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Label Polynomial Discriminant Galois group Class group Regulator
8.0.47775744.1 $x^{8} + 3 x^{4} + 9$ $2^{16}\cdot 3^{6}$ $D_4$ (as 8T4) trivial $20.8957982344$
8.0.55115776.3 $x^{8} - 4 x^{5} - x^{4} + 4 x^{3} + 8 x^{2} + 4 x + 1$ $2^{16}\cdot 29^{2}$ $S_4\times C_2$ (as 8T24) trivial $8.52019638775$
8.0.321978368.4 $x^{8} - 4 x^{6} + 11 x^{4} - 20 x^{2} + 17$ $2^{16}\cdot 17^{3}$ $D_{8}$ (as 8T6) trivial $20.282622579$
8.0.375455744.1 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 22 x^{4} - 16 x^{3} + 20 x^{2} - 8 x + 4$ $2^{16}\cdot 17\cdot 337$ $S_4\wr C_2$ (as 8T47) trivial $22.7577294403$
8.0.430505984.1 $x^{8} - 4 x^{7} + 12 x^{6} - 20 x^{5} + 23 x^{4} - 20 x^{3} + 20 x^{2} - 8 x + 1$ $2^{16}\cdot 6569$ $S_4\wr C_2$ (as 8T47) trivial $25.0864433646$
8.0.451477504.5 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 21 x^{4} - 20 x^{3} + 20 x^{2} - 12 x + 5$ $2^{16}\cdot 83^{2}$ $S_4\times C_2$ (as 8T24) trivial $35.694160127$
8.0.481361920.1 $x^{8} + 2 x^{6} - 8 x^{5} + x^{4} - 12 x^{3} + 16 x^{2} + 13$ $2^{16}\cdot 5\cdot 13\cdot 113$ $S_4\wr C_2$ (as 8T47) trivial $29.9300203392$
8.0.514916352.6 $x^{8} - 8 x^{6} + 2 x^{4} + 56 x^{2} + 97$ $2^{16}\cdot 3^{4}\cdot 97$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $53.6338974265$
8.0.536412160.1 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 14 x^{4} - 4 x^{3} - 10 x^{2} + 8 x + 5$ $2^{16}\cdot 5\cdot 1637$ $S_4\wr C_2$ (as 8T47) trivial $34.747638937$
8.0.642318336.9 $x^{8} - 12 x^{6} + 59 x^{4} - 132 x^{2} + 121$ $2^{16}\cdot 3^{4}\cdot 11^{2}$ $D_4\times C_2$ (as 8T9) trivial $85.4809876926$
8.0.750321664.3 $x^{8} - 6 x^{6} - 4 x^{5} + 14 x^{4} + 32 x^{3} - 34 x^{2} - 60 x + 61$ $2^{16}\cdot 107^{2}$ $S_4\times C_2$ (as 8T24) trivial $29.8794137621$
8.0.881917952.2 $x^{8} - 2 x^{6} - 8 x^{5} + 14 x^{4} - 4 x^{2} + 8 x + 4$ $2^{16}\cdot 13457$ $S_4\wr C_2$ (as 8T47) trivial $45.7293913147$
8.0.897122304.10 $x^{8} - 8 x^{6} + 51 x^{4} - 104 x^{2} + 169$ $2^{16}\cdot 3^{4}\cdot 13^{2}$ $D_4\times C_2$ (as 8T9) trivial $80.5956958474$
8.0.921763840.1 $x^{8} - 4 x^{7} + 6 x^{6} - 14 x^{4} + 16 x^{3} + 4 x^{2} - 24 x + 20$ $2^{16}\cdot 5\cdot 29\cdot 97$ $S_4\wr C_2$ (as 8T47) trivial $47.8521365508$
8.0.1024000000.6 $x^{8} + 4 x^{6} + 16 x^{4} - 56 x^{2} + 36$ $2^{16}\cdot 5^{6}$ $D_4$ (as 8T4) $[2]$ $24.6646630038$
8.0.1145110528.2 $x^{8} - 4 x^{6} + 9 x^{4} - 4 x^{3} - 2 x^{2} - 4 x + 5$ $2^{16}\cdot 101\cdot 173$ $S_4\wr C_2$ (as 8T47) trivial $37.7270188141$
8.0.1174470656.1 $x^{8} + 4 x^{6} - 4 x^{5} + x^{4} - 8 x^{3} + 2 x^{2} + 8 x + 13$ $2^{16}\cdot 17921$ $S_4\wr C_2$ (as 8T47) trivial $43.7260685499$
8.0.1266221056.1 $x^{8} - 4 x^{6} - 4 x^{5} + 25 x^{4} + 8 x^{3} - 38 x^{2} - 24 x + 45$ $2^{16}\cdot 139^{2}$ $S_4\times C_2$ (as 8T24) trivial $55.5478932997$
8.0.1364787200.1 $x^{8} + 2 x^{6} - 12 x^{5} + 22 x^{4} - 16 x^{3} + 6 x^{2} - 4 x + 5$ $2^{16}\cdot 5^{2}\cdot 7^{2}\cdot 17$ $S_4\wr C_2$ (as 8T47) trivial $54.2440615096$
8.0.1382612992.4 $x^{8} - 4 x^{6} + 11 x^{4} + 4 x^{2} + 73$ $2^{16}\cdot 17^{2}\cdot 73$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $63.3566161084$
8.0.1506344960.1 $x^{8} - 4 x^{5} + 5 x^{4} + 2 x^{2} - 8 x + 5$ $2^{16}\cdot 5\cdot 4597$ $S_4\wr C_2$ (as 8T47) trivial $75.0156014077$
8.0.1560346624.1 $x^{8} + 4 x^{6} - 4 x^{5} + 15 x^{4} - 20 x^{3} + 12 x^{2} - 4 x + 1$ $2^{16}\cdot 29\cdot 821$ $S_4\wr C_2$ (as 8T47) trivial $55.7849224907$
8.0.1615396864.3 $x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 13 x^{4} - 12 x^{3} + 6 x^{2} - 8 x + 5$ $2^{16}\cdot 157^{2}$ $S_4\times C_2$ (as 8T24) trivial $73.2862051196$
8.0.1629552640.1 $x^{8} - 4 x^{7} + 10 x^{6} - 8 x^{5} - 2 x^{4} + 20 x^{3} - 10 x^{2} - 8 x + 5$ $2^{16}\cdot 5\cdot 4973$ $S_4\wr C_2$ (as 8T47) trivial $52.8989617706$
8.0.1637941248.2 $x^{8} + 4 x^{6} + x^{4} - 4 x^{3} - 2 x^{2} - 4 x + 5$ $2^{16}\cdot 3^{2}\cdot 2777$ $S_4\wr C_2$ (as 8T47) trivial $61.0440450374$
8.0.1698234368.3 $x^{8} - 4 x^{7} + 16 x^{6} - 32 x^{5} + 59 x^{4} - 56 x^{3} + 48 x^{2} - 4 x + 1$ $2^{16}\cdot 25913$ $S_4\wr C_2$ (as 8T47) trivial $54.2092673956$
8.2.1863254016.1 $x^{8} - 6 x^{6} - 12 x^{5} - 18 x^{4} - 24 x^{3} - 18 x^{2} - 12 x - 3$ $-\,2^{16}\cdot 3^{7}\cdot 13$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $45.6290093489$
8.0.1916338176.6 $x^{8} - 37 x^{4} + 361$ $2^{16}\cdot 3^{4}\cdot 19^{2}$ $D_4\times C_2$ (as 8T9) trivial $150.856250519$
8.0.2062614528.1 $x^{8} + 4 x^{6} + 9 x^{4} - 36 x^{3} + 46 x^{2} - 36 x + 13$ $2^{16}\cdot 3^{2}\cdot 13\cdot 269$ $S_4\wr C_2$ (as 8T47) trivial $55.8690749893$
8.0.2096168960.1 $x^{8} - 4 x^{7} + 2 x^{6} + 14 x^{4} - 4 x^{3} - 2 x^{2} - 8 x + 5$ $2^{16}\cdot 5\cdot 6397$ $S_4\wr C_2$ (as 8T47) trivial $75.6061907174$
8.0.2163802112.1 $x^{8} - 4 x^{7} + 6 x^{6} - 6 x^{4} + 8 x^{3} + 12 x^{2} - 24 x + 20$ $2^{16}\cdot 137\cdot 241$ $S_4\wr C_2$ (as 8T47) trivial $51.1032575152$
8.0.2298544128.3 $x^{8} - 4 x^{6} - 21 x^{4} + 140 x^{2} + 433$ $2^{16}\cdot 3^{4}\cdot 433$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $157.057924835$
8.0.2341011456.19 $x^{8} - 4 x^{7} + 8 x^{6} - 8 x^{5} + 11 x^{4} - 16 x^{3} + 8 x^{2} + 4 x + 1$ $2^{16}\cdot 3^{6}\cdot 7^{2}$ $S_4\times C_2$ (as 8T24) trivial $58.704350859$
8.0.2357264384.1 $x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 10 x^{4} - 4 x^{3} + 30 x^{2} - 32 x + 13$ $2^{16}\cdot 35969$ $S_4\wr C_2$ (as 8T47) trivial $55.9164140875$
8.0.2553348096.6 $x^{8} - 16 x^{6} + 107 x^{4} - 344 x^{2} + 481$ $2^{16}\cdot 3^{4}\cdot 13\cdot 37$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $149.879530135$
8.0.2636185600.1 $x^{8} + 2 x^{6} - 8 x^{5} + 2 x^{4} - 8 x^{3} + 36 x^{2} + 24 x + 52$ $2^{16}\cdot 5^{2}\cdot 1609$ $S_4\wr C_2$ (as 8T47) trivial $72.8785050392$
8.0.2723217408.3 $x^{8} - 6 x^{6} - 12 x^{5} + 6 x^{4} + 48 x^{3} + 78 x^{2} + 60 x + 21$ $2^{16}\cdot 3^{7}\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $61.2644178686$
8.0.2746286080.3 $x^{8} - 8 x^{6} + 34 x^{4} - 104 x^{2} + 145$ $2^{16}\cdot 5\cdot 17^{2}\cdot 29$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $54.4782307065$
8.0.2775646208.2 $x^{8} - 4 x^{6} - 4 x^{5} + 7 x^{4} + 12 x^{3} + 4 x^{2} - 4 x + 1$ $2^{16}\cdot 41\cdot 1033$ $S_4\wr C_2$ (as 8T47) trivial $63.3440411985$
8.0.2780364800.1 $x^{8} - 6 x^{6} - 8 x^{5} + 10 x^{4} + 24 x^{3} + 4 x^{2} + 8 x + 20$ $2^{16}\cdot 5^{2}\cdot 1697$ $S_4\wr C_2$ (as 8T47) trivial $87.4600906248$
8.0.2872115200.1 $x^{8} - 4 x^{6} - 4 x^{5} + 17 x^{4} - 16 x^{3} + 18 x^{2} - 16 x + 5$ $2^{16}\cdot 5^{2}\cdot 1753$ $S_4\wr C_2$ (as 8T47) $[2]$ $31.8474482789$
8.0.2917728256.2 $x^{8} + 6 x^{6} - 12 x^{5} + 13 x^{4} - 24 x^{3} + 44 x^{2} - 36 x + 13$ $2^{16}\cdot 211^{2}$ $S_4\times C_2$ (as 8T24) trivial $73.1642624161$
8.2.3031367680.1 $x^{8} - 4 x^{7} + 6 x^{6} - 2 x^{4} - 20 x^{3} + 2 x^{2} + 8 x - 3$ $-\,2^{16}\cdot 5\cdot 11\cdot 29^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $79.3357626143$
8.0.3436773376.5 $x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 3 x^{4} - 12 x^{3} + 4 x^{2} + 4 x + 5$ $2^{16}\cdot 229^{2}$ $S_4\times C_2$ (as 8T24) trivial $85.124441204$
8.0.3503882240.6 $x^{8} - 21 x^{4} - 16 x^{2} + 185$ $2^{16}\cdot 5\cdot 17^{2}\cdot 37$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $52.7367208067$
8.0.3572563968.1 $x^{8} - 24 x^{6} + 194 x^{4} - 600 x^{2} + 673$ $2^{16}\cdot 3^{4}\cdot 673$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) trivial $187.714428389$
8.4.3582525440.1 $x^{8} - 6 x^{6} - 8 x^{5} - 3 x^{4} + 20 x^{3} + 36 x^{2} - 27$ $2^{16}\cdot 5\cdot 13\cdot 29^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $77.1972984677$
8.0.3619225600.2 $x^{8} + 2 x^{6} + 15 x^{4} - 2 x^{2} + 9$ $2^{16}\cdot 5^{2}\cdot 47^{2}$ $S_4\times C_2$ (as 8T24) trivial $149.280568435$
8.0.3645440000.13 $x^{8} - 4 x^{6} + 3 x^{4} - 28 x^{2} + 89$ $2^{16}\cdot 5^{4}\cdot 89$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) $[2]$ $41.7020798514$
8.0.3655401472.4 $x^{8} - 8 x^{6} + 27 x^{4} - 64 x^{2} + 193$ $2^{16}\cdot 17^{2}\cdot 193$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $52.743171598$
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