + 13x19 + 57x18 - 98x17 + 19x16 + 228x15 - 267x14 - 159x13 + 711x12 - 318x11 - 1068x10 + 1824x9 + 304x8 - 3136x7 + 3648x6 + 1664x5 - 5120x4 + 5120x3 + 2048x2 - 4096x + 4096 \( 3^{12}\cdot 7^{20}\cdot 239^{4} \) $C_2^3\times A_4$ (as 24T135) $[3]$ (GRH)
24.0.326829122755018756096000000000000.1 x24 - 3x22 + 8x20 - 21x18 + 55x16 - 144x14 + 377x12 - 144x10 + 55x8 - 21x6 + 8x4 - 3x2 + 1 \( 2^{24}\cdot 5^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.614787626176508399616000000000000.1 x24 - 18x18 + 323x12 - 18x6 + 1 \( 2^{24}\cdot 3^{36}\cdot 5^{12} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.784140351063197047157560791015625.1 x24 - x23 + 2x22 - 3x21 + 5x20 - 8x19 + 13x18 - 21x17 + 34x16 - 55x15 + 89x14 - 144x13 + 233x12 + 144x11 + 89x10 + 55x9 + 34x8 + 21x7 + 13x6 + 8x5 + 5x4 + 3x3 + 2x2 + x + 1 \( 5^{12}\cdot 13^{22} \) $C_2\times C_{12}$ (as 24T2) $[2, 2]$ (GRH)
24.0.1041229780068396944496497143054336.1 x24 + 9x22 + 42x20 + 139x18 + 376x16 + 896x14 + 1905x12 + 3584x10 + 6016x8 + 8896x6 + 10752x4 + 9216x2 + 4096 \( 2^{24}\cdot 7^{20}\cdot 167^{4} \) $C_2^3\times A_4$ (as 24T135) $[4]$ (GRH)
24.0.1312855308850436212414726439933209.1 x24 - x + 1 \( 6361\cdot 61167766669\cdot 3374184647743911301 \) $S_{24}$ (as 24T25000) Trivial (GRH)
24.2.1354616244850132036483436505754343.1 x24 - x - 1 \( -\,101\cdot 2347\cdot 5714547093403974893094772369 \) $S_{24}$ (as 24T25000) Trivial (GRH)
24.0.2126907556454464000000000000000000.1 x24 - 5x22 + 19x20 - 66x18 + 221x16 - 358x14 + 530x12 - 723x10 + 793x8 - 157x6 + 31x4 - 6x2 + 1 \( 2^{24}\cdot 5^{18}\cdot 7^{16} \) $C_2\times C_{12}$ (as 24T2) $[3]$ (GRH)
24.0.2243572222946525052726785077149696.1 x24 - 4x23 + 8x22 - 12x21 + 24x20 - 56x19 + 104x18 - 152x17 + 224x16 - 376x15 + 608x14 - 848x13 + 1156x12 - 1696x11 + 2432x10 - 3008x9 + 3584x8 - 4864x7 + 6656x6 - 7168x5 + 6144x4 - 6144x3 + 8192x2 - 8192x + 4096 \( 2^{32}\cdot 3^{12}\cdot 23^{4}\cdot 37^{8} \) $C_2^3\times S_4$ (as 24T400) $[2]$ (GRH)
24.0.2914041287899137980901233132568576.1 x24 - 2x22 + 8x18 - 16x16 + 64x12 - 256x8 + 512x6 - 2048x2 + 4096 \( 2^{36}\cdot 3^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[6]$ (GRH)
24.0.2914041287899137980901233132568576.2 x24 + 2x22 - 8x18 - 16x16 + 64x12 - 256x8 - 512x6 + 2048x2 + 4096 \( 2^{36}\cdot 3^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[7]$ (GRH)
24.0.3785323726785214561740247642669056.1 x24 - 6x23 + 18x22 - 32x21 + 30x20 + 4x19 - 62x18 + 110x17 - 118x16 + 44x15 + 206x14 - 696x13 + 1249x12 - 1392x11 + 824x10 + 352x9 - 1888x8 + 3520x7 - 3968x6 + 512x5 + 7680x4 - 16384x3 + 18432x2 - 12288x + 4096 \( 2^{24}\cdot 3^{12}\cdot 23^{4}\cdot 79^{8} \) $C_2^3\times S_4$ (as 24T400) $[4]$ (GRH)
24.0.3949093091982271355222362303758336.1 x24 + 6x22 + 9x20 - 21x18 - 72x16 + 33x14 + 341x12 + 132x10 - 1152x8 - 1344x6 + 2304x4 + 6144x2 + 4096 \( 2^{24}\cdot 3^{36}\cdot 199^{4} \) $C_2^3\times A_4$ (as 24T135) $[3]$ (GRH)
24.0.4367896108464230086685082523795456.1 x24 + 10x20 - 14x18 + 37x16 - 154x14 + 97x12 - 616x10 + 592x8 - 896x6 + 2560x4 + 4096 \( 2^{24}\cdot 7^{20}\cdot 239^{4} \) $C_2^3\times A_4$ (as 24T135) $[4]$ (GRH)
24.0.4426749135366626687982375069024256.1 x24 + 32x16 + 16x12 + 512x8 + 4096 \( 2^{52}\cdot 23^{4}\cdot 37^{8} \) $C_2^3\times S_4$ (as 24T400) $[2]$ (GRH)
24.0.4971225787269833056964369392336896.1 x24 - 13x20 + 143x16 - 336x12 + 663x8 - 26x4 + 1 \( 2^{48}\cdot 3^{12}\cdot 7^{16} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.7404154726819150028835278894923776.1 x24 - 4x23 + 8x22 - 12x21 + 12x20 - 4x19 - 8x18 + 24x17 - 56x16 + 88x15 - 88x14 + 56x13 - 28x12 + 112x11 - 352x10 + 704x9 - 896x8 + 768x7 - 512x6 - 512x5 + 3072x4 - 6144x3 + 8192x2 - 8192x + 4096 \( 2^{32}\cdot 3^{12}\cdot 31^{4}\cdot 37^{8} \) $C_2^3\times S_4$ (as 24T400) $[3]$ (GRH)
24.0.14608995065922872079188435597787136.1 x24 - 8x20 + 16x16 + 16x12 + 256x8 - 2048x4 + 4096 \( 2^{52}\cdot 31^{4}\cdot 37^{8} \) $C_2^3\times S_4$ (as 24T400) $[4]$ (GRH)
24.0.34854715807867200628629234134286336.1 x24 - 9x18 + 17x12 - 576x6 + 4096 \( 2^{24}\cdot 3^{36}\cdot 7^{12} \) $C_2^2\times C_6$ (as 24T3) $[7]$ (GRH)
24.0.42870299553219194916193841757290496.1 x24 - 2x22 - 5x20 + 8x18 + 19x16 - 5x14 - 91x12 - 20x10 + 304x8 + 512x6 - 1280x4 - 2048x2 + 4096 \( 2^{24}\cdot 3^{12}\cdot 23^{4}\cdot 107^{8} \) $C_2^3\times S_4$ (as 24T400) $[4]$ (GRH)
24.0.43732136908774182106643650057610721.1 x24 - x23 - 2x22 + 3x21 - x20 - 3x19 + 22x18 - 10x17 - 34x16 + 42x15 - 35x14 - 36x13 + 213x12 - 72x11 - 140x10 + 336x9 - 544x8 - 320x7 + 1408x6 - 384x5 - 256x4 + 1536x3 - 2048x2 - 2048x + 4096 \( 3^{12}\cdot 7^{12}\cdot 11^{4}\cdot 67^{8} \) $C_2^3\times S_4$ (as 24T400) $[3]$ (GRH)
24.0.44455984353110737022824200630534169.1 x24 - x23 - x22 + 3x21 - x20 - 5x19 + 7x18 + 3x17 - 17x16 + 11x15 + 23x14 - 45x13 - x12 - 90x11 + 92x10 + 88x9 - 272x8 + 96x7 + 448x6 - 640x5 - 256x4 + 1536x3 - 1024x2 - 2048x + 4096 \( 7^{12}\cdot 13^{22} \) $C_2\times C_{12}$ (as 24T2) $[7]$ (GRH)
24.0.52792842355679189725978706186699601.1 x24 + 42x22 + 717x20 + 6498x18 + 34350x16 + 110088x14 + 216407x12 + 257262x10 + 175920x8 + 61818x6 + 8772x4 + 423x2 + 1 \( 3^{36}\cdot 7^{12}\cdot 71^{4} \) $C_2^3\times A_4$ (as 24T135) $[5]$ (GRH)
24.0.59344171108947314029391991313268736.1 x24 - 4x21 + 4x20 - 4x19 + 8x18 - 16x17 + 40x16 - 24x15 + 40x14 - 104x13 + 100x12 - 208x11 + 160x10 - 192x9 + 640x8 - 512x7 + 512x6 - 512x5 + 1024x4 - 2048x3 + 4096 \( 2^{32}\cdot 3^{12}\cdot 7^{4}\cdot 101^{8} \) $C_2^3\times S_4$ (as 24T400) $[2, 2]$ (GRH)
24.0.72340856237421875367936000000000000.1 x24 - 15x22 + 158x20 - 789x18 + 2798x16 - 5124x14 + 6639x12 - 5271x10 + 3030x8 - 1062x6 + 253x4 - 18x2 + 1 \( 2^{24}\cdot 3^{12}\cdot 5^{12}\cdot 7^{16} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.72498183345339963679508209228515625.1 x24 - x23 + 6x22 - 7x21 + 27x20 - 19x19 + 94x18 - 58x17 + 317x16 - 205x15 + 643x14 - 353x13 + 1114x12 - 86x11 + 1318x10 - 237x9 + 1501x8 - 593x7 + 614x6 - 193x5 + 250x4 + 59x3 + 15x2 + 3x + 1 \( 5^{18}\cdot 13^{20} \) $C_2\times C_{12}$ (as 24T2) $[2, 2, 2, 2]$ (GRH)
24.0.92534566049630892119774472900390625.1 x24 - x23 - 2x22 + 3x21 + x20 - 2x19 + x18 + 34x17 - 37x16 - 59x15 + 98x14 + 17x13 - 45x12 + 34x11 + 392x10 - 472x9 - 592x8 + 1088x7 + 64x6 - 256x5 + 256x4 + 1536x3 - 2048x2 - 2048x + 4096 \( 5^{12}\cdot 7^{20}\cdot 41^{6} \) $C_6\times D_4$ (as 24T38) $[2, 2]$ (GRH)
24.0.96596555035261369442314470090080256.1 x24 - 8x21 + 3x20 - 4x19 + 32x18 - 20x17 + 37x16 - 116x15 + 72x14 - 128x13 + 380x12 - 256x11 + 288x10 - 928x9 + 592x8 - 640x7 + 2048x6 - 512x5 + 768x4 - 4096x3 + 4096 \( 2^{48}\cdot 3^{12}\cdot 71^{8} \) $C_2^3\times S_3$ (as 24T30) $[8]$ (GRH)
24.0.117090840873653968654439037792157696.1 x24 - 8x20 + 48x16 - 240x12 + 768x8 - 2048x4 + 4096 \( 2^{52}\cdot 7^{4}\cdot 101^{8} \) $C_2^3\times S_4$ (as 24T400) $[6]$ (GRH)
24.0.118593292086517824000000000000000000.1 x24 - 6x22 + 27x20 - 109x18 + 417x16 - 927x14 + 1918x12 - 3582x10 + 5157x8 - 622x6 + 75x4 - 9x2 + 1 \( 2^{24}\cdot 3^{32}\cdot 5^{18} \) $C_2\times C_{12}$ (as 24T2) $[3]$ (GRH)
24.0.119499989263531662609135295535251456.1 x24 - 7x20 + 8x16 + 48x12 + 128x8 - 1792x4 + 4096 \( 2^{48}\cdot 23^{4}\cdot 79^{8} \) $C_2^3\times S_4$ (as 24T400) $[2, 4]$ (GRH)
24.0.132353116631035821576664572214902784.1 x24 - 2x23 - x22 + 8x21 - 5x20 - 22x19 + 39x18 - 102x17 + 107x16 + 184x15 - 573x14 + 2x13 + 1911x12 - 1908x11 + 766x10 + 360x9 - 740x8 + 432x7 - 136x6 + 352x5 - 272x4 + 64x3 + 96x2 - 128x + 64 \( 2^{36}\cdot 7^{20}\cdot 17^{6} \) $C_6\times D_4$ (as 24T38) $[6]$ (GRH)
24.0.133084684332123489494188901166116961.1 x24 - x23 + 3x22 - 8x21 + 8x20 - 24x19 + 37x18 - 120x17 + 194x16 - 329x15 + 744x14 - 904x13 + 1633x12 - 2712x11 + 6696x10 - 8883x9 + 15714x8 - 29160x7 + 26973x6 - 52488x5 + 52488x4 - 157464x3 + 177147x2 - 177147x + 531441 \( 3^{12}\cdot 7^{20}\cdot 11^{12} \) $C_2^2\times C_6$ (as 24T3) $[9]$ (GRH)
24.0.141478989546523004521132546458648576.1 x24 + 2x22 + 3x20 + 12x18 + 7x16 + 11x14 + 85x12 + 44x10 + 112x8 + 768x6 + 768x4 + 2048x2 + 4096 \( 2^{24}\cdot 3^{12}\cdot 31^{4}\cdot 107^{8} \) $C_2^3\times S_4$ (as 24T400) $[3]$ (GRH)
24.0.156938077449417789520626992646455296.1 x24 + 117x16 + 650x8 + 1 \( 2^{72}\cdot 7^{16} \) $C_2\times C_{12}$ (as 24T2) $[3, 3]$ (GRH)
24.0.161761786626698377317203521728515625.1 x24 - x23 + 7x22 - 7x21 + 35x20 - 34x19 + 153x18 - 146x17 + 629x16 - 588x15 + 1618x14 - 1394x13 + 3557x12 - 2395x11 + 6504x10 - 4802x9 + 10534x8 - 8224x7 + 6187x6 - 3548x5 + 2534x4 - 378x3 + 56x2 - 8x + 1 \( 3^{12}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[26]$ (GRH)
24.24.161761786626698377317203521728515625.1 x24 - x23 - 23x22 + 23x21 + 230x20 - 229x19 - 1312x18 + 1294x17 + 4709x16 - 4573x15 - 11067x14 + 10506x13 + 17187x12 - 15810x11 - 17391x10 + 15333x9 + 11034x8 - 9189x7 - 4088x6 + 3142x5 + 784x4 - 528x3 - 64x2 + 32x + 1 \( 3^{12}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) Trivial (GRH)
24.0.161761786626698377317203521728515625.2 x24 - x23 + 5x22 - 5x21 + 20x20 - 19x19 + 74x18 - 99x17 + 299x16 - 380x15 + 1106x14 - 1331x13 + 3936x12 - 4456x11 + 5996x10 - 6745x9 + 8969x8 - 7509x7 + 10409x6 + 2176x5 + 455x4 + 95x3 + 20x2 + 4x + 1 \( 3^{12}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[26]$ (GRH)
24.0.161761786626698377317203521728515625.3 x24 - x23 + 13x22 - 10x21 + 101x20 - 67x19 + 500x18 - 254x17 + 1781x16 - 706x15 + 4524x14 - 1119x13 + 8400x12 - 1296x11 + 11097x10 - 456x9 + 10104x8 - 327x7 + 5722x6 + 151x5 + 1858x4 - 228x3 + 104x2 + 8x + 1 \( 3^{12}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[26]$ (GRH)
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