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Label Polynomial Discriminant Galois group Class group
8.0.15587564.1 x8 - 3x7 + 7x6 - 11x5 + 15x4 - 17x3 + 15x2 - 8x + 2 \( 2^{2}\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.33276059.1 x8 - x7 + x6 - 3x5 + 3x4 + 2x3 + 4x2 + 2x - 1 \( -\,59\cdot 751^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.56103513.1 x8 - 3x7 + 8x6 - 11x5 + 13x4 - 11x3 + 8x2 - 3x + 1 \( 3\cdot 59\cdot 563^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.74040929.1 x8 - x7 + x5 - 8x4 + 2x3 + 13x2 + 4x + 1 \( 19\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.85988193.1 x8 - 2x7 - x6 + 6x4 - 7x3 + 10x2 - 5x + 1 \( 3\cdot 17^{2}\cdot 41^{2}\cdot 59 \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.89628493.1 x8 - x7 + 2x6 - 6x5 + 10x4 - 13x3 + 18x2 - 17x + 8 \( 23\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.136672556.1 x8 - 2x7 - x6 + 10x5 - 8x4 - 7x3 + 15x2 - 7x + 1 \( 2^{2}\cdot 59\cdot 761^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.148782896.1 x8 - 3x7 + 5x6 - x5 - 5x4 + 10x3 + 3x2 - 8x - 4 \( -\,2^{4}\cdot 59\cdot 397^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.239176973.1 x8 - x7 - x6 - x5 + 5x4 + 2x3 + 2x2 + x + 2 \( 7\cdot 59\cdot 761^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.276679261.1 x8 - 4x7 + 3x6 + 5x5 - 3x4 - 7x3 - 7x2 + 12x + 13 \( 59\cdot 71\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.281009920.1 x8 - 4x7 + 7x6 - 2x5 - 14x4 + 32x3 - 34x2 + 20x - 5 \( -\,2^{8}\cdot 5\cdot 59\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.282792192.1 x8 - 4x7 + 6x6 - 4x5 + 4x4 - 6x3 + 5x2 - 2x + 1 \( 2^{8}\cdot 3\cdot 59\cdot 79^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.307782704.1 x8 - 4x7 + 9x6 - 13x5 + 19x4 - 21x3 + 20x2 - 11x + 2 \( -\,2^{4}\cdot 59\cdot 571^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.316591817.1 x8 - x6 - 7x5 - 6x4 + 5x3 + 23x2 + 35x + 17 \( 59\cdot 67\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) $[2]$
8.2.317919907.1 x8 - 5x6 - 6x5 + 13x4 + 33x3 + 19x2 - x - 3 \( -\,17\cdot 59\cdot 563^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.323441953.2 x8 - 4x7 + 10x6 - 16x5 + 20x4 - 18x3 + 20x2 - 13x + 22 \( 59\cdot 83\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.339035712.1 x8 - 3x7 + 4x6 - 5x5 + 8x4 - 3x3 - 3x2 + 4 \( 2^{6}\cdot 3\cdot 59\cdot 173^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.356301295.1 x8 - x7 + x5 - 3x4 - x3 + 2x2 - 5x - 1 \( -\,5\cdot 7^{2}\cdot 59\cdot 157^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.365218496.1 x8 - 2x7 + x6 + 5x5 - 8x4 - 3x3 + 5x2 + 7x + 1 \( -\,2^{6}\cdot 59\cdot 311^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.382745331.1 x8 - 4x7 + 9x6 - 11x5 - 4x4 + 16x3 - 30x2 - 19x - 11 \( -\,3^{4}\cdot 59\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.392195833.1 x8 - 4x7 + 6x6 - 4x5 - x4 + 4x3 + 13x2 - 15x + 23 \( 59\cdot 83\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) $[2]$
8.0.405276664.1 x8 - 3x7 + 13x5 - 13x4 - 27x3 + 21x2 + 35x + 11 \( 2^{3}\cdot 13\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.425978171.1 x8 - 2x7 - x6 - 4x4 - 8x3 - 5x2 - 5x - 2 \( -\,59\cdot 2687^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.4.429997841.1 x8 - 7x6 - 4x5 + 23x4 + 2x3 - 25x2 + 6x + 11 \( 7\cdot 13\cdot 59\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.457946200.1 x8 - x7 + 6x5 - 8x4 - 2x3 + 16x2 - 15x + 5 \( 2^{3}\cdot 5^{2}\cdot 59\cdot 197^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.498821813.1 x8 - 3x7 + 4x6 + 3x5 - 6x4 + 3x3 + 12x2 - 14x + 7 \( 7^{3}\cdot 59\cdot 157^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.511013691.1 x8 - 4x7 + 9x6 - 13x5 + 7x4 + 3x3 - 15x2 + 12x - 3 \( -\,3^{6}\cdot 59\cdot 109^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.516385936.1 x8 - x7 - x6 + 6x5 - 7x4 + 3x3 + 15x2 - 28x + 16 \( 2^{4}\cdot 11\cdot 59\cdot 223^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.525351104.1 x8 - 3x7 + 5x6 - 4x5 + 4x3 - 5x2 + x + 3 \( 2^{6}\cdot 59\cdot 373^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.529977176.1 x8 - 3x7 + 7x6 - 17x5 + 14x4 - 2x3 + x2 + 26x + 19 \( 2^{3}\cdot 17\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.592327432.1 x8 - 2x7 - 7x6 + 18x5 + 10x4 - 54x3 + 3x2 + 56x + 22 \( 2^{3}\cdot 19\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.639090124.1 x8 - 3x7 + 6x6 - 10x5 + 4x3 + 35x2 - 54x + 38 \( 2^{2}\cdot 41\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) $[2]$
8.0.675710893.1 x8 - 4x7 + 16x6 - 31x5 + 64x4 - 71x3 + 99x2 - 54x + 61 \( 11\cdot 13\cdot 59\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) $[2]$
8.2.696559664.1 x8 - 4x7 + 9x6 - 13x5 + 11x4 - 5x3 + 10x2 - 9x + 2 \( -\,2^{4}\cdot 59\cdot 859^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.4.713512901.1 x8 - x7 - 9x6 + 5x5 + 34x4 - 22x3 - 39x2 + 21x + 17 \( 59\cdot 151\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.730625792.1 x8 - x6 + 3x4 - 6x3 - 17x2 - 18x - 5 \( -\,2^{8}\cdot 13\cdot 59\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.741864407.1 x8 + 6x6 - 7x5 + 17x4 - 44x3 + 16x2 - 56x - 16 \( -\,59\cdot 157\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.751106816.2 x8 - 2x7 + 6x6 - 14x5 + 13x4 - 10x3 + 12x2 - 8x + 3 \( 2^{8}\cdot 59\cdot 223^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.752370419.1 x8 - x7 - x6 + 3x5 + 2x3 + x2 - 5x - 3 \( -\,59\cdot 3571^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.760765411.1 x8 - 4x7 + 2x6 + 6x5 - 15x4 + 35x3 + 2x2 - 31x - 13 \( -\,7\cdot 23\cdot 59\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.775481309.1 x8 - 4x7 - x6 + 17x5 + 4x4 - 41x3 - 17x2 + 41x + 34 \( 59\cdot 199\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.777599232.1 x8 - 4x7 + 8x6 - 10x5 + 13x4 - 10x3 + 8x2 - 4x + 1 \( 2^{8}\cdot 3\cdot 59\cdot 131^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.858649125.1 x8 - 2x7 + 9x6 - 9x5 + 17x4 - 9x3 + 9x2 - 2x + 1 \( 3\cdot 5^{3}\cdot 59\cdot 197^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.859149504.1 x8 - x7 + 2x6 + 8x4 + 9x3 - x2 + 2x - 2 \( -\,2^{6}\cdot 3^{4}\cdot 53^{2}\cdot 59 \) $C_2 \wr S_4$ (as 8T44) trivial
8.4.876345644.1 x8 - x7 + 6x5 - 4x3 - 5x2 - 6x - 2 \( 2^{2}\cdot 41^{2}\cdot 47^{2}\cdot 59 \) $C_2 \wr S_4$ (as 8T44) trivial
8.2.899231744.1 x8 - 2x6 - 8x5 - 2x4 + 12x3 + 22x2 + 12x - 7 \( -\,2^{12}\cdot 59\cdot 61^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.902522941.1 x8 - 3x7 + 12x6 - 15x5 + 35x4 + 7x3 + 29x2 + 62x + 23 \( 59\cdot 191\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) $[2]$
8.6.935053299.1 x8 - x7 - 7x6 + 4x5 + 14x4 + 2x3 - 10x2 - 5x + 1 \( -\,3^{2}\cdot 59\cdot 1327^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
8.0.959225953.1 x8 - 3x7 + 8x6 - 13x5 + 11x4 - 9x3 - 20x2 + 11x + 67 \( 7\cdot 29\cdot 59\cdot 283^{2} \) $C_2 \wr S_4$ (as 8T44) $[2]$
8.0.962532077.1 x8 - x7 - 6x6 - 4x5 + 30x4 + 21x3 - 56x2 - 59x + 82 \( 13\cdot 19\cdot 59\cdot 257^{2} \) $C_2 \wr S_4$ (as 8T44) trivial
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