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Label Polynomial Discriminant Galois group Class group
24.0.965...256.1 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)
24.0.226...056.1 x24 - 4x22 + 3x20 + 4x18 + 5x16 - 12x14 - 20x12 - 48x10 + 80x8 + 256x6 + 768x4 - 4096x2 + 4096 \( 2^{48}\cdot 3^{12}\cdot 79^{8} \) $C_2^3\times S_3$ (as 24T30) $[8]$ (GRH)
24.0.593...456.1 x24 - 51x20 + 2430x16 - 8703x12 + 28782x8 - 1539x4 + 81 \( 2^{52}\cdot 3^{28}\cdot 7^{8} \) $C_2^3\times S_3$ (as 24T30) $[3, 3]$ (GRH)
24.0.330...000.1 x24 - 2x23 - x22 + 26x21 - 26x20 - 88x19 + 233x18 + 326x17 - 1593x16 + 1102x15 + 5510x14 - 6356x13 + 3000x12 + 12712x11 + 22040x10 - 8816x9 - 25488x8 - 10432x7 + 14912x6 + 11264x5 - 6656x4 - 13312x3 - 1024x2 + 4096x + 4096 \( 2^{24}\cdot 3^{12}\cdot 5^{12}\cdot 79^{8} \) $C_2^3\times S_3$ (as 24T30) $[17]$ (GRH)
24.0.501...296.1 x24 - 4x22 + 4x20 + 2x18 - 4x16 + 20x14 - 79x12 + 80x10 - 64x8 + 128x6 + 1024x4 - 4096x2 + 4096 \( 2^{24}\cdot 3^{12}\cdot 7^{12}\cdot 67^{8} \) $C_2^3\times S_3$ (as 24T30) $[6, 6]$ (GRH)
24.0.138...000.1 x24 - 39x22 + 642x20 - 5775x18 + 31086x16 - 107523x14 + 272681x12 - 504912x10 + 711384x8 - 746184x6 + 554784x4 - 256752x2 + 59536 \( 2^{32}\cdot 3^{28}\cdot 5^{12}\cdot 7^{8} \) $C_2^3\times S_3$ (as 24T30) $[3, 9]$ (GRH)
24.0.187...816.1 x24 - 2x23 - 11x22 + 2x21 + 122x20 - 22x19 - 603x18 + 126x17 + 2838x16 - 4554x15 - 11143x14 + 38030x13 - 5743x12 - 74196x11 + 192820x10 + 2152x9 - 196612x8 + 432432x7 - 65552x6 - 178400x5 + 381072x4 - 166208x3 + 51840x2 - 8704x + 1024 \( 2^{24}\cdot 3^{12}\cdot 7^{12}\cdot 79^{8} \) $C_2^3\times S_3$ (as 24T30) $[55]$ (GRH)
24.0.504...896.1 x24 - 66x20 + 867x16 + 9854x12 + 60993x8 - 6624x4 + 256 \( 2^{48}\cdot 3^{28}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 24]$ (GRH)
24.0.729...625.1 x24 - 2x23 + 8x22 - 16x21 + 22x20 - 64x19 + 86x18 - 358x17 + 696x16 - 2792x15 + 4514x14 - 7304x13 + 12417x12 + 14608x11 + 18056x10 + 22336x9 + 11136x8 + 11456x7 + 5504x6 + 8192x5 + 5632x4 + 8192x3 + 8192x2 + 4096x + 4096 \( 3^{12}\cdot 5^{12}\cdot 7^{12}\cdot 67^{8} \) $C_2^3\times S_3$ (as 24T30) $[3, 33]$ (GRH)
24.0.158...696.1 x24 - 8x20 + 40x16 - 143x12 + 640x8 - 2048x4 + 4096 \( 2^{48}\cdot 7^{12}\cdot 67^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 8]$ (GRH)
24.0.251...416.1 x24 - 18x22 + 167x20 - 956x18 + 2327x16 + 846x14 - 8599x12 + 12832x10 + 162248x8 - 112928x6 + 633232x4 + 33024x2 + 1024 \( 2^{48}\cdot 7^{12}\cdot 71^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 78]$ (GRH)
24.0.549...456.1 x24 - 81x20 + 2913x16 - 59920x12 + 745728x8 - 5308416x4 + 16777216 \( 2^{48}\cdot 3^{28}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 6, 24]$ (GRH)
24.0.575...000.1 x24 - 2x23 + 5x22 - 2x21 - 10x20 - 14x19 - 49x18 - 46x17 - 229x16 - 1464x15 + 4190x14 - 6920x13 + 11088x12 + 13840x11 + 16760x10 + 11712x9 - 3664x8 + 1472x7 - 3136x6 + 1792x5 - 2560x4 + 1024x3 + 5120x2 + 4096x + 4096 \( 2^{36}\cdot 3^{12}\cdot 5^{12}\cdot 71^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 22]$ (GRH)
24.0.591...216.1 x24 - 8x22 + 67x20 - 320x18 + 2315x16 + 7064x14 - 14367x12 - 58928x10 + 82856x8 - 58880x6 + 282768x4 + 17664x2 + 1024 \( 2^{48}\cdot 7^{12}\cdot 79^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 66]$ (GRH)
24.0.733...000.1 x24 - 39x22 + 648x20 - 5829x18 + 30363x16 - 94896x14 + 196451x12 - 293637x10 + 327912x8 - 264279x6 + 203193x4 - 165600x2 + 92416 \( 2^{24}\cdot 3^{28}\cdot 5^{12}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 90]$ (GRH)
24.0.799...000.1 x24 + 30x22 + 423x20 + 3156x18 + 11967x16 + 32862x14 + 196601x12 + 135120x10 + 1571520x8 + 770688x6 + 4961280x4 + 3182592x2 + 3936256 \( 2^{24}\cdot 3^{28}\cdot 5^{12}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[12, 24]$ (GRH)
24.0.205...416.1 x24 - 4x23 + 36x22 - 116x21 + 548x20 - 1432x19 + 4646x18 - 9804x17 + 23936x16 - 39532x15 + 73740x14 - 84792x13 + 112745x12 - 74000x11 + 128108x10 - 284032x9 + 775996x8 - 892608x7 - 10272x6 + 683904x5 - 148880x4 - 116992x3 + 42176x2 - 3072x + 64 \( 2^{36}\cdot 3^{12}\cdot 7^{12}\cdot 67^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 96]$ (GRH)
24.0.205...416.2 x24 - 4x23 + 24x22 - 60x21 + 240x20 - 480x19 + 1686x18 - 3012x17 + 9534x16 - 11972x15 + 25612x14 + 17340x13 - 34863x12 + 220216x11 - 73466x10 - 125792x9 + 306584x8 - 15136x7 - 209480x6 - 97088x5 + 148576x4 + 23296x3 - 23968x2 + 3136 \( 2^{36}\cdot 3^{12}\cdot 7^{12}\cdot 67^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 42]$ (GRH)
24.0.326...536.1 x24 - 2x23 - 7x22 + 10x21 + 34x20 - 6x19 - 247x18 - 290x17 + 2390x16 - 2722x15 - 9827x14 + 32414x13 - 9183x12 - 57028x11 + 186964x10 + 1112x9 - 122188x8 + 510080x7 + 131792x6 - 21952x5 + 623632x4 + 227712x3 + 57984x2 + 9216x + 1024 \( 2^{36}\cdot 3^{12}\cdot 7^{12}\cdot 71^{8} \) $C_2^3\times S_3$ (as 24T30) $[117]$ (GRH)
24.0.416...056.1 x24 + 27x22 + 501x20 + 4718x18 + 31614x16 + 112722x14 + 286161x12 + 475107x10 + 575709x8 + 424868x6 + 203712x4 + 7488x2 + 256 \( 2^{24}\cdot 3^{28}\cdot 7^{12}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[4, 48]$ (GRH)
24.0.566...000.1 x24 - 6x23 + 75x22 - 338x21 + 2223x20 - 7956x19 + 35336x18 - 103140x17 + 337851x16 - 813410x15 + 2046819x14 - 4063794x13 + 7994884x12 - 12969990x11 + 20002383x10 - 25939270x9 + 30969063x8 - 30818088x7 + 27014186x6 - 18391692x5 + 10444713x4 - 2828110x3 + 8181x2 + 207954x + 609121 \( 2^{44}\cdot 3^{28}\cdot 5^{12}\cdot 7^{8} \) $C_2^3\times S_3$ (as 24T30) $[3, 51]$ (GRH)
24.0.453...216.1 x24 - 42x22 + 765x20 - 7506x18 + 39156x16 - 83922x14 - 130219x12 + 723918x10 + 3868401x8 + 4392264x6 + 927120x4 - 3674112x2 + 1048576 \( 2^{24}\cdot 3^{28}\cdot 7^{12}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 224]$ (GRH)
24.0.605...625.1 x24 - 6x23 + 78x22 - 392x21 + 2556x20 - 10386x19 + 44933x18 - 145902x17 + 460860x16 - 1187632x15 + 2848656x14 - 5775900x13 + 10594843x12 - 16507914x11 + 22656126x10 - 25834416x9 + 25004868x8 - 19088658x7 + 12519519x6 - 6912450x5 + 4180536x4 - 1559448x3 + 473328x2 + 44928x + 251136 \( 3^{28}\cdot 5^{12}\cdot 7^{12}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[8, 120]$ (GRH)
24.0.235...000.1 x24 + 2x22 - 19x20 - 92x18 + 68x16 + 1152x14 + 1920x12 + 18432x10 + 17408x8 - 376832x6 - 1245184x4 + 2097152x2 + 16777216 \( 2^{48}\cdot 3^{12}\cdot 5^{12}\cdot 71^{8} \) $C_2^3\times S_3$ (as 24T30) $[4, 4, 88]$ (GRH)
24.0.300...000.1 x24 - 12x23 + 138x22 - 1012x21 + 6567x20 - 33792x19 + 152944x18 - 586476x17 + 1983438x16 - 5828596x15 + 15127302x14 - 34412484x13 + 68977551x12 - 121089960x11 + 185961780x10 - 248010596x9 + 285514431x8 - 280702824x7 + 232942588x6 - 160321752x5 + 89445036x4 - 39017264x3 + 12566880x2 - 2673888x + 283024 \( 2^{36}\cdot 3^{28}\cdot 5^{12}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 330]$ (GRH)
24.0.659...625.1 x24 - 6x23 + 66x22 - 298x21 + 1755x20 - 6246x19 + 25559x18 - 73254x17 + 224988x16 - 510168x15 + 1140603x14 - 2014104x13 + 3960599x12 - 7179042x11 + 15967722x10 - 21892554x9 + 36438585x8 - 40807974x7 + 29748257x6 + 14966094x5 - 28976136x4 - 5965108x3 + 9478257x2 + 4458276x + 700144 \( 3^{28}\cdot 5^{12}\cdot 7^{12}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[6, 210]$ (GRH)
24.0.327...000.1 x24 - 66x22 - 8x21 + 1860x20 + 408x19 - 27668x18 - 7488x17 + 237498x16 + 58984x15 - 1240668x14 - 180132x13 + 4010886x12 + 120480x11 - 6473694x10 + 596120x9 + 3024492x8 - 1421952x7 - 2459420x6 - 3154656x5 + 26476854x4 + 21395960x3 - 17515860x2 - 7883700x + 15732025 \( 2^{36}\cdot 3^{28}\cdot 5^{12}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[6, 12, 24]$ (GRH)
24.0.170...376.1 x24 + 66x22 - 12x21 + 1755x20 - 336x19 + 24476x18 - 4968x17 + 201618x16 - 52032x15 + 1010118x14 - 380748x13 + 3016387x12 - 1771632x11 + 4911816x10 - 4596408x9 + 3744627x8 - 5693616x7 - 1016220x6 - 1840104x5 + 1692972x4 + 7178544x3 - 3071232x2 - 2969568x + 1434384 \( 2^{36}\cdot 3^{28}\cdot 7^{12}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 8, 144]$ (GRH)
24.0.170...376.2 x24 + 78x22 + 2421x20 + 39474x18 + 376092x16 + 2183742x14 + 7748525x12 + 16261674x10 + 18591153x8 + 9415392x6 + 875496x4 + 15840x2 + 16 \( 2^{36}\cdot 3^{28}\cdot 7^{12}\cdot 23^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 4, 240]$ (GRH)
24.0.122...000.1 x24 + 4x22 - 20x20 - 83x18 + 320x16 + 256x14 - 7552x12 + 4096x10 + 81920x8 - 339968x6 - 1310720x4 + 4194304x2 + 16777216 \( 2^{24}\cdot 3^{12}\cdot 5^{12}\cdot 7^{12}\cdot 67^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 2, 660]$ (GRH)
24.0.185...736.1 x24 - 6x22 - 12x21 + 165x20 + 180x19 - 226x18 + 648x17 - 23244x16 - 117288x15 - 222138x14 + 219384x13 + 547477x12 + 5606064x11 + 28237566x10 + 14850228x9 + 29776521x8 + 106963380x7 - 310672020x6 - 76948200x5 + 606651408x4 - 581982480x3 + 263674800x2 - 63828000x + 7110000 \( 2^{36}\cdot 3^{28}\cdot 7^{12}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 42, 42]$ (GRH)
24.0.185...736.2 x24 + 42x22 - 12x21 + 813x20 - 108x19 + 7686x18 - 4968x17 + 40332x16 + 18648x15 + 488070x14 + 450648x13 + 1146125x12 - 386640x11 + 8799702x10 + 24955764x9 + 57927489x8 + 41923764x7 + 48457788x6 + 171593352x5 + 718221312x4 + 1401006960x3 + 1828544112x2 + 1355445792x + 600532528 \( 2^{36}\cdot 3^{28}\cdot 7^{12}\cdot 31^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 42, 42]$ (GRH)
24.0.457...000.1 x24 - 8x23 + 102x22 - 612x21 + 4179x20 - 19236x19 + 89532x18 - 321504x17 + 1103631x16 - 3152176x15 + 8359414x14 - 19416180x13 + 40793493x12 - 76852756x11 + 129341224x10 - 193089256x9 + 258275000x8 - 296026256x7 + 300495808x6 - 266701408x5 + 208845136x4 - 178117888x3 + 171891200x2 - 95447040x + 58491904 \( 2^{24}\cdot 3^{12}\cdot 5^{12}\cdot 7^{12}\cdot 79^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 66572]$ (GRH)
24.0.796...000.1 x24 - 8x23 + 94x22 - 540x21 + 3479x20 - 15300x19 + 67880x18 - 232592x17 + 760111x16 - 2060912x15 + 5198726x14 - 11410156x13 + 22425193x12 - 38226676x11 + 56373604x10 - 71188168x9 + 74723232x8 - 45518288x7 - 37167216x6 + 150845152x5 - 182838480x4 - 18130304x3 + 316436992x2 - 338027520x + 142468096 \( 2^{36}\cdot 3^{12}\cdot 5^{12}\cdot 7^{12}\cdot 71^{8} \) $C_2^3\times S_3$ (as 24T30) $[2, 2, 2, 40612]$ (GRH)
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