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Results (1-50 of 413 matches)

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Label Polynomial Discriminant Galois group Class group Regulator
8.4.327680000000.3 $x^{8} - 60 x^{4} + 160 x^{2} + 20$ $2^{22}\cdot 5^{7}$ $C_8:C_2$ (as 8T7) trivial $992.539183029$
8.6.720896000000.3 $x^{8} - 4 x^{6} - 14 x^{4} + 56 x^{2} - 44$ $-\,2^{22}\cdot 5^{6}\cdot 11$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $2287.02451566$
8.2.720896000000.15 $x^{8} + 8 x^{6} - 56 x^{4} - 448 x^{2} - 704$ $-\,2^{22}\cdot 5^{6}\cdot 11$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $696.910218174$
8.0.1585971200000.5 $x^{8} + 4 x^{6} - 6 x^{4} + 40 x^{2} + 20$ $2^{22}\cdot 5^{5}\cdot 11^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$ $454.229806422$
8.4.1585971200000.10 $x^{8} - 8 x^{6} - 24 x^{4} - 320 x^{2} + 320$ $2^{22}\cdot 5^{5}\cdot 11^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) trivial $2981.25834847$
8.4.1900544000000.2 $x^{8} + 4 x^{6} - 54 x^{4} - 216 x^{2} + 116$ $2^{22}\cdot 5^{6}\cdot 29$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1962.44516113$
8.4.1900544000000.8 $x^{8} - 12 x^{6} - 166 x^{4} + 72 x^{2} + 116$ $2^{22}\cdot 5^{6}\cdot 29$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $1057.83178836$
8.0.3146319396864.13 $x^{8} - 24 x^{6} + 264 x^{4} - 960 x^{2} + 1344$ $2^{22}\cdot 3^{7}\cdot 7^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $1318.69465375$
8.0.3146319396864.45 $x^{8} + 12 x^{6} + 66 x^{4} + 120 x^{2} + 84$ $2^{22}\cdot 3^{7}\cdot 7^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $1318.69465375$
8.0.6717651812352.8 $x^{8} - 48 x^{6} + 612 x^{4} + 468$ $2^{22}\cdot 3^{6}\cdot 13^{3}$ $C_4\wr C_2$ (as 8T17) $[4]$ $1495.44989841$
8.0.6717651812352.10 $x^{8} + 36 x^{4} + 288 x^{2} + 468$ $2^{22}\cdot 3^{6}\cdot 13^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $1187.677409$
8.0.6717651812352.21 $x^{8} + 144 x^{4} - 2304 x^{2} + 7488$ $2^{22}\cdot 3^{6}\cdot 13^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $1187.677409$
8.0.6717651812352.35 $x^{8} + 48 x^{6} + 900 x^{4} + 7488 x^{2} + 22932$ $2^{22}\cdot 3^{6}\cdot 13^{3}$ $C_4\wr C_2$ (as 8T17) $[4]$ $1360.88602925$
8.0.11023155200000.2 $x^{8} + 12 x^{6} - 14 x^{4} - 360 x^{2} + 2420$ $2^{22}\cdot 5^{5}\cdot 29^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[6]$ $419.408216924$
8.0.11023155200000.7 $x^{8} - 4 x^{6} + 34 x^{4} - 200 x^{2} + 500$ $2^{22}\cdot 5^{5}\cdot 29^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[6]$ $226.07681119$
8.4.14015841435648.8 $x^{8} - 12 x^{6} + 10 x^{4} - 312 x^{2} + 52$ $2^{22}\cdot 3^{2}\cdot 13^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) trivial $4868.98675746$
8.0.14015841435648.10 $x^{8} + 20 x^{6} + 74 x^{4} + 104 x^{2} + 52$ $2^{22}\cdot 3^{2}\cdot 13^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$ $1235.64693153$
8.4.14832757637120.1 $x^{8} - 16 x^{6} - 16 x^{5} + 78 x^{4} + 128 x^{3} - 48 x^{2} - 112 x + 20$ $2^{22}\cdot 5\cdot 29^{4}$ $S_4\wr C_2$ (as 8T47) trivial $11472.7121883$
8.2.17980456960000.7 $x^{8} - 4 x^{6} - 30 x^{4} - 72 x^{2} - 76$ $-\,2^{22}\cdot 5^{4}\cdot 19^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[3]$ $691.139951607$
8.2.17980456960000.19 $x^{8} + 8 x^{6} - 120 x^{4} + 576 x^{2} - 1216$ $-\,2^{22}\cdot 5^{4}\cdot 19^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[3]$ $691.139951607$
8.6.22024235778048.1 $x^{8} - 24 x^{6} - 8 x^{5} + 126 x^{4} + 96 x^{3} - 104 x^{2} - 96 x + 60$ $-\,2^{22}\cdot 3^{7}\cdot 7^{4}$ $S_4\wr C_2$ (as 8T47) $[2]$ $14377.4353598$
8.4.26542080000000.1 $x^{8} - 540 x^{4} - 4320 x^{2} + 1620$ $2^{22}\cdot 3^{4}\cdot 5^{7}$ $C_8:C_2$ (as 8T7) $[2]$ $2298.44041066$
8.0.36573882089472.8 $x^{8} + 20 x^{6} + 74 x^{4} - 56 x^{2} + 2548$ $2^{22}\cdot 3^{4}\cdot 7^{2}\cdot 13^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $3364.54624666$
8.0.36573882089472.11 $x^{8} + 4 x^{6} + 122 x^{4} + 1064 x^{2} + 2548$ $2^{22}\cdot 3^{4}\cdot 7^{2}\cdot 13^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $2670.64367298$
8.0.36573882089472.29 $x^{8} - 8 x^{6} + 488 x^{4} - 8512 x^{2} + 40768$ $2^{22}\cdot 3^{4}\cdot 7^{2}\cdot 13^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $3364.54624666$
8.0.36573882089472.31 $x^{8} - 40 x^{6} + 296 x^{4} + 448 x^{2} + 40768$ $2^{22}\cdot 3^{4}\cdot 7^{2}\cdot 13^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $2670.64367298$
8.4.39649280000000.2 $x^{8} - 940 x^{4} - 5280 x^{2} + 2420$ $2^{22}\cdot 5^{7}\cdot 11^{2}$ $(C_8:C_2):C_2$ (as 8T16) $[2]$ $3953.02231911$
8.8.39649280000000.2 $x^{8} - 60 x^{6} + 1050 x^{4} - 5720 x^{2} + 2420$ $2^{22}\cdot 5^{7}\cdot 11^{2}$ $C_8:C_2$ (as 8T7) trivial $19408.0869068$
8.4.39649280000000.10 $x^{8} - 20 x^{6} - 190 x^{4} + 440 x^{2} + 2420$ $2^{22}\cdot 5^{7}\cdot 11^{2}$ $(C_8:C_2):C_2$ (as 8T16) $[2]$ $4103.21203402$
8.0.39649280000000.14 $x^{8} + 60 x^{6} + 1170 x^{4} + 7480 x^{2} + 2420$ $2^{22}\cdot 5^{7}\cdot 11^{2}$ $C_8:C_2$ (as 8T7) $[2, 4, 8]$ $36.02606833$
8.6.60735312887808.7 $x^{8} - 20 x^{6} + 98 x^{4} - 136 x^{2} - 12$ $-\,2^{22}\cdot 3\cdot 13^{6}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $34292.5680775$
8.2.60735312887808.12 $x^{8} + 12 x^{6} + 2 x^{4} - 360 x^{2} - 972$ $-\,2^{22}\cdot 3\cdot 13^{6}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $17405.4720746$
8.0.69084905472000.4 $x^{8} - 4 x^{6} + 82 x^{4} - 552 x^{2} + 1620$ $2^{22}\cdot 3^{2}\cdot 5^{3}\cdot 11^{4}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $2647.20241081$
8.0.69084905472000.5 $x^{8} + 4 x^{6} - 6 x^{4} - 504 x^{2} + 1620$ $2^{22}\cdot 3^{2}\cdot 5^{3}\cdot 11^{4}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $5726.26352627$
8.0.69084905472000.23 $x^{8} - 12 x^{6} + 298 x^{4} + 936 x^{2} + 4500$ $2^{22}\cdot 3^{2}\cdot 5^{3}\cdot 11^{4}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $5726.26352627$
8.0.69084905472000.26 $x^{8} + 12 x^{6} + 386 x^{4} + 2232 x^{2} + 4500$ $2^{22}\cdot 3^{2}\cdot 5^{3}\cdot 11^{4}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $2647.20241081$
8.6.87228416000000.6 $x^{8} - 28 x^{6} + 154 x^{4} + 968 x^{2} - 5324$ $-\,2^{22}\cdot 5^{6}\cdot 11^{3}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $14078.3412009$
8.2.87228416000000.13 $x^{8} + 56 x^{6} + 616 x^{4} - 7744 x^{2} - 85184$ $-\,2^{22}\cdot 5^{6}\cdot 11^{3}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2, 2]$ $2269.26657042$
8.8.118292480000000.2 $x^{8} - 80 x^{6} + 1780 x^{4} - 12160 x^{2} + 7220$ $2^{22}\cdot 5^{7}\cdot 19^{2}$ $C_8:C_2$ (as 8T7) trivial $24474.5476319$
8.0.118292480000000.8 $x^{8} + 80 x^{6} + 2100 x^{4} + 18240 x^{2} + 7220$ $2^{22}\cdot 5^{7}\cdot 19^{2}$ $C_8:C_2$ (as 8T7) $[2, 58]$ $36.02606833$
8.0.126142572920832.1 $x^{8} + 16 x^{6} - 92 x^{4} + 468$ $2^{22}\cdot 3^{4}\cdot 13^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2, 2]$ $3280.2531072$
8.4.126142572920832.3 $x^{8} - 20 x^{6} + 178 x^{4} - 2184 x^{2} + 468$ $2^{22}\cdot 3^{4}\cdot 13^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$ $15578.0097032$
8.0.191902515200000.2 $x^{8} + 28 x^{6} + 306 x^{4} + 2200 x^{2} + 2420$ $2^{22}\cdot 5^{5}\cdot 11^{4}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2, 2]$ $2958.10992039$
8.4.191902515200000.13 $x^{8} - 56 x^{6} + 1224 x^{4} - 17600 x^{2} + 38720$ $2^{22}\cdot 5^{5}\cdot 11^{4}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$ $9175.93404672$
8.2.212241626431488.1 $x^{8} + 28 x^{6} + 162 x^{4} - 1512 x^{2} - 13068$ $-\,2^{22}\cdot 3^{3}\cdot 37^{4}$ $Z_8 : Z_8^\times$ (as 8T15) trivial $26536.0154476$
8.2.212241626431488.16 $x^{8} - 36 x^{6} + 402 x^{4} - 1256 x^{2} - 588$ $-\,2^{22}\cdot 3^{3}\cdot 37^{4}$ $Z_8 : Z_8^\times$ (as 8T15) trivial $26536.0154476$
8.4.263186355847168.2 $x^{8} - 156 x^{4} + 416 x^{2} + 468$ $2^{22}\cdot 13^{7}$ $C_8:C_2$ (as 8T7) trivial $308654.847587$
8.0.273271140384768.4 $x^{8} + 36 x^{6} + 522 x^{4} + 2376 x^{2} + 3348$ $2^{22}\cdot 3^{7}\cdot 31^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $6744.54511866$
8.0.273271140384768.8 $x^{8} + 60 x^{6} + 1698 x^{4} + 15960 x^{2} + 62868$ $2^{22}\cdot 3^{7}\cdot 31^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $6744.54511866$
8.2.449511424000000.5 $x^{8} - 240 x^{4} - 6400 x^{2} - 30400$ $-\,2^{22}\cdot 5^{6}\cdot 19^{3}$ $Z_8 : Z_8^\times$ (as 8T15) $[2]$ $7384.97119791$
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