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Label Polynomial Discriminant Galois group Class group
10.0.64248054784.1 x10 - 4x9 + 11x8 - 22x7 + 41x6 - 62x5 + 80x4 - 78x3 + 57x2 - 28x + 8 \( -\,2^{10}\cdot 89^{4} \) $S_5$ (as 10T12) Trivial
10.2.131220000000.1 x10 - 3x9 + 5x8 - 17x6 + 33x5 - 17x4 + 5x2 - 3x + 1 \( 2^{8}\cdot 3^{8}\cdot 5^{7} \) $S_5$ (as 10T12) Trivial
10.0.175784940288.1 x10 - 5x9 + 3x8 + 14x7 - 5x6 - 27x5 - 7x4 + 26x3 + 25x2 + 9x + 3 \( -\,2^{8}\cdot 3^{5}\cdot 41^{4} \) $S_5$ (as 10T12) Trivial
10.2.256461670625.1 x10 - 2x9 + 2x8 - 7x6 + 13x5 - 7x4 + 2x2 - 2x + 1 \( 5^{4}\cdot 17^{7} \) $S_5$ (as 10T12) Trivial
10.0.260807798403.2 x10 - x9 - 4x8 + 9x7 + 10x6 - 25x5 - 6x4 + 13x3 + 28x2 - 33x + 9 \( -\,3^{5}\cdot 181^{4} \) $S_5$ (as 10T12) $[2]$
10.2.262608484333.1 x10 - 4x9 + 3x8 + 9x7 - 12x6 - 9x5 + 17x4 - x3 - 4x2 - 5x + 1 \( 13^{5}\cdot 29^{4} \) $S_5$ (as 10T12) Trivial
10.2.276654003125.1 x10 - 4x9 + 2x8 + 8x7 - 4x6 - 21x5 + 48x4 - 58x3 + 24x2 - 4x - 1 \( 5^{5}\cdot 97^{4} \) $S_5$ (as 10T12) Trivial
10.2.292820000000.2 x10 - x9 + x8 + 6x7 - x6 - 13x5 - x4 + 6x3 + x2 - x + 1 \( 2^{8}\cdot 5^{7}\cdot 11^{4} \) $S_5$ (as 10T12) Trivial
10.0.461008408576.1 x10 + 6x8 - 12x7 + 13x6 - 8x5 + 13x4 - 12x3 + 6x2 + 1 \( -\,2^{12}\cdot 103^{4} \) $S_5$ (as 10T12) Trivial
10.2.626668503125.2 x10 + 3x8 + 22x6 - 11x5 + 9x4 - 4x3 + 9x2 - 3x - 1 \( 5^{5}\cdot 7^{4}\cdot 17^{4} \) $S_5$ (as 10T12) Trivial
10.2.639589548032.2 x10 - 4x9 + 6x8 - 10x7 + 23x6 - 36x5 + 51x4 - 66x3 + 56x2 - 36x + 17 \( 2^{17}\cdot 47^{4} \) $S_5$ (as 10T12) Trivial
10.0.663963962112.1 x10 - 4x9 + 2x8 + 12x7 - 22x6 + 4x5 + 36x4 - 56x3 + 44x2 - 20x + 4 \( -\,2^{8}\cdot 3^{11}\cdot 11^{4} \) $S_5$ (as 10T12) Trivial
10.2.714892578125.2 x10 + 5x6 - 33x5 + 75x4 - 115x3 + 110x2 - 55x + 11 \( 5^{11}\cdot 11^{4} \) $S_5$ (as 10T12) Trivial
10.0.785877504731.1 x10 + x8 - 2x7 + 21x5 + 49x4 - 8x3 - 17x2 + 11x + 11 \( -\,11^{5}\cdot 47^{4} \) $S_5$ (as 10T12) Trivial
10.0.861322076928.1 x10 + 4x8 - 8x7 + 10x6 - 22x5 + 40x4 - 24x3 + 60x2 - 36x + 36 \( -\,2^{8}\cdot 3^{5}\cdot 61^{4} \) $S_5$ (as 10T12) Trivial
10.2.946668828125.1 x10 - 4x9 + 6x8 + x7 - 21x6 + 35x5 - 29x4 - 14x3 + 16x2 - 16x - 16 \( 5^{7}\cdot 59^{4} \) $S_5$ (as 10T12) Trivial
10.0.958348132352.1 x10 - 2x9 + 3x8 - x6 + 2x5 - x4 + 3x2 - 2x + 1 \( -\,2^{25}\cdot 13^{4} \) $S_5$ (as 10T12) Trivial
10.0.964497618243.1 x10 + x8 - x7 - 17x5 - x4 + 5x3 - 11x2 + 30x + 36 \( -\,3^{5}\cdot 251^{4} \) $S_5$ (as 10T12) Trivial
10.2.1015264874437.1 x10 - 4x9 + 11x8 - 20x7 + 73x5 - 227x4 + 454x3 - 515x2 + 445x - 271 \( 11^{4}\cdot 37^{5} \) $S_5$ (as 10T12) Trivial
10.2.1230700078125.1 x10 - x8 + 16x6 - 6x4 + 36x2 - 45 \( 3^{8}\cdot 5^{7}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
10.2.1343692800000.3 x10 - x9 + 5x8 - 10x7 + 9x6 - 19x5 - 9x4 - 22x3 - 5x2 + 23x + 59 \( 2^{16}\cdot 3^{8}\cdot 5^{5} \) $S_5$ (as 10T12) Trivial
10.0.1410076263168.1 x10 + 2x8 - 12x7 + 16x6 - 6x5 + 12x4 - 48x3 + 108x2 - 72x + 36 \( -\,2^{8}\cdot 3^{9}\cdot 23^{4} \) $S_5$ (as 10T12) Trivial
10.2.1670420000000.1 x10 - x9 + x8 - 4x7 + 14x6 - 38x5 + 14x4 - 4x3 + x2 - x + 1 \( 2^{8}\cdot 5^{7}\cdot 17^{4} \) $S_5$ (as 10T12) Trivial
10.2.1875781250000.1 x10 - 5x6 - 28x5 - 5x4 + 1 \( 2^{4}\cdot 5^{11}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
10.0.1912538334375.1 x10 + 2x8 - 3x7 + 17x6 - 20x5 + 22x4 - 26x3 + 22x2 - x + 1 \( -\,3^{7}\cdot 5^{5}\cdot 23^{4} \) $S_5$ (as 10T12) $[2]$
10.2.2339717120000.1 x10 + 4x8 - 2x7 + 5x6 + 4x5 + 5x4 + 10x3 - 22x2 - 12x + 9 \( 2^{17}\cdot 5^{4}\cdot 13^{4} \) $S_5$ (as 10T12) Trivial
10.2.3116068382096.1 x10 - 2x9 + 7x8 - 6x7 + 9x6 + 14x5 - 14x4 + 42x3 + 8 \( 2^{4}\cdot 41^{7} \) $S_5$ (as 10T12) Trivial
10.2.3200000000000.2 x10 - 5x9 + 15x8 - 30x7 + 45x6 - 51x5 + 45x4 - 30x3 + 55x2 - 45x + 9 \( 2^{16}\cdot 5^{11} \) $S_5$ (as 10T12) Trivial
10.0.3247296480000.1 x10 - 2x9 - 12x7 + 26x6 - 14x5 + 32x4 - 28x3 + 32x2 - 12x + 4 \( -\,2^{8}\cdot 3^{5}\cdot 5^{4}\cdot 17^{4} \) $S_5$ (as 10T12) Trivial
10.0.3903069328128.1 x10 - 2x9 + 6x8 + 14x6 - 26x5 - 4x4 - 4x3 + 32x2 - 12x + 4 \( -\,2^{8}\cdot 3^{5}\cdot 89^{4} \) $S_5$ (as 10T12) $[3]$
10.0.4129544208384.1 x10 - 2x9 + 2x8 + 16x7 + 18x6 + 28x5 + 36x4 + 16x3 + x2 - 2x + 2 \( -\,2^{18}\cdot 3^{8}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
10.2.4415968335104.2 x10 - 5x9 + 13x8 - 22x7 + 13x6 + 17x5 - 69x4 + 94x3 - 69x2 + 27x - 5 \( 2^{8}\cdot 29^{7} \) $S_5$ (as 10T12) Trivial
10.2.5125781250000.1 x10 - 5x6 - 12x5 - 5x4 + 1 \( 2^{4}\cdot 3^{8}\cdot 5^{11} \) $S_5$ (as 10T12) Trivial
10.0.5910009391872.1 x10 - x9 + 3x8 + 6x7 + 9x6 + 3x5 + 3x4 + 66x3 + 75x2 - 91x + 169 \( -\,2^{8}\cdot 3^{11}\cdot 19^{4} \) $S_5$ (as 10T12) Trivial
10.2.6802444800000.3 x10 - 5x9 + 14x8 - 17x7 - 3x6 + 76x5 - 163x4 + 207x3 - 154x2 + 35x + 25 \( 2^{12}\cdot 3^{12}\cdot 5^{5} \) $S_5$ (as 10T12) Trivial
10.2.6859721385216.1 x10 - 4x9 - x8 + 22x7 - 8x6 - 60x5 + 30x4 + 90x3 - 33x2 - 84x - 21 \( 2^{8}\cdot 3^{13}\cdot 7^{5} \) $S_5$ (as 10T12) Trivial
10.0.7255941120000.1 x10 - 4x9 + 2x8 + 16x7 - 35x6 + 12x5 + 66x4 - 132x3 + 123x2 - 60x + 12 \( -\,2^{16}\cdot 3^{11}\cdot 5^{4} \) $S_5$ (as 10T12) Trivial
10.2.7812500000000.2 x10 - 10x6 + 25x2 - 20 \( 2^{8}\cdot 5^{15} \) $S_5$ (as 10T12) Trivial
10.0.8174985898247.1 x10 - 4x9 + 5x8 - x7 - x5 - x3 + 5x2 - 4x + 1 \( -\,7^{4}\cdot 23^{7} \) $S_5$ (as 10T12) $[3]$
10.0.8649755859375.1 x10 + 5x8 - 5x7 + 10x6 - 7x5 + 10x4 - 5x3 + 5x2 + 1 \( -\,3^{11}\cdot 5^{11} \) $S_5$ (as 10T12) $[2]$
10.2.9788549234688.1 x10 - 2x9 + 2x8 - 4x7 - 4x6 + 84x5 - 140x4 + 116x3 - 167x2 + 170x - 74 \( 2^{24}\cdot 3^{5}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
10.2.10059713635257.1 x10 - 3x9 - 5x8 + 21x7 - 15x6 + 12x5 - 41x4 + 45x3 + 37x2 + 12x + 3 \( 3^{7}\cdot 11^{5}\cdot 13^{4} \) $S_5$ (as 10T12) Trivial
10.2.10628820000000.1 x10 - x9 + 5x8 - 10x7 + 3x6 - 19x5 - 3x4 - 10x3 - 5x2 - x - 1 \( 2^{8}\cdot 3^{12}\cdot 5^{7} \) $S_5$ (as 10T12) Trivial
10.2.10628820000000.2 x10 - 3x9 + 5x8 - 2x7 - 5x6 + 17x5 - 5x4 - 2x3 + 5x2 - 3x + 1 \( 2^{8}\cdot 3^{12}\cdot 5^{7} \) $S_5$ (as 10T12) Trivial
10.2.10628820000000.4 x10 - 5x9 + 11x8 - 14x7 + 33x6 - 71x5 + 101x4 - 90x3 + 107x2 - 73x - 11 \( 2^{8}\cdot 3^{12}\cdot 5^{7} \) $S_5$ (as 10T12) Trivial
10.2.11209998860288.1 x10 - 2x9 + 7x8 - 8x7 + 10x6 - 12x5 + 2x4 - 24x3 + 6x2 - 12x + 14 \( 2^{27}\cdot 17^{4} \) $S_5$ (as 10T12) Trivial
10.2.12590724022272.1 x10 + 2x8 - 8x6 - 26x4 + 8x2 - 8 \( 2^{17}\cdot 3^{8}\cdot 11^{4} \) $S_5$ (as 10T12) Trivial
10.2.12602368800000.1 x10 - x9 + 5x8 - 4x7 + 3x6 - x5 + 27x4 + 62x3 + 19x2 + 35x + 5 \( 2^{8}\cdot 3^{8}\cdot 5^{5}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
10.2.12602368800000.2 x10 - x9 - x8 + 2x7 - 3x6 + 5x5 - x4 - 42x3 + 5x2 + 61x + 19 \( 2^{8}\cdot 3^{8}\cdot 5^{5}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
10.2.12602368800000.3 x10 - x9 - 13x8 + 14x7 + 45x6 - 31x5 - 45x4 + 86x3 - 5x2 - 31x + 29 \( 2^{8}\cdot 3^{8}\cdot 5^{5}\cdot 7^{4} \) $S_5$ (as 10T12) Trivial
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