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Results (1-50 of 685 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
8.0.681574400.4 $x^{8} - 2 x^{6} + 12 x^{2} + 26$ $2^{21}\cdot 5^{2}\cdot 13$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $36.4661805615$
8.0.782237696.1 $x^{8} + 6 x^{6} - 4 x^{5} + 20 x^{4} - 16 x^{3} + 42 x^{2} - 28 x + 29$ $2^{21}\cdot 373$ $S_4\wr C_2$ (as 8T47) trivial $54.288180526$
8.0.1520435200.2 $x^{8} - 10 x^{6} + 40 x^{4} - 76 x^{2} + 58$ $2^{21}\cdot 5^{2}\cdot 29$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $81.4464686512$
8.0.1772093440.2 $x^{8} - 2 x^{6} + 8 x^{4} - 16 x^{2} + 10$ $2^{21}\cdot 5\cdot 13^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $50.0091446202$
8.0.2443182080.1 $x^{8} + 2 x^{6} - 4 x^{5} + 8 x^{4} - 16 x^{3} - 6 x^{2} + 12 x + 5$ $2^{21}\cdot 5\cdot 233$ $S_4\wr C_2$ (as 8T47) trivial $94.5070654246$
8.0.2778726400.5 $x^{8} - 2 x^{6} - 16 x^{4} + 8 x^{2} + 106$ $2^{21}\cdot 5^{2}\cdot 53$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $100.229814482$
8.0.2946498560.1 $x^{8} + 2 x^{6} - 4 x^{5} + 20 x^{4} - 24 x^{3} + 2 x^{2} + 12 x + 9$ $2^{21}\cdot 5\cdot 281$ $S_4\wr C_2$ (as 8T47) trivial $135.475439653$
8.0.4456448000.4 $x^{8} - 2 x^{6} + 8 x^{4} + 80 x^{2} + 170$ $2^{21}\cdot 5^{3}\cdot 17$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $82.2482767152$
8.0.8818524160.3 $x^{8} - 2 x^{6} - 4 x^{2} + 10$ $2^{21}\cdot 5\cdot 29^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $190.357673786$
8.0.17039360000.1 $x^{8} - 18 x^{6} + 136 x^{4} - 480 x^{2} + 650$ $2^{21}\cdot 5^{4}\cdot 13$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $122.934378087$
8.0.21233664000.14 $x^{8} - 4 x^{6} + 8 x^{4} + 40 x^{2} + 40$ $2^{21}\cdot 3^{4}\cdot 5^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $202.53493307$
8.0.29454499840.2 $x^{8} - 2 x^{6} + 8 x^{2} + 10$ $2^{21}\cdot 5\cdot 53^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $390.19360291$
8.0.31719424000.4 $x^{8} - 2 x^{6} - 56 x^{4} + 1210$ $2^{21}\cdot 5^{3}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $330.949726342$
8.0.38010880000.7 $x^{8} - 14 x^{6} + 64 x^{4} + 120 x^{2} + 1450$ $2^{21}\cdot 5^{4}\cdot 29$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $133.471200763$
8.2.41278242816.3 $x^{8} - 2 x^{6} - 4 x^{5} + 8 x^{3} - 38 x^{2} + 36 x - 23$ $-\,2^{21}\cdot 3^{9}$ $S_8$ (as 8T50) trivial $442.366391272$
8.0.41466986496.3 $x^{8} - 10 x^{6} + 56 x^{4} - 156 x^{2} + 234$ $2^{21}\cdot 3^{2}\cdot 13^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $565.168983799$
8.0.44302336000.7 $x^{8} - 14 x^{6} + 80 x^{4} - 200 x^{2} + 250$ $2^{21}\cdot 5^{3}\cdot 13^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $326.94719033$
8.0.55207526400.2 $x^{8} - 18 x^{6} + 144 x^{4} - 648 x^{2} + 2106$ $2^{21}\cdot 3^{4}\cdot 5^{2}\cdot 13$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $287.98469107$
8.0.69468160000.1 $x^{8} - 26 x^{6} + 264 x^{4} - 1180 x^{2} + 2650$ $2^{21}\cdot 5^{4}\cdot 53$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $188.732758858$
8.0.75759616000.16 $x^{8} - 8 x^{6} + 8 x^{4} + 40 x^{2} + 40$ $2^{21}\cdot 5^{3}\cdot 17^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $289.612976655$
8.0.94633984000.3 $x^{8} - 2 x^{6} - 64 x^{4} + 380 x^{2} + 3610$ $2^{21}\cdot 5^{3}\cdot 19^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $493.745310842$
8.4.105740500992.1 $x^{8} + 10 x^{6} - 4 x^{5} + 20 x^{4} + 8 x^{3} - 14 x^{2} - 4 x + 1$ $2^{21}\cdot 3\cdot 7^{5}$ $S_4\wr C_2$ (as 8T47) trivial $1172.13097671$
8.0.111411200000.1 $x^{8} - 30 x^{6} + 360 x^{4} - 2000 x^{2} + 4250$ $2^{21}\cdot 5^{5}\cdot 17$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $191.849909922$
8.0.115186073600.8 $x^{8} - 10 x^{6} - 104 x^{4} + 676 x^{2} + 4394$ $2^{21}\cdot 5^{2}\cdot 13^{3}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $297.565332194$
8.0.143539568640.4 $x^{8} - 18 x^{6} + 144 x^{4} - 324 x^{2} + 810$ $2^{21}\cdot 3^{4}\cdot 5\cdot 13^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $242.653837101$
8.0.143539568640.7 $x^{8} - 6 x^{6} + 8 x^{4} + 12 x^{2} + 10$ $2^{21}\cdot 3^{4}\cdot 5\cdot 13^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $575.88571186$
8.0.143539568640.11 $x^{8} - 4 x^{6} + 56 x^{4} - 8 x^{2} + 40$ $2^{21}\cdot 3^{4}\cdot 5\cdot 13^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $363.225552572$
8.4.163840000000.1 $x^{8} - 10 x^{6} + 20 x^{4} - 16 x^{3} + 40 x^{2} - 40 x + 10$ $2^{21}\cdot 5^{7}$ $S_8$ (as 8T50) trivial $1524.1868055$
8.0.220463104000.9 $x^{8} - 14 x^{6} + 304 x^{4} - 1740 x^{2} + 8410$ $2^{21}\cdot 5^{3}\cdot 29^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $441.157038441$
8.0.220463104000.12 $x^{8} - 18 x^{6} + 304 x^{4} - 1160 x^{2} + 8410$ $2^{21}\cdot 5^{3}\cdot 29^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $320.462834987$
8.0.220463104000.18 $x^{8} - 6 x^{6} + 40 x^{4} - 100 x^{2} + 250$ $2^{21}\cdot 5^{3}\cdot 29^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $680.026311432$
8.0.299483791360.3 $x^{8} - 6 x^{6} + 152 x^{4} + 156 x^{2} + 1690$ $2^{21}\cdot 5\cdot 13^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $576.202904214$
8.0.312217698304.1 $x^{8} - 4 x^{7} - 2 x^{6} + 16 x^{5} + 84 x^{4} - 404 x^{3} + 622 x^{2} - 352 x + 121$ $2^{21}\cdot 53^{3}$ $S_4\wr C_2$ (as 8T47) $[2]$ $495.801483388$
8.6.329930244096.4 $x^{8} + 2 x^{6} - 16 x^{4} + 20 x^{2} - 6$ $-\,2^{21}\cdot 3\cdot 229^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $2135.64970459$
8.6.329930244096.8 $x^{8} - 8 x^{6} + 8 x^{4} + 40 x^{2} - 24$ $-\,2^{21}\cdot 3\cdot 229^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $2016.22870263$
8.2.371504185344.12 $x^{8} - 2 x^{6} - 24 x^{2} - 6$ $-\,2^{21}\cdot 3^{11}$ $C_2 \wr S_4$ (as 8T44) trivial $811.70889952$
8.2.371504185344.15 $x^{8} + 2 x^{6} + 24 x^{2} - 6$ $-\,2^{21}\cdot 3^{11}$ $C_2 \wr S_4$ (as 8T44) trivial $2278.89724885$
8.0.496867737600.3 $x^{8} - 24 x^{6} + 168 x^{4} - 216 x^{2} + 936$ $2^{21}\cdot 3^{6}\cdot 5^{2}\cdot 13$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4]$ $559.61200487$
8.0.496867737600.4 $x^{8} - 12 x^{6} + 24 x^{4} + 72 x^{2} + 936$ $2^{21}\cdot 3^{6}\cdot 5^{2}\cdot 13$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[4]$ $209.055828442$
8.0.530841600000.7 $x^{8} - 20 x^{6} + 120 x^{4} - 200 x^{2} + 1000$ $2^{21}\cdot 3^{4}\cdot 5^{5}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2, 2]$ $482.962656431$
8.0.619173642240.3 $x^{8} - 16 x^{5} + 24 x^{4} + 96 x^{3} + 344 x^{2} + 384 x + 360$ $2^{21}\cdot 3^{10}\cdot 5$ $S_4\wr C_2$ (as 8T47) trivial $2655.18332865$
8.0.619173642240.7 $x^{8} - 4 x^{7} + 2 x^{6} - 16 x^{5} + 40 x^{4} + 28 x^{3} + 154 x^{2} + 80 x + 125$ $2^{21}\cdot 3^{10}\cdot 5$ $S_4\wr C_2$ (as 8T47) trivial $3280.43810937$
8.0.736362496000.3 $x^{8} - 2 x^{6} + 40 x^{4} + 250$ $2^{21}\cdot 5^{3}\cdot 53^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $826.585125444$
8.0.792985600000.1 $x^{8} - 50 x^{6} + 960 x^{4} - 7700 x^{2} + 30250$ $2^{21}\cdot 5^{5}\cdot 11^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $990.639029226$
8.2.861029793792.2 $x^{8} - 8 x^{4} - 168 x^{2} - 152$ $-\,2^{21}\cdot 3^{2}\cdot 7^{4}\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $3122.28146471$
8.2.861029793792.4 $x^{8} + 8 x^{6} + 8 x^{4} - 88 x^{2} - 152$ $-\,2^{21}\cdot 3^{2}\cdot 7^{4}\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $1541.19233525$
8.2.861029793792.5 $x^{8} - 8 x^{6} + 8 x^{4} + 88 x^{2} - 152$ $-\,2^{21}\cdot 3^{2}\cdot 7^{4}\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $2653.33182601$
8.2.861029793792.7 $x^{8} - 8 x^{4} + 168 x^{2} - 152$ $-\,2^{21}\cdot 3^{2}\cdot 7^{4}\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $1134.49793106$
8.2.1223568654336.2 $x^{8} + 12 x^{6} + 24 x^{4} - 72 x^{2} - 216$ $-\,2^{21}\cdot 3^{5}\cdot 7^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $815.978656106$
8.2.1223568654336.4 $x^{8} - 12 x^{6} + 24 x^{4} + 72 x^{2} - 216$ $-\,2^{21}\cdot 3^{5}\cdot 7^{4}$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $1139.94030439$
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