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Label Polynomial Discriminant Galois group Class group Regulator
8.0.37822859361.1 $x^{8} - 4 x^{7} + 7 x^{6} - 7 x^{5} + 7 x^{4} - 7 x^{3} + 7 x^{2} + 5 x + 1$ $3^{8}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[4]$ $105.427780643$
8.0.40904253504.1 $x^{8} - x^{7} + 7 x^{6} - x^{5} + 33 x^{4} + x^{3} + 61 x^{2} + 13 x + 58$ $2^{6}\cdot 3^{4}\cdot 53^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $105.18211721$
8.0.46352367616.5 $x^{8} - 4 x^{7} + 14 x^{6} - 24 x^{5} + 29 x^{4} - 32 x^{3} + 18 x^{2} - 16 x + 17$ $2^{16}\cdot 29^{4}$ $\PSL(2,7)$ (as 8T37) trivial $149.071221207$
8.0.62816399424.1 $x^{8} - 3 x^{7} + 4 x^{6} + 2 x^{5} - 10 x^{4} + 16 x^{3} - 20 x + 28$ $2^{6}\cdot 3^{4}\cdot 59^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $134.076160439$
8.0.64537845849.1 $x^{8} - 2 x^{7} + 10 x^{6} - 17 x^{5} + 28 x^{4} - 38 x^{3} + 34 x^{2} - 17 x + 10$ $3^{6}\cdot 97^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $133.045725397$
8.0.82653950016.1 $x^{8} - 2 x^{7} + 2 x^{6} - 8 x^{5} + 16 x^{4} - 16 x^{3} + 14 x^{2} - 10 x + 4$ $2^{6}\cdot 3^{6}\cdot 11^{6}$ $\PSL(2,7)$ (as 8T37) $[6]$ $114.892889153$
8.0.89685275625.1 $x^{8} - 3 x^{7} + 9 x^{6} - 21 x^{5} + 44 x^{4} - 69 x^{3} + 84 x^{2} - 84 x + 73$ $3^{4}\cdot 5^{4}\cdot 11^{6}$ $\PSL(2,7)$ (as 8T37) $[4]$ $71.0336379898$
8.0.116101021696.1 $x^{8} - 4 x^{7} + 10 x^{6} - 12 x^{5} - 7 x^{4} + 44 x^{3} - 46 x^{2} - 4 x + 95$ $2^{16}\cdot 11^{6}$ $\PSL(2,7)$ (as 8T37) trivial $247.420996309$
8.0.118861526169.4 $x^{8} - 3 x^{7} + x^{6} + 9 x^{5} - 3 x^{4} - 57 x^{3} + 133 x^{2} - 132 x + 76$ $3^{6}\cdot 113^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $376.455315845$
8.0.119538913536.1 $x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 49 x^{4} - 56 x^{3} + 56 x^{2} - 14 x + 7$ $2^{8}\cdot 3^{4}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $162.393113987$
8.0.159507579456.5 $x^{8} - x^{7} + 5 x^{6} - 19 x^{5} + 31 x^{4} - 47 x^{3} + 47 x^{2} - 17 x + 4$ $2^{6}\cdot 3^{6}\cdot 43^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $377.191026972$
8.0.230592040000.1 $x^{8} - x^{7} + 14 x^{4} - 28 x^{3} + 28 x^{2} - 14 x + 14$ $2^{6}\cdot 5^{4}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $427.619207221$
8.0.264287499921.2 $x^{8} - 4 x^{7} + 11 x^{6} - 17 x^{5} + 37 x^{4} - 78 x^{3} + 132 x^{2} - 153 x + 72$ $3^{4}\cdot 239^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $115.474365966$
8.0.268962555456.1 $x^{8} - x^{7} - 7 x^{6} - 7 x^{5} + 7 x^{4} + 49 x^{3} + 77 x^{2} + 31 x + 4$ $2^{6}\cdot 3^{6}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $725.315525886$
8.0.279841000000.2 $x^{8} - x^{7} + x^{6} - 11 x^{5} + 11 x^{4} + 35 x^{3} + 45 x^{2} + 35 x + 10$ $2^{6}\cdot 5^{6}\cdot 23^{4}$ $\PSL(2,7)$ (as 8T37) $[8]$ $186.497702651$
8.0.283449760000.1 $x^{8} - 2 x^{7} + 4 x^{6} + 2 x^{5} + 27 x^{4} - 46 x^{3} + 84 x^{2} - 10 x + 59$ $2^{8}\cdot 5^{4}\cdot 11^{6}$ $\PSL(2,7)$ (as 8T37) $[2]$ $267.801351995$
8.0.296990121024.3 $x^{8} - 3 x^{7} + 6 x^{6} + 2 x^{5} + 6 x^{3} + 4 x^{2} + 6 x + 6$ $2^{6}\cdot 3^{8}\cdot 29^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $499.574622179$
8.0.313044726016.12 $x^{8} - 2 x^{7} + 2 x^{6} - 14 x^{5} + 46 x^{4} - 86 x^{3} + 126 x^{2} - 118 x + 49$ $2^{8}\cdot 11^{4}\cdot 17^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $271.50036974$
8.0.377801998336.1 $x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 63 x^{4} - 84 x^{3} + 98 x^{2} - 52 x + 19$ $2^{16}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $439.97985619$
8.0.377801998336.3 $x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 49 x^{4} - 56 x^{3} + 56 x^{2} - 24 x + 5$ $2^{16}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $341.76186703$
8.0.377801998336.4 $x^{8} + 28 x^{4} + 112 x^{2} - 32 x + 84$ $2^{16}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) trivial $606.504184113$
8.0.481481944321.1 $x^{8} - 4 x^{7} + 49 x^{4} - 42 x^{3} + 77 x^{2} - 31 x + 19$ $7^{8}\cdot 17^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $217.328974873$
8.0.507422576896.1 $x^{8} - 4 x^{7} + 9 x^{6} - 12 x^{5} + 4 x^{4} - 4 x^{3} + 13 x^{2} + 4 x + 1$ $2^{8}\cdot 211^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $170.901924653$
8.0.531901827856.1 $x^{8} + 10 x^{6} + 12 x^{4} - 28 x^{3} - 58 x^{2} + 28 x + 51$ $2^{4}\cdot 7^{4}\cdot 61^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $197.128415537$
8.0.646274503744.1 $x^{8} - x^{7} - 4 x^{6} - 12 x^{5} + 8 x^{4} + 64 x^{3} + 16 x^{2} - 32 x + 24$ $2^{6}\cdot 317^{4}$ $\PSL(2,7)$ (as 8T37) $[6]$ $396.731744368$
8.0.667841990656.8 $x^{8} - 2 x^{7} + 16 x^{6} - 34 x^{5} + 44 x^{4} - 22 x^{3} - 44 x^{2} + 26 x + 23$ $2^{12}\cdot 113^{4}$ $\PSL(2,7)$ (as 8T37) trivial $1852.09272958$
8.0.731763906624.1 $x^{8} - 3 x^{7} + 19 x^{6} - 19 x^{5} + 41 x^{4} + 7 x^{3} + 9 x^{2} + 7 x + 10$ $2^{6}\cdot 3^{4}\cdot 109^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $434.846705204$
8.0.743885550144.2 $x^{8} - x^{7} - 16 x^{6} + 38 x^{5} + 34 x^{4} - 236 x^{3} + 380 x^{2} - 296 x + 100$ $2^{6}\cdot 3^{8}\cdot 11^{6}$ $\PSL(2,7)$ (as 8T37) $[2]$ $901.454958126$
8.0.743885550144.3 $x^{8} - 2 x^{7} + 10 x^{6} - 16 x^{5} + 38 x^{4} - 34 x^{3} + 40 x^{2} - 50 x + 148$ $2^{6}\cdot 3^{8}\cdot 11^{6}$ $\PSL(2,7)$ (as 8T37) $[4]$ $852.463345636$
8.0.767418048576.8 $x^{8} - 2 x^{7} - 2 x^{6} + 4 x^{5} + 12 x^{4} - 4 x^{3} - 20 x^{2} - 4 x + 16$ $2^{6}\cdot 3^{4}\cdot 23^{6}$ $\PSL(2,7)$ (as 8T37) $[12]$ $112.589321972$
8.0.922368160000.1 $x^{8} - 2 x^{7} + 14 x^{6} - 28 x^{5} + 147 x^{4} - 196 x^{3} + 518 x^{2} - 322 x + 497$ $2^{8}\cdot 5^{4}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $614.312041188$
8.0.1151964303616.16 $x^{8} - 2 x^{7} + 8 x^{5} + 7 x^{4} - 68 x^{3} + 218 x^{2} - 336 x + 239$ $2^{8}\cdot 7^{4}\cdot 37^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $397.93149977$
8.0.1156418486161.1 $x^{8} - 2 x^{7} - 11 x^{6} - 16 x^{5} + 49 x^{4} + 183 x^{3} + 303 x^{2} + 244 x + 103$ $17^{4}\cdot 61^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $1307.6413861$
8.0.1157018619904.4 $x^{8} - 28 x^{5} + 7 x^{4} + 196 x^{2} - 80 x + 28$ $2^{12}\cdot 7^{10}$ $\PSL(2,7)$ (as 8T37) $[4]$ $304.501766539$
8.0.1157018619904.5 $x^{8} - 14 x^{5} + 49 x^{4} - 98 x^{3} + 126 x^{2} - 104 x + 42$ $2^{12}\cdot 7^{10}$ $\PSL(2,7)$ (as 8T37) trivial $2274.71708801$
8.0.1292841769024.1 $x^{8} - x^{7} + 4 x^{6} + 2 x^{5} - 6 x^{4} + 14 x^{3} - 2 x^{2} - 2 x + 30$ $2^{6}\cdot 13^{4}\cdot 29^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $824.17328043$
8.0.1442919878656.7 $x^{8} - 6 x^{5} - 3 x^{4} + 10 x^{3} + 10 x^{2} - 8 x + 2$ $2^{12}\cdot 137^{4}$ $\PSL(2,7)$ (as 8T37) trivial $2501.19269299$
8.0.1464351690816.2 $x^{8} - x^{7} + 14 x^{5} - 28 x^{4} - 14 x^{3} + 70 x^{2} - 48 x + 34$ $2^{6}\cdot 3^{4}\cdot 7^{10}$ $\PSL(2,7)$ (as 8T37) $[4]$ $754.175880686$
8.0.1636073786281.3 $x^{8} - 3 x^{7} - 2 x^{6} + 12 x^{5} - 36 x^{3} + 62 x^{2} - 51 x + 18$ $11^{6}\cdot 31^{4}$ $\PSL(2,7)$ (as 8T37) $[12]$ $187.663119448$
8.0.1636073786281.4 $x^{8} - x^{7} - 3 x^{6} - 13 x^{5} + 78 x^{4} - 153 x^{3} + 222 x^{2} - 268 x + 163$ $11^{6}\cdot 31^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $474.183807006$
8.0.1706808989601.1 $x^{8} - 3 x^{7} + 6 x^{6} - 6 x^{4} + 12 x^{2} + 9 x + 9$ $3^{8}\cdot 127^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $1762.91957641$
8.0.1853320108689.1 $x^{8} - 7 x^{5} + 21 x^{4} - 63 x^{3} + 112 x^{2} - 156 x + 168$ $3^{8}\cdot 7^{10}$ $\PSL(2,7)$ (as 8T37) $[4]$ $1582.14024862$
8.0.1912622616576.1 $x^{8} - 2 x^{7} + 14 x^{6} + 14 x^{4} + 168 x^{3} + 56 x^{2} - 176 x + 184$ $2^{12}\cdot 3^{4}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[2]$ $1769.53517413$
8.0.1935192596544.2 $x^{8} - x^{7} - 5 x^{6} - x^{5} - 3 x^{4} + 13 x^{3} + 103 x^{2} + 181 x + 106$ $2^{6}\cdot 3^{4}\cdot 139^{4}$ $\PSL(2,7)$ (as 8T37) $[2, 4]$ $375.454626395$
8.0.2046089933056.12 $x^{8} - 6 x^{6} - 2 x^{5} + 19 x^{4} + 6 x^{3} - 16 x^{2} + 16 x + 25$ $2^{8}\cdot 13^{4}\cdot 23^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $603.163309977$
8.0.2048997570624.2 $x^{8} - 3 x^{7} - 3 x^{6} + 9 x^{5} + 21 x^{4} - 27 x^{3} - 15 x^{2} - 45 x + 108$ $2^{6}\cdot 3^{8}\cdot 47^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $1210.97139228$
8.0.2048997570624.3 $x^{8} - 3 x^{7} + 6 x^{5} + 18 x^{4} + 18 x^{3} + 36 x^{2} + 54 x + 54$ $2^{6}\cdot 3^{8}\cdot 47^{4}$ $\PSL(2,7)$ (as 8T37) $[4]$ $1150.90294062$
8.0.2122409008801.1 $x^{8} - 4 x^{7} + 12 x^{6} + 12 x^{5} - 58 x^{4} + 80 x^{3} + 243 x^{2} + 88 x + 13$ $17^{4}\cdot 71^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $580.669884116$
8.0.2214215424576.2 $x^{8} - 4 x^{7} + 20 x^{6} - 40 x^{5} + 88 x^{4} - 80 x^{3} + 68 x^{2} - 110 x + 61$ $2^{6}\cdot 3^{6}\cdot 83^{4}$ $\PSL(2,7)$ (as 8T37) $[2]$ $2065.80396308$
8.0.2420662999104.1 $x^{8} - x^{7} + 7 x^{6} + 21 x^{5} + 63 x^{4} + 105 x^{3} + 105 x^{2} + 51 x + 12$ $2^{6}\cdot 3^{8}\cdot 7^{8}$ $\PSL(2,7)$ (as 8T37) $[4]$ $1879.66125263$
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