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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)
24.0.42247883974617233597120303333376.1 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)
24.0.67372672480923938907623291015625.1 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)
24.0.326829122755018756096000000000000.1 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)
24.0.1312855308850436212414726439933209.1 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)
24.0.2914041287899137980901233132568576.1 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)
24.0.4971225787269833056964369392336896.1 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)
24.0.34854715807867200628629234134286336.1 x24 - 9x18 + 17x12 - 576x6 + 4096 \( 2^{24}\cdot 3^{36}\cdot 7^{12} \) $C_2^2\times C_6$ (as 24T3) $[7]$ (GRH)
24.0.44455984353110737022824200630534169.1 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)
24.0.72340856237421875367936000000000000.1 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)
24.0.118593292086517824000000000000000000.1 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)
24.0.133084684332123489494188901166116961.1 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)
24.0.156938077449417789520626992646455296.1 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)
24.0.169450166032303737749261229339181056.1 x24 - 11x22 + 76x20 - 327x18 + 1031x16 - 2261x14 + 3677x12 - 4001x10 + 3091x8 - 1302x6 + 371x4 - 21x2 + 1 \( 2^{24}\cdot 3^{12}\cdot 13^{20} \) $C_2^2\times C_6$ (as 24T3) $[6]$ (GRH)
24.0.220715887053399008657112652614467584.1 x24 - 2x22 + 4x20 - 8x18 + 16x16 - 32x14 + 64x12 - 128x10 + 256x8 - 512x6 + 1024x4 - 2048x2 + 4096 \( 2^{36}\cdot 13^{22} \) $C_2\times C_{12}$ (as 24T2) $[9]$ (GRH)
24.0.220715887053399008657112652614467584.2 x24 + 2x22 + 4x20 + 8x18 + 16x16 + 32x14 + 64x12 + 128x10 + 256x8 + 512x6 + 1024x4 + 2048x2 + 4096 \( 2^{36}\cdot 13^{22} \) $C_2\times C_{12}$ (as 24T2) $[13]$ (GRH)
24.0.507202869744901554493542558837890625.1 x24 + 26x18 - 53x12 + 18954x6 + 531441 \( 3^{36}\cdot 5^{12}\cdot 7^{12} \) $C_2^2\times C_6$ (as 24T3) $[3, 3]$ (GRH)
24.0.987952545632990645956882874687477121.1 x24 - x23 - 3x22 + 10x21 - 10x20 - 30x19 + 127x18 + 210x17 - 718x16 + 529x15 + 1830x14 - 7990x13 + 8719x12 + 23970x11 + 16470x10 - 14283x9 - 58158x8 - 51030x7 + 92583x6 + 65610x5 - 65610x4 - 196830x3 - 177147x2 + 177147x + 531441 \( 3^{12}\cdot 7^{20}\cdot 13^{12} \) $C_2^2\times C_6$ (as 24T3) $[2, 4, 4]$ (GRH)
24.0.1338692086804556824969216000000000000.1 x24 - 6x22 + 32x20 - 168x18 + 880x16 - 4608x14 + 24128x12 - 18432x10 + 14080x8 - 10752x6 + 8192x4 - 6144x2 + 4096 \( 2^{36}\cdot 5^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[3, 3]$ (GRH)
24.0.1338692086804556824969216000000000000.2 x24 + 6x22 + 32x20 + 168x18 + 880x16 + 4608x14 + 24128x12 + 18432x10 + 14080x8 + 10752x6 + 8192x4 + 6144x2 + 4096 \( 2^{36}\cdot 5^{12}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[28]$ (GRH)
24.0.1348990128329918967746280670166015625.1 x24 - x23 - 4x22 + 15x21 - 16x20 + 62x19 + 163x18 - 809x17 + 670x16 + 3344x15 + 2796x14 - 2771x13 - 4594x12 - 11446x11 - 11444x10 + 8739x9 + 34835x8 + 8891x7 - 162x6 - 698x5 - 196x4 - 50x3 + x2 + 4x + 1 \( 3^{12}\cdot 5^{18}\cdot 13^{16} \) $C_2\times C_{12}$ (as 24T2) $[4, 4]$ (GRH)
24.0.2283749599146799148302336000000000000.1 x24 + 91x20 + 1391x16 + 2688x12 + 1287x8 + 182x4 + 1 \( 2^{48}\cdot 5^{12}\cdot 7^{16} \) $C_2^2\times C_6$ (as 24T3) $[3, 3, 3]$ (GRH)
24.0.2465824451534772200819297422119140625.1 x24 - x23 + 17x22 - 6x21 + 188x20 - 47x19 + 1066x18 + 111x17 + 4083x16 + 396x15 + 8622x14 + 1407x13 + 12820x12 + 2029x11 + 11865x10 + 2619x9 + 7679x8 + 1542x7 + 2678x6 + 721x5 + 616x4 + 85x3 + 36x2 - 3x + 1 \( 3^{12}\cdot 5^{12}\cdot 13^{20} \) $C_2^2\times C_6$ (as 24T3) $[4, 4, 4]$ (GRH)
24.0.2518170116818978404827136000000000000.1 x24 - 144x18 + 20672x12 - 9216x6 + 4096 \( 2^{36}\cdot 3^{36}\cdot 5^{12} \) $C_2^2\times C_6$ (as 24T3) $[21]$ (GRH)
24.0.2518170116818978404827136000000000000.2 x24 + 144x18 + 20672x12 + 9216x6 + 4096 \( 2^{36}\cdot 3^{36}\cdot 5^{12} \) $C_2^2\times C_6$ (as 24T3) $[14]$ (GRH)
24.0.4201389232919273300173938291676020736.1 x24 + 5x22 + 16x20 + 35x18 + 31x16 - 160x14 - 1079x12 - 1440x10 + 2511x8 + 25515x6 + 104976x4 + 295245x2 + 531441 \( 2^{24}\cdot 7^{20}\cdot 11^{12} \) $C_2^2\times C_6$ (as 24T3) $[14]$ (GRH)
24.0.5106705043047168064000000000000000000.1 x24 + 25x22 + 274x20 + 1729x18 + 6936x16 + 18427x14 + 32745x12 + 38377x10 + 28468x8 + 12278x6 + 2556x4 + 144x2 + 1 \( 2^{24}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[78]$ (GRH)
24.24.5106705043047168064000000000000000000.1 x24 - 23x22 + 230x20 - 1311x18 + 4692x16 - 10949x14 + 16757x12 - 16511x10 + 10032x8 - 3498x6 + 628x4 - 48x2 + 1 \( 2^{24}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) Trivial (GRH)
24.0.5106705043047168064000000000000000000.2 x24 + 7x22 + 35x20 + 154x18 + 637x16 + 1666x14 + 3822x12 + 7889x10 + 13377x8 + 9947x6 + 7203x4 + 4802x2 + 2401 \( 2^{24}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[26]$ (GRH)
24.0.5106705043047168064000000000000000000.3 x24 + 5x22 + 20x20 + 75x18 + 275x16 + 1000x14 + 3625x12 + 5000x10 + 6875x8 + 9375x6 + 12500x4 + 15625x2 + 15625 \( 2^{24}\cdot 5^{18}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[26]$ (GRH)
24.0.5349421735921433961299014349756563456.1 x24 + 31x20 + 317x16 + 1216x12 + 1462x8 + 301x4 + 1 \( 2^{48}\cdot 13^{20} \) $C_2^2\times C_6$ (as 24T3) $[3, 9]$ (GRH)
24.0.5887630061813314259984772021002174464.1 x24 - 4x22 + 14x20 - 48x18 + 164x16 - 560x14 + 1912x12 - 1120x10 + 656x8 - 384x6 + 224x4 - 128x2 + 64 \( 2^{66}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[3, 6]$ (GRH)
24.0.5887630061813314259984772021002174464.2 x24 + 4x22 + 14x20 + 48x18 + 164x16 + 560x14 + 1912x12 + 1120x10 + 656x8 + 384x6 + 224x4 + 128x2 + 64 \( 2^{66}\cdot 7^{20} \) $C_2\times C_{12}$ (as 24T2) $[52]$ (GRH)
24.0.7484085902451519080029070374597558272.1 x24 + 3 \( 2^{48}\cdot 3^{47} \) $C_3:D_8:C_2$ (as 24T118) Trivial (GRH)

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