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Results (displaying all 16 matches)

Label Polynomial Discriminant Galois group Class group
18.4.169287115250035851264.1 x18 - x14 + 3x12 - 9x10 - 2x8 - 24x6 - 9x4 - x2 + 1 \( -\,2^{24}\cdot 3^{6}\cdot 7^{12} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial
18.4.303256405652583481344.1 x18 - 3x16 + 6x14 - 4x12 - 3x10 + 9x8 - 15x6 - 3x4 + 3x2 + 1 \( -\,2^{30}\cdot 3^{24} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial
18.2.2426051245220667850752.1 x18 + 6x16 + 18x14 + 38x12 + 57x10 + 60x8 + 37x6 - 6x4 - 24x2 - 8 \( 2^{33}\cdot 3^{24} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial
18.2.4501668940782471645733.1 x18 - 2x17 + 2x16 + 2x15 + 4x13 + x12 + 4x11 + 4x10 + 8x8 + 10x7 - 5x6 + 12x5 - 4x4 + 5x3 + 1 \( 7^{12}\cdot 13^{3}\cdot 23^{6} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial
18.0.9543175480174580217820007.1 x18 - 2x17 + 5x16 - 8x15 + 14x14 - 30x13 + 44x12 - 77x11 + 106x10 - 211x9 + 270x8 - 400x7 + 344x6 - 304x5 + 544x4 - 64x3 + 768x2 + 512 \( -\,7^{12}\cdot 23^{6}\cdot 167^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.6.12150082333447607737387549.1 x18 - 2x17 - 4x16 + 22x15 + 26x14 - 60x13 - 67x12 + 178x11 + 118x10 - 226x9 - 150x8 + 140x7 + 95x6 - 82x5 - 44x4 + 17x3 + 12x2 - 1 \( 7^{12}\cdot 23^{6}\cdot 181^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.6.16970877618561921677524992.1 x18 - 6x17 + 15x16 - 6x15 - 111x14 + 510x13 - 1182x12 + 1260x11 + 1002x10 - 6382x9 + 13323x8 - 19698x7 + 23997x6 - 22986x5 + 14415x4 - 4578x3 + 426x2 + 54x - 1 \( 2^{24}\cdot 3^{30}\cdot 17^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial
18.0.50912632855685765032574976.1 x18 + 3x16 - 24x15 + 15x14 - 18x13 + 348x12 - 30x11 + 60x10 - 2302x9 - 1107x8 - 294x7 + 7647x6 + 11526x5 + 15561x4 + 16230x3 + 14298x2 + 9978x + 5041 \( -\,2^{24}\cdot 3^{31}\cdot 17^{3} \) $C_2\times S_3\times A_4$ (as 18T60) $[2, 2]$
18.12.80421398252924334225227776.1 x18 - 3x16 - 35x14 + 95x12 + 212x10 - 555x8 + 380x6 - 90x4 + 2x2 + 1 \( -\,2^{18}\cdot 7^{12}\cdot 53^{6} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.12.109801113396081548259298319.1 x18 - 4x17 - 6x16 + 16x15 + 52x14 - 12x13 - 205x12 + 246x11 + 491x10 - 1017x9 - 970x8 + 886x7 + 539x6 - 344x5 - 72x4 + 58x3 - 6x2 - 3x + 1 \( -\,7^{12}\cdot 53^{6}\cdot 71^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.6.279992823820843547402730217.1 x18 - 4x17 + 17x16 - 57x15 + 140x14 - 389x13 + 418x12 - 390x11 - 814x10 + 1436x9 + 128x8 + 978x7 + 224x6 + 111x5 + 144x4 - 21x3 + 10x2 + 2x - 1 \( 7^{12}\cdot 53^{6}\cdot 97^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.18.1819145441046500375949998389.1 x18 - 4x17 - 25x16 + 105x15 + 200x14 - 957x13 - 568x12 + 4008x11 - 85x10 - 8113x9 + 2772x8 + 7493x7 - 3445x6 - 3093x5 + 1357x4 + 499x3 - 146x2 - x + 1 \( 7^{12}\cdot 53^{6}\cdot 181^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.6.23969878594169966578599985152.1 x18 + 3x16 - 75x14 - 585x12 - 1620x10 - 1737x8 - 213x6 + 423x4 + 27x2 - 3 \( 2^{18}\cdot 3^{31}\cdot 23^{6} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.18.363795314284140453335088294421.1 x18 - 8x17 - 9x16 + 207x15 - 213x14 - 1907x13 + 3519x12 + 7244x11 - 18098x10 - 9525x9 + 36868x8 + 3181x7 - 35376x6 + 2017x5 + 15769x4 - 1586x3 - 2460x2 + 432x + 27 \( 7^{14}\cdot 67^{6}\cdot 181^{3} \) $C_2\times S_3\times A_4$ (as 18T60) Trivial (GRH)
18.0.677479543132411644552981573632.1 x18 - 10x16 - 5x15 + 84x14 - 15x13 - 186x12 - 92x11 + 1232x10 - 405x9 + 2987x8 - 2817x7 + 13566x6 + 895x5 + 29602x4 - 626x3 + 31305x2 - 11895x + 61027 \( -\,2^{12}\cdot 7^{12}\cdot 37^{6}\cdot 167^{3} \) $C_2\times S_3\times A_4$ (as 18T60) $[216]$ (GRH)
18.0.7262160664015682731094650299851.1 x18 - 8x17 + 24x16 - 23x15 + 40x14 - 380x13 + 1228x12 - 1433x11 + 1810x10 - 8213x9 + 24013x8 - 34802x7 + 62185x6 - 114144x5 + 281649x4 - 476930x3 + 979440x2 - 520209x + 692091 \( -\,7^{14}\cdot 67^{6}\cdot 491^{3} \) $C_2\times S_3\times A_4$ (as 18T60) $[2, 298]$ (GRH)


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