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Label Polynomial Discriminant Galois group Class group Regulator
8.2.743008370688.4 $x^{8} + 12 x^{6} + 30 x^{4} - 56 x^{2} - 108$ $-\,2^{22}\cdot 3^{11}$ $\textrm{GL(2,3)}$ (as 8T23) $[2]$ $391.452366271$
8.2.743008370688.8 $x^{8} - 36 x^{4} + 96 x^{2} - 108$ $-\,2^{22}\cdot 3^{11}$ $\textrm{GL(2,3)}$ (as 8T23) $[2]$ $391.452366271$
8.0.746405756928.6 $x^{8} - 20 x^{6} + 142 x^{4} - 408 x^{2} + 468$ $2^{22}\cdot 3^{4}\cdot 13^{3}$ $D_{8}$ (as 8T6) $[4]$ $1547.54229064$
8.0.1900544000000.3 $x^{8} + 8 x^{6} + 24 x^{4} + 192 x^{2} + 1856$ $2^{22}\cdot 5^{6}\cdot 29$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[4]$ $119.701767244$
8.2.3234424946688.1 $x^{8} + 12 x^{6} + 30 x^{4} - 88 x^{2} - 108$ $-\,2^{22}\cdot 3^{3}\cdot 13^{4}$ $D_{8}$ (as 8T6) $[2]$ $3697.8932121$
8.2.3489136640000.8 $x^{8} + 16 x^{6} - 4 x^{4} + 256 x^{2} - 44$ $-\,2^{22}\cdot 5^{4}\cdot 11^{3}$ $D_{8}$ (as 8T6) $[2]$ $1913.6135089$
8.4.3787980800000.1 $x^{8} - 8 x^{6} - 8 x^{5} + 34 x^{4} + 32 x^{3} - 136 x^{2} - 32 x + 76$ $2^{22}\cdot 5^{5}\cdot 17^{2}$ $A_4^2:C_4$ (as 8T46) $[2]$ $1435.94931535$
8.2.5138202755072.8 $x^{8} - 4 x^{6} - 34 x^{4} - 120 x^{2} - 428$ $-\,2^{22}\cdot 107^{3}$ $\textrm{GL(2,3)}$ (as 8T23) $[2]$ $2843.67268928$
8.2.5138202755072.11 $x^{8} + 20 x^{6} + 134 x^{4} + 312 x^{2} - 428$ $-\,2^{22}\cdot 107^{3}$ $\textrm{GL(2,3)}$ (as 8T23) $[2]$ $2843.67268928$
8.2.5733089280000.3 $x^{8} + 16 x^{6} + 60 x^{4} - 300$ $-\,2^{22}\cdot 3^{7}\cdot 5^{4}$ $\textrm{GL(2,3)}$ (as 8T23) $[2]$ $2506.00029794$
8.2.5733089280000.8 $x^{8} - 36 x^{4} - 32 x^{2} - 108$ $-\,2^{22}\cdot 3^{7}\cdot 5^{4}$ $\textrm{GL(2,3)}$ (as 8T23) $[6]$ $835.333432648$
8.0.6717651812352.36 $x^{8} + 48 x^{6} + 924 x^{4} + 7488 x^{2} + 22932$ $2^{22}\cdot 3^{6}\cdot 13^{3}$ $C_4\wr C_2$ (as 8T17) $[4]$ $1214.4065591$
8.0.7676100608000.2 $x^{8} + 4 x^{6} + 54 x^{4} + 56 x^{2} + 20$ $2^{22}\cdot 5^{3}\cdot 11^{4}$ $D_{8}$ (as 8T6) $[4]$ $1988.32760257$
8.4.11023155200000.2 $x^{8} + 4 x^{6} - 26 x^{4} - 40 x^{2} + 20$ $2^{22}\cdot 5^{5}\cdot 29^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$ $1625.22440994$
8.2.51597803520000.9 $x^{8} - 4 x^{7} - 6 x^{6} + 16 x^{5} + 41 x^{4} + 24 x^{3} - 26 x^{2} + 44 x - 9$ $-\,2^{22}\cdot 3^{9}\cdot 5^{4}$ $\PGL(2,7)$ (as 8T43) $[2, 2]$ $6077.06743939$
8.8.63934300160000.3 $x^{8} - 36 x^{6} + 414 x^{4} - 1880 x^{2} + 2900$ $2^{22}\cdot 5^{4}\cdot 29^{3}$ $D_{8}$ (as 8T6) $[2]$ $12278.6001431$
8.2.87228416000000.4 $x^{8} - 20 x^{6} - 130 x^{4} + 5000 x^{2} - 27500$ $-\,2^{22}\cdot 5^{6}\cdot 11^{3}$ $QD_{16}$ (as 8T8) $[4]$ $2989.9449825$
8.0.118292480000000.10 $x^{8} - 40 x^{6} + 440 x^{4} - 6080 x^{2} + 115520$ $2^{22}\cdot 5^{7}\cdot 19^{2}$ $(C_8:C_2):C_2$ (as 8T16) $[4]$ $1459.94767878$
8.0.126142572920832.11 $x^{8} + 44 x^{6} + 510 x^{4} + 2184 x^{2} + 468$ $2^{22}\cdot 3^{4}\cdot 13^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2, 4]$ $2537.91556323$
8.4.126142572920832.11 $x^{8} - 20 x^{6} + 126 x^{4} - 312 x^{2} + 468$ $2^{22}\cdot 3^{4}\cdot 13^{5}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2]$ $16649.8325698$
8.2.143327232000000.6 $x^{8} + 60 x^{4} - 2080 x^{2} - 300$ $-\,2^{22}\cdot 3^{7}\cdot 5^{6}$ $\textrm{GL(2,3)}$ (as 8T23) $[2, 2]$ $8359.7330129$
8.2.143327232000000.8 $x^{8} + 20 x^{6} + 390 x^{4} - 360 x^{2} - 300$ $-\,2^{22}\cdot 3^{7}\cdot 5^{6}$ $\textrm{GL(2,3)}$ (as 8T23) $[2, 2]$ $8359.7330129$
8.4.238878720000000.4 $x^{8} - 420 x^{4} - 1440 x^{2} + 21780$ $2^{22}\cdot 3^{6}\cdot 5^{7}$ $C_8:C_2$ (as 8T7) $[4]$ $8711.20420998$
8.2.282620067840000.36 $x^{8} - 48 x^{6} - 36 x^{4} - 6912 x^{2} - 3564$ $-\,2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 11^{3}$ $D_{8}$ (as 8T6) $[4]$ $3952.20256105$
8.4.290368331448320.2 $x^{8} - 16 x^{6} - 16 x^{5} + 82 x^{4} + 128 x^{3} - 80 x^{2} - 144 x + 20$ $2^{22}\cdot 5\cdot 61^{4}$ $S_4\wr C_2$ (as 8T47) $[2]$ $23527.3283801$
8.8.370818940928000.1 $x^{8} - 44 x^{6} + 502 x^{4} - 1672 x^{2} + 980$ $2^{22}\cdot 5^{3}\cdot 29^{4}$ $D_{8}$ (as 8T6) $[2]$ $42030.7472431$
8.4.370818940928000.17 $x^{8} + 16 x^{6} - 356 x^{4} + 1280 x^{2} + 20$ $2^{22}\cdot 5^{3}\cdot 29^{4}$ $C_4\wr C_2$ (as 8T17) $[2]$ $8882.01249509$
8.0.439971370500096.14 $x^{8} + 44 x^{6} + 1326 x^{4} + 23816 x^{2} + 157396$ $2^{22}\cdot 3^{4}\cdot 109^{3}$ $D_{8}$ (as 8T6) $[20]$ $18915.0024688$
8.2.464380231680000.30 $x^{8} + 60 x^{6} + 750 x^{4} - 7000 x^{2} - 67500$ $-\,2^{22}\cdot 3^{11}\cdot 5^{4}$ $\textrm{GL(2,3)}$ (as 8T23) $[2, 2]$ $15567.3550861$
8.2.464380231680000.34 $x^{8} - 900 x^{4} + 12000 x^{2} - 67500$ $-\,2^{22}\cdot 3^{11}\cdot 5^{4}$ $\textrm{GL(2,3)}$ (as 8T23) $[2, 2]$ $15567.3550861$
8.0.466503598080000.11 $x^{8} - 100 x^{6} + 3550 x^{4} - 51000 x^{2} + 292500$ $2^{22}\cdot 3^{4}\cdot 5^{4}\cdot 13^{3}$ $D_{8}$ (as 8T6) $[2, 4]$ $7217.53060799$
8.2.546617815990272.3 $x^{8} + 156 x^{4} - 5408 x^{2} - 2028$ $-\,2^{22}\cdot 3^{3}\cdot 13^{6}$ $QD_{16}$ (as 8T8) $[4]$ $5821.86141334$
8.2.550605894451200.21 $x^{8} + 48 x^{6} + 252 x^{4} + 960 x^{2} - 300$ $-\,2^{22}\cdot 3^{7}\cdot 5^{2}\cdot 7^{4}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $8134.77596246$
8.2.550605894451200.22 $x^{8} + 36 x^{6} + 294 x^{4} + 1560 x^{2} - 300$ $-\,2^{22}\cdot 3^{7}\cdot 5^{2}\cdot 7^{4}$ $Z_8 : Z_8^\times$ (as 8T15) $[4]$ $8134.77596246$
8.0.621764149248000.2 $x^{8} - 12 x^{6} + 486 x^{4} - 1512 x^{2} + 1620$ $2^{22}\cdot 3^{4}\cdot 5^{3}\cdot 11^{4}$ $D_{8}$ (as 8T6) $[2, 4]$ $4106.51022609$
8.2.1079187553124352.2 $x^{8} - 420 x^{4} + 4704 x^{2} - 14700$ $-\,2^{22}\cdot 3^{7}\cdot 7^{6}$ $QD_{16}$ (as 8T8) $[4]$ $10705.7748233$
8.0.1135283156287488.28 $x^{8} + 7644 x^{4} + 146016 x^{2} + 711828$ $2^{22}\cdot 3^{6}\cdot 13^{5}$ $C_4\wr C_2$ (as 8T17) $[2, 2, 20]$ $2477.18723452$
8.0.1598357504000000.1 $x^{8} + 80 x^{6} + 1660 x^{4} + 6400 x^{2} + 2900$ $2^{22}\cdot 5^{6}\cdot 29^{3}$ $QD_{16}$ (as 8T8) $[2, 2, 132]$ $52.2683814915$
8.0.1598357504000000.9 $x^{8} + 12 x^{6} + 174 x^{4} + 6728 x^{2} + 97556$ $2^{22}\cdot 5^{6}\cdot 29^{3}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2, 2, 4]$ $1267.78353729$
8.2.1783963098021888.51 $x^{8} - 1764 x^{4} - 32928 x^{2} - 259308$ $-\,2^{22}\cdot 3^{11}\cdot 7^{4}$ $\textrm{GL(2,3)}$ (as 8T23) $[4]$ $31279.9046433$
8.2.1783963098021888.55 $x^{8} - 84 x^{6} + 1470 x^{4} + 19208 x^{2} - 259308$ $-\,2^{22}\cdot 3^{11}\cdot 7^{4}$ $\textrm{GL(2,3)}$ (as 8T23) $[4]$ $31279.9046433$
8.0.1792120222384128.12 $x^{8} + 140 x^{6} + 6958 x^{4} + 139944 x^{2} + 1123668$ $2^{22}\cdot 3^{4}\cdot 7^{4}\cdot 13^{3}$ $D_{8}$ (as 8T6) $[2, 4]$ $12297.966856$
8.2.2021515591680000.15 $x^{8} + 60 x^{6} + 750 x^{4} - 11000 x^{2} - 67500$ $-\,2^{22}\cdot 3^{3}\cdot 5^{4}\cdot 13^{4}$ $D_{8}$ (as 8T6) $[2, 2]$ $17246.4801801$
8.6.4919560343912448.6 $x^{8} - 16 x^{6} - 164 x^{4} + 576 x^{2} - 108$ $-\,2^{22}\cdot 3^{5}\cdot 13^{6}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[4]$ $66709.4008607$
8.2.4919560343912448.10 $x^{8} + 16 x^{6} - 164 x^{4} - 3072 x^{2} - 10092$ $-\,2^{22}\cdot 3^{5}\cdot 13^{6}$ $((C_8 : C_2):C_2):C_2$ (as 8T27) $[2, 4]$ $20336.8803799$
8.0.6476605685760000.1 $x^{8} - 28 x^{6} - 168 x^{5} + 126 x^{4} + 2912 x^{3} + 6496 x^{2} + 9520 x + 40460$ $2^{22}\cdot 3\cdot 5^{4}\cdot 7^{7}$ $S_4\wr C_2$ (as 8T47) $[2, 4]$ $14812.344105$
8.2.7765854296997888.12 $x^{8} - 84 x^{6} + 1470 x^{4} + 30184 x^{2} - 259308$ $-\,2^{22}\cdot 3^{3}\cdot 7^{4}\cdot 13^{4}$ $D_{8}$ (as 8T6) $[4]$ $29386.316894$
8.4.9270473523200000.4 $x^{8} - 60 x^{6} - 1770 x^{4} - 9800 x^{2} + 12500$ $2^{22}\cdot 5^{5}\cdot 29^{4}$ $C_4\wr C_2$ (as 8T17) $[2, 2, 2]$ $46132.5367321$
8.4.9270473523200000.12 $x^{8} + 24 x^{6} - 3336 x^{4} - 64960 x^{2} + 269120$ $2^{22}\cdot 5^{5}\cdot 29^{4}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) $[2, 2, 2]$ $17213.0520607$
8.2.15985626461503488.3 $x^{8} - 44 x^{6} + 934 x^{4} - 744 x^{2} - 5292$ $-\,2^{22}\cdot 3^{3}\cdot 109^{4}$ $D_{8}$ (as 8T6) $[10]$ $210506.389808$
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