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Label Polynomial Discriminant Galois group Class group
24.0.368...000.1 x24 - 6x23 + 21x22 - 54x21 + 107x20 - 178x19 + 265x18 - 376x17 + 537x16 - 744x15 + 966x14 - 1140x13 + 1221x12 - 1228x11 + 1176x10 - 1074x9 + 914x8 - 696x7 + 471x6 - 280x5 + 140x4 - 58x3 + 21x2 - 6x + 1 \( 2^{24}\cdot 5^{18}\cdot 7^{8} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.275...000.1 x24 - 2x23 + 5x22 - 12x21 + 16x20 - 30x19 + 35x18 - 36x17 + 47x16 - 36x15 + 9x14 - 16x13 + 39x12 + 80x11 + 53x10 - 46x8 - 20x7 + 34x6 + 50x5 + 38x4 + 18x3 + 9x2 + 4x + 1 \( 2^{24}\cdot 3^{16}\cdot 5^{18} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.344...625.1 x24 - x23 - 4x22 + x21 + x20 - 5x19 + 37x18 + 33x17 - 39x16 - 57x15 - 111x14 - 16x13 + 118x12 + 13x11 + 47x9 + 156x8 + 319x7 + 175x6 - 76x5 - 127x4 - 44x3 + 48x2 + 56x + 16 \( 3^{12}\cdot 5^{18}\cdot 19^{8} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.304...625.1 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)
24.0.572...625.1 x24 - x21 + x15 - x12 + x9 - x3 + 1 \( 3^{36}\cdot 5^{18} \) $C_2\times C_{12}$ (as 24T2) trivial (GRH)
24.0.572...625.2 x24 - 2x21 - 2x15 + 9x12 - 8x9 + 5x6 - 3x3 + 1 \( 3^{36}\cdot 5^{18} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.711...256.1 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)
24.0.170...729.1 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)
24.0.172...625.1 x24 - 8x23 + 35x22 - 105x21 + 233x20 - 377x19 + 373x18 + 86x17 - 1310x16 + 3226x15 - 4893x14 + 4424x13 - 205x12 - 6944x11 + 13153x10 - 14094x9 + 9116x8 - 2660x7 - 525x6 + 689x5 - 175x4 - 37x3 + 37x2 - 10x + 1 \( 3^{12}\cdot 5^{18}\cdot 31^{8} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.227...625.1 x24 - 5x23 + 7x22 + 9x21 - 43x20 + 66x19 - 38x18 - 93x17 + 491x16 - 1291x15 + 2386x14 - 3246x13 + 3278x12 - 2354x11 + 1061x10 - 234x9 + 126x8 - 282x7 + 277x6 - 136x5 + 42x4 - 19x3 + 12x2 - 5x + 1 \( 3^{16}\cdot 5^{18}\cdot 7^{12} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.385...816.1 x24 - 3x16 - 8x12 + 18x8 + 8x4 + 1 \( 2^{72}\cdot 13^{8} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.0.103...625.1 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)
24.0.180...000.1 x24 - 6x23 + 23x22 - 58x21 + 100x20 - 160x19 + 242x18 - 156x17 - 228x16 + 452x15 + 164x14 - 1190x13 + 1288x12 - 326x11 - 800x10 + 832x9 + 514x8 - 1302x7 + 500x6 + 664x5 - 155x4 - 1418x3 + 1951x2 - 1112x + 241 \( 2^{24}\cdot 3^{24}\cdot 5^{18} \) $C_{12}\times S_3$ (as 24T65) $[2]$ (GRH)
24.0.224...656.1 x24 - x20 + x16 - x12 + x8 - x4 + 1 \( 2^{48}\cdot 7^{20} \) $C_2^2\times C_6$ (as 24T3) $[2]$ (GRH)
24.0.329...561.1 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)
24.0.422...376.1 x24 - x12 + 1 \( 2^{48}\cdot 3^{36} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.430...625.1 x24 - x23 + 3x22 + x21 + 7x20 + 20x19 + 16x18 - 5x17 + 80x16 + 120x15 - 277x14 + 191x13 + 511x12 - 356x11 - 47x10 + 255x9 - 75x8 - 130x7 + 96x6 + 20x5 - 43x4 + 14x3 + 3x2 - 4x + 1 \( 5^{18}\cdot 7^{12}\cdot 13^{8} \) $C_{12}\times S_3$ (as 24T65) trivial (GRH)
24.4.491...064.1 x24 - 5x23 + x22 + 40x21 - 89x20 + 10x19 + 240x18 - 427x17 + 266x16 + 215x15 - 599x14 + 533x13 - 153x12 - 191x11 + 195x10 + 9x9 + 160x8 - 37x7 - 186x6 - 202x5 - 123x4 - 10x3 + x2 + 5x - 1 \( 2^{16}\cdot 487^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.4.491...064.2 x24 - 4x23 + 7x22 - 10x21 + 23x20 - 32x19 - 21x18 + 156x17 - 359x16 + 654x15 - 876x14 + 646x13 + 61x12 - 1012x11 + 2338x10 - 3178x9 + 2897x8 - 2474x7 + 1335x6 - 52x5 - 44x4 + 454x3 - 524x2 + 62x - 197 \( 2^{16}\cdot 487^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.0.538...704.1 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)
24.0.639...616.1 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)
24.0.673...625.1 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)
24.0.138...681.1 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)
24.0.326...000.1 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)
24.0.614...000.1 x24 - 18x18 + 323x12 - 18x6 + 1 \( 2^{24}\cdot 3^{36}\cdot 5^{12} \) $C_2^2\times C_6$ (as 24T3) $[3]$ (GRH)
24.0.784...625.1 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)
24.4.940...625.1 x24 - 10x23 + 48x22 - 158x21 + 381x20 - 714x19 + 1213x18 - 1907x17 + 2614x16 - 3516x15 + 4694x14 - 5466x13 + 6009x12 - 6785x11 + 7506x10 - 8491x9 + 9365x8 - 8498x7 + 5899x6 - 3118x5 + 1203x4 - 296x3 + 36x2 - 7x + 1 \( 5^{16}\cdot 151^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.4.940...625.2 x24 - 2x23 + 6x22 - 5x21 + 11x20 - 17x19 + 2x18 - 34x17 - 139x16 - 108x15 - 455x14 - 497x13 - 1230x12 - 1691x11 - 2719x10 - 4214x9 - 4936x8 - 6130x7 - 5653x6 - 4317x5 - 2323x4 - 45x3 - 323x2 + 428x + 173 \( 5^{16}\cdot 151^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.0.104...336.1 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)
24.0.131...209.1 x24 - x + 1 \( 6361\cdot 61167766669\cdot 3374184647743911301 \) $S_{24}$ (as 24T25000) trivial (GRH)
24.2.135...343.1 x24 - x - 1 \( -\,101\cdot 2347\cdot 5714547093403974893094772369 \) $S_{24}$ (as 24T25000) trivial (GRH)
24.4.153...449.1 x24 - 2x23 - 8x22 - 2x21 + 70x20 - 33x19 - 156x18 + 43x17 + 433x16 - 998x15 + 433x14 + 1850x13 - 1996x12 - 1334x11 + 1462x10 + 5x9 - 1195x8 - 1071x7 - 747x6 - 160x5 + 26x4 - 66x3 - 57x2 - 14x - 1 \( 2083^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.4.153...449.2 x24 + 5x22 - 9x21 - 17x20 - 76x19 - 136x18 - 174x17 - 166x16 + 28x15 + 141x14 + 361x13 + 448x12 + 1384x11 + 3389x10 + 8270x9 + 11234x8 + 16185x7 + 17718x6 + 15868x5 + 15966x4 + 10226x3 + 4276x2 + 3258x + 1459 \( 2083^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.0.212...000.1 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)
24.0.224...696.1 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)
24.0.291...576.1 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)
24.0.291...576.2 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)
24.4.374...536.1 x24 - 4x23 + 18x22 - 59x21 + 167x20 - 420x19 + 919x18 - 1828x17 + 3235x16 - 4879x15 + 6403x14 - 6415x13 + 2571x12 + 6076x11 - 21326x10 + 40942x9 - 60476x8 + 73984x7 - 73764x6 + 61224x5 - 43696x4 + 17928x3 - 3216x2 + 720x + 16 \( 2^{16}\cdot 751^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.4.374...536.2 x24 - 3x23 + x22 + 10x21 - 43x20 + 48x19 + 120x18 - 317x17 + 184x16 + 607x15 - 1095x14 - 247x13 + 1345x12 - 781x11 + 2081x10 + 2799x9 - 6866x8 - 6853x7 + 2370x6 + 3678x5 + 629x4 - 178x3 - 33x2 - x + 1 \( 2^{16}\cdot 751^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.0.378...056.1 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)
24.0.394...336.1 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)
24.0.436...456.1 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)
24.0.442...256.1 x24 + 32x16 + 16x12 + 512x8 + 4096 \( 2^{52}\cdot 23^{4}\cdot 37^{8} \) $C_2^3\times S_4$ (as 24T400) $[2]$ (GRH)
24.0.497...896.1 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)
24.0.740...776.1 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)
24.4.765...384.1 x24 - 6x23 + 9x22 + 14x21 - 42x20 + 30x19 - 252x18 + 1092x17 - 1758x16 + 564x15 + 3066x14 - 8784x13 + 15708x12 - 20460x11 + 17904x10 - 7740x9 - 3195x8 + 7842x7 - 5979x6 + 2034x5 + 342x4 - 770x3 + 420x2 - 120x + 16 \( 2^{16}\cdot 3^{26}\cdot 11^{16} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.4.765...384.2 x24 - 3x23 + 6x22 - 19x21 + 39x20 - 30x19 - 9x18 - 45x17 + 93x16 + 204x15 - 201x14 - 129x13 - 793x12 + 738x11 + 141x10 + 1177x9 - 666x8 - 597x7 - 913x6 + 168x5 + 474x4 + 464x3 + 168x2 + 24x - 4 \( 2^{16}\cdot 3^{26}\cdot 11^{16} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.0.146...136.1 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)
24.4.197...064.1 x24 - 2x23 - 8x22 + 22x21 + 51x20 - 228x19 - 3x18 + 1321x17 - 2220x16 - 1748x15 + 9722x14 - 7588x13 - 14572x12 + 34524x11 - 16026x10 - 34263x9 + 60097x8 - 26110x7 - 33112x6 + 60245x5 - 45651x4 + 20521x3 - 6288x2 + 1547x - 241 \( 2^{16}\cdot 887^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
24.4.197...064.2 x24 - 11x23 + 53x22 - 131x21 + 131x20 + 144x19 - 585x18 + 471x17 + 846x16 - 3226x15 + 6073x14 - 7616x13 + 4239x12 + 5146x11 - 14303x10 + 15630x9 - 9886x8 + 3829x7 - 1007x6 + 240x5 - 15x4 - 39x3 + 19x2 - 3x + 1 \( 2^{16}\cdot 887^{10} \) $C_4.A_5$ (as 24T576) trivial (GRH)
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