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Label Polynomial Discriminant Galois group Class group
18.0.923324627983045303.1 x18 - 4x17 + 10x16 - 17x15 + 24x14 - 28x13 + 28x12 - 22x11 + 14x10 - 8x9 + 5x8 - 3x7 + 2x6 - 3x5 + 2x4 + x3 - 2x2 + 1 \( -\,31^{6}\cdot 463\cdot 1499^{2} \) 18T912 Trivial
18.0.1115906277282951168.1 x18 - 4x17 + 14x16 - 31x15 + 64x14 - 100x13 + 146x12 - 176x11 + 202x10 - 205x9 + 202x8 - 176x7 + 146x6 - 100x5 + 64x4 - 31x3 + 14x2 - 4x + 1 \( -\,2^{12}\cdot 3^{9}\cdot 7^{12} \) $S_3 \times C_3$ (as 18T3) Trivial
18.0.1186012071116620699.1 x18 - 5x17 + 16x16 - 39x15 + 80x14 - 141x13 + 221x12 - 312x11 + 400x10 - 465x9 + 489x8 - 463x7 + 395x6 - 300x5 + 195x4 - 101x3 + 38x2 - 9x + 1 \( -\,7^{4}\cdot 139\cdot 1373^{4} \) 18T966 Trivial
18.0.1198241002273018867.1 x18 - 4x17 + 9x16 - 14x15 + 17x14 - 16x13 + 15x12 - 23x11 + 45x10 - 65x9 + 62x8 - 40x7 + 29x6 - 39x5 + 49x4 - 41x3 + 22x2 - 7x + 1 \( -\,31^{6}\cdot 67^{5} \) 18T284 Trivial
18.0.1417200615982289707.1 x18 - 3x17 + 6x16 - 9x15 + 12x14 - 15x13 + 21x12 - 29x11 + 36x10 - 38x9 + 36x8 - 32x7 + 31x6 - 32x5 + 30x4 - 23x3 + 13x2 - 5x + 1 \( -\,23^{6}\cdot 43^{3}\cdot 347^{2} \) 18T556 Trivial
18.0.1548507685660102467.1 x18 + 9x16 - 9x15 + 36x14 - 63x13 + 109x12 - 189x11 + 252x10 - 335x9 + 378x8 - 378x7 + 334x6 - 243x5 + 147x4 - 67x3 + 21x2 - 3x + 1 \( -\,3^{21}\cdot 23^{6} \) $C_3.S_3^2$ (as 18T57) Trivial
18.0.1678237502892756571.1 x18 - 2x17 + x16 + 5x15 - 10x14 + 5x13 + 13x12 - 29x11 + 24x10 + 9x9 - 48x8 + 56x7 - 16x6 - 44x5 + 74x4 - 60x3 + 29x2 - 8x + 1 \( -\,139\cdot 367^{2}\cdot 299401^{2} \) 18T968 Trivial
18.0.1963375693486812487.1 x18 - x17 - 7x15 + 5x14 + 6x13 + 21x12 - 29x11 - 13x10 - 11x9 + 49x8 - 8x7 - 3x6 - 24x5 + 14x4 + 3x3 - 3x + 1 \( -\,31^{6}\cdot 1303^{3} \) 18T314 Trivial
18.0.1999004627104432128.1 x18 - 6x17 + 24x16 - 68x15 + 159x14 - 300x13 + 479x12 - 630x11 + 702x10 - 636x9 + 480x8 - 270x7 + 114x6 - 12x5 - 12x4 + 14x3 - 3x2 + 1 \( -\,2^{18}\cdot 3^{27} \) $S_3 \times C_6$ (as 18T6) Trivial
18.0.2529990231179046912.1 x18 - 9x17 + 36x16 - 81x15 + 105x14 - 63x13 - 21x12 + 72x11 - 63x10 + 27x9 - 6x6 - 9x5 + 18x4 - 9x2 + 3 \( -\,2^{12}\cdot 3^{31} \) $S_3 \times C_3$ (as 18T3) Trivial
18.0.2745546730527991447.1 x18 - 5x17 + 12x16 - 17x15 + 12x14 - 2x13 + 8x12 - 46x11 + 111x10 - 168x9 + 188x8 - 173x7 + 137x6 - 102x5 + 70x4 - 40x3 + 19x2 - 5x + 1 \( -\,23^{6}\cdot 2647^{3} \) 18T314 Trivial
18.0.3190851810094053743.1 x18 - 5x17 + 15x16 - 36x15 + 75x14 - 137x13 + 221x12 - 312x11 + 384x10 - 411x9 + 384x8 - 312x7 + 221x6 - 137x5 + 75x4 - 36x3 + 15x2 - 5x + 1 \( -\,11^{6}\cdot 23^{9} \) 18T221 Trivial
18.0.4052555153018976267.1 x18 - 3x15 + 15x12 + 20x9 + 33x6 + 6x3 + 1 \( -\,3^{39} \) $S_3 \times C_3$ (as 18T3) Trivial
18.0.4558310746519570263.1 x18 + 6x16 - 2x15 + 15x14 - 10x13 + 22x12 - 20x11 + 23x10 - 20x9 + 18x8 - 10x7 + 9x6 - 2x5 + 2x4 - x3 - x + 1 \( -\,3^{9}\cdot 229\cdot 433^{3}\cdot 12457 \) 18T951 Trivial
18.2.4837319251866194741.1 x18 - 3x17 + 2x16 - 5x15 + 15x14 - 6x13 + 2x12 - 29x11 + 17x10 + 11x9 + 17x8 - 29x7 + 2x6 - 6x5 + 15x4 - 5x3 + 2x2 - 3x + 1 \( 23^{6}\cdot 59^{2}\cdot 149\cdot 251^{2} \) 18T912 Trivial
18.0.5040742784941043712.1 x18 - x15 + 2x12 - 9x9 + 12x6 - 5x3 + 1 \( -\,2^{12}\cdot 3^{21}\cdot 7^{6} \) $C_3\times C_3:S_3$ (as 18T23) Trivial
18.0.5132738882980786176.1 x18 - 6x17 + 16x16 - 20x15 - 2x14 + 51x13 - 87x12 + 64x11 + 16x10 - 108x9 + 181x8 - 232x7 + 253x6 - 224x5 + 154x4 - 79x3 + 29x2 - 7x + 1 \( -\,2^{12}\cdot 3^{12}\cdot 11^{9} \) $C_3\times C_3:S_3$ (as 18T23) Trivial
18.0.5460912335827351107.1 x18 - 9x17 + 35x16 - 76x15 + 100x14 - 84x13 + 57x12 - 56x11 + 62x10 - 35x9 + 3x8 - 28x7 + 63x6 - 32x5 - 10x3 + 16x2 - 7x + 1 \( -\,3^{9}\cdot 23^{6}\cdot 37^{4} \) $C_3\wr S_3:C_2$ (as 18T137) Trivial
18.0.5585027926119911424.1 x18 - 2x17 + 5x16 - 7x15 + 10x14 - 13x13 + 17x12 - 24x11 + 28x10 - 28x9 + 25x8 - 24x7 + 28x6 - 31x5 + 29x4 - 22x3 + 13x2 - 5x + 1 \( -\,2^{12}\cdot 3^{12}\cdot 37^{6} \) 18T189 Trivial
18.0.6107453226347659264.1 x18 + 5x16 + 12x14 + 29x12 + 55x10 + 57x8 + 39x6 + 22x4 + 8x2 + 1 \( -\,2^{18}\cdot 13^{12} \) $S_3 \times C_3$ (as 18T3) Trivial
18.0.6222062031041447163.1 x18 - 4x15 + 6x12 - 5x9 + 6x6 - 4x3 + 1 \( -\,3^{21}\cdot 29^{6} \) $C_2\times C_3\wr S_3$ (as 18T119) Trivial
18.2.6425148232879087321.1 x18 - 2x17 - x16 + 6x15 - 4x14 - 10x13 + 11x12 + 9x11 - 16x10 - 5x9 + 16x8 + 5x7 - 15x6 - 5x5 + 12x4 + x3 - 5x2 + 1 \( 23^{6}\cdot 208333^{2} \) 18T776 Trivial
18.0.6646436567333419399.1 x18 - 9x17 + 42x16 - 132x15 + 310x14 - 574x13 + 865x12 - 1082x11 + 1139x10 - 1020x9 + 787x8 - 532x7 + 321x6 - 174x5 + 85x4 - 37x3 + 14x2 - 4x + 1 \( -\,17^{2}\cdot 43^{2}\cdot 2311\cdot 73363^{2} \) 18T968 Trivial
18.2.7182890828838813137.1 x18 - 5x17 + 12x16 - 22x15 + 39x14 - 63x13 + 85x12 - 97x11 + 99x10 - 98x9 + 91x8 - 71x7 + 53x6 - 44x5 + 29x4 - 15x3 + 10x2 - 4x + 1 \( 7^{12}\cdot 113\cdot 2143^{2} \) 18T879 Trivial
18.0.8173509334225000000.1 x18 + x16 - 6x14 - 5x12 + 2x10 + 7x8 + 18x6 + 7x4 - 3x2 + 1 \( -\,2^{6}\cdot 5^{8}\cdot 83^{6} \) $C_2\times (C_3\times A_4):S_3$ (as 18T156) Trivial
18.2.8678645063271073481.1 x18 - x17 + 2x16 - 5x15 + x14 - 6x13 + 2x12 + 4x10 + 3x9 + 4x8 + 2x6 - 6x5 + x4 - 5x3 + 2x2 - x + 1 \( 41^{3}\cdot 11221481^{2} \) 18T968 Trivial
18.2.8975765936889758489.1 x18 - x17 + 3x15 - x14 + x13 + 7x12 + 2x11 + 3x10 + 11x9 + 3x8 + 2x7 + 7x6 + x5 - x4 + 3x3 - x + 1 \( 7^{12}\cdot 41^{3}\cdot 97^{2} \) 18T472 Trivial
18.0.9283601972222640243.1 x18 - 9x16 - 11x15 + 21x14 + 69x13 + 54x12 - 75x11 - 219x10 - 205x9 - 6x8 + 231x7 + 342x6 + 303x5 + 201x4 + 103x3 + 39x2 + 9x + 1 \( -\,3^{21}\cdot 31^{6} \) $C_3.S_3^2$ (as 18T57) Trivial
18.0.9291932134821949543.1 x18 - 4x17 + 10x16 - 21x15 + 37x14 - 58x13 + 80x12 - 97x11 + 107x10 - 106x9 + 92x8 - 71x7 + 52x6 - 39x5 + 30x4 - 20x3 + 11x2 - 4x + 1 \( -\,7^{15}\cdot 1399^{2} \) 18T286 Trivial
18.0.9651146816936671875.1 x18 - 9x17 + 36x16 - 78x15 + 84x14 - 111x12 + 90x11 + 72x10 - 156x9 + 45x8 + 81x7 - 57x6 - 27x5 + 36x4 - 9x2 + 3 \( -\,3^{31}\cdot 5^{6} \) $S_3 \times C_6$ (as 18T6) Trivial
18.0.10383286663954563863.1 x18 - 4x17 + 11x16 - 22x15 + 36x14 - 53x13 + 80x12 - 116x11 + 154x10 - 173x9 + 154x8 - 116x7 + 80x6 - 53x5 + 36x4 - 22x3 + 11x2 - 4x + 1 \( -\,7^{8}\cdot 23^{9} \) $D_9:C_3$ (as 18T18) Trivial
18.0.10490638424730354432.1 x18 - 4x17 + 11x16 - 20x15 + 31x14 - 41x13 + 56x12 - 69x11 + 64x10 - 59x9 + 49x8 - 48x7 + 28x6 - 5x5 + 17x4 - 5x3 - 2x2 - x + 1 \( -\,2^{8}\cdot 3^{9}\cdot 113^{6} \) $C_2\times C_3^2:S_3$ (as 18T52) Trivial
18.0.10839257382142572103.1 x18 - 3x17 + 6x16 - 6x15 - 2x14 + 21x13 - 47x12 + 61x11 - 35x10 - 37x9 + 119x8 - 155x7 + 130x6 - 79x5 + 43x4 - 27x3 + 16x2 - 6x + 1 \( -\,7^{15}\cdot 1511^{2} \) 18T286 Trivial
18.2.10910724785335819009.1 x18 - 2x17 + 4x15 - 7x14 + x13 + 7x12 + 2x11 - 10x10 + x9 + 20x8 - 22x7 - 2x6 + 7x5 + 2x4 - 10x3 + 11x2 - 5x + 1 \( 43^{2}\cdot 83\cdot 107\cdot 311^{2}\cdot 2621^{2} \) 18T968 Trivial
18.2.10913148516977234837.1 x18 - x17 + 3x16 - 5x15 + 4x14 - 6x13 - 5x12 - 2x11 - 16x10 + x9 - 16x8 - 2x7 - 5x6 - 6x5 + 4x4 - 5x3 + 3x2 - x + 1 \( 53\cdot 453771377^{2} \) 18T968 Trivial
18.2.10992670662263790889.1 x18 - x16 - 4x15 - x14 + 3x13 + 9x12 + x11 - 2x10 - 13x9 - 2x8 + x7 + 9x6 + 3x5 - x4 - 4x3 - x2 + 1 \( 23^{6}\cdot 379^{2}\cdot 719^{2} \) 18T776 Trivial
18.0.11126075312143749771.1 x18 - 8x17 + 28x16 - 54x15 + 55x14 - 8x13 - 55x12 + 69x11 - 19x10 - 37x9 + 44x8 - 16x7 - 6x6 + 15x5 - 14x4 + 3x3 + 7x2 - 5x + 1 \( -\,3^{4}\cdot 11^{5}\cdot 31^{8} \) 18T485 Trivial
18.0.11436479389438477403.1 x18 - 4x17 + 7x16 - 9x15 + 15x14 - 24x13 + 28x12 - 30x11 + 36x10 - 39x9 + 36x8 - 30x7 + 28x6 - 24x5 + 15x4 - 9x3 + 7x2 - 4x + 1 \( -\,23^{6}\cdot 43^{2}\cdot 347^{3} \) 18T556 Trivial
18.2.11675081596366988689.1 x18 - 4x17 + 4x16 + 9x15 - 27x14 + 17x13 + 26x12 - 46x11 + 12x10 + 20x9 - 12x8 + 15x7 - 48x6 + 48x5 - x4 - 29x3 + 20x2 - 5x + 1 \( 5881\cdot 44555813^{2} \) 18T968 Trivial
18.0.12213256064722484031.1 x18 - 3x17 - 3x16 + 9x15 + 24x14 - 30x13 - 78x12 + 60x11 + 141x10 - 56x9 - 150x8 + 12x7 + 81x6 + 12x5 - 15x4 - 3x3 + 3x2 + 3x + 1 \( -\,3^{33}\cdot 13^{3} \) $C_3\times S_3\wr C_2$ (as 18T93) Trivial
18.0.12619972448180608967.1 x18 - 3x17 + 6x16 - 7x15 + 4x14 + 2x13 - 4x12 - 3x11 + 14x10 - 19x9 + 17x8 - 6x7 - 10x6 + 18x5 - 9x4 - 6x3 + 10x2 - 5x + 1 \( -\,23^{9}\cdot 2647^{2} \) 18T319 Trivial
18.0.12827848719622496283.1 x18 - 3x17 + 6x16 - 9x15 + 3x14 + 18x13 - 47x12 + 90x11 - 87x10 + 43x9 + 63x8 - 186x7 + 274x6 - 270x5 + 198x4 - 106x3 + 39x2 - 9x + 1 \( -\,3^{27}\cdot 1297^{2} \) 18T286 Trivial
18.0.12906538539418320896.1 x18 - 9x17 + 41x16 - 124x15 + 276x14 - 476x13 + 646x12 - 678x11 + 517x10 - 231x9 - 15x8 + 98x7 - 48x6 - 18x5 + 36x4 - 22x3 + 9x2 - 3x + 1 \( -\,2^{16}\cdot 11^{9}\cdot 17^{4} \) $C_3\wr C_3:C_2$ (as 18T88) Trivial
18.0.13415474159898041623.1 x18 - 6x17 + 15x16 - 23x15 + 37x14 - 78x13 + 152x12 - 240x11 + 302x10 - 308x9 + 300x8 - 298x7 + 220x6 - 85x5 + 25x4 - 26x3 + 12x2 + 1 \( -\,7^{15}\cdot 41^{4} \) $C_3^3:C_6$ (as 18T85) Trivial
18.0.13950087665617805207.1 x18 - x17 + 4x15 - 5x14 + x13 + 6x12 - 9x11 + 7x10 + x9 - 12x8 + 11x7 - 2x6 - 5x5 + 6x4 - x3 - x2 - x + 1 \( -\,11^{4}\cdot 23^{11} \) 18T217 Trivial
18.0.14929107797061341783.1 x18 - x17 - x16 + x15 + 3x14 + 2x13 - 5x12 + 4x11 + 5x10 + 5x9 + 6x8 - 4x7 + 8x6 - 5x5 + 5x4 + x3 + 2x2 - x + 1 \( -\,23^{9}\cdot 2879^{2} \) 18T319 Trivial
18.2.15335719659532189696.1 x18 + 5x16 + 5x14 - 8x12 - 8x10 + 17x8 + 19x6 + x4 - 2x2 - 1 \( 2^{18}\cdot 37^{6}\cdot 151^{2} \) 18T483 Trivial
18.0.16230968037754638343.1 x18 - x17 - 5x16 + 9x15 + 2x14 - 32x13 + 37x12 + 40x11 - 100x10 + 31x9 + 83x8 - 97x7 + 27x6 + 18x5 - 15x4 + 5x2 - 3x + 1 \( -\,7^{15}\cdot 43^{4} \) $C_3^3:C_6$ (as 18T85) Trivial
18.0.16369786239449258043.1 x18 - 3x15 - 3x12 + 20x9 + 33x6 - 12x3 + 1 \( -\,3^{30}\cdot 43^{3} \) $C_3\times S_3\wr C_2$ (as 18T93) Trivial
18.0.16481672572799864375.1 x18 + 2x16 - x15 - 5x14 - 5x12 + 10x11 - 11x10 + 19x9 - 8x8 - 17x7 + 46x6 - 57x5 + 52x4 - 37x3 + 14x2 - 3x + 1 \( -\,5^{4}\cdot 11^{4}\cdot 23^{9} \) $C_3\wr C_3:C_2$ (as 18T88) Trivial

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