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Label Polynomial Discriminant Galois group Class group Regulator
8.0.4432460726281.1 $x^{8} - 12 x^{6} + 54 x^{4} - 41 x^{2} + 81$ $7^{2}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $656.938447984$
8.0.23157345835264.1 $x^{8} - 4 x^{7} + 28 x^{6} - 70 x^{5} + 215 x^{4} - 318 x^{3} + 512 x^{2} - 364 x + 199$ $2^{8}\cdot 67^{6}$ $S_4$ (as 8T14) trivial $1803.33818217$
8.0.56536488855625.3 $x^{8} - 3 x^{7} - 3 x^{6} - 2 x^{5} - 27 x^{4} + 200 x^{3} - 118 x^{2} + 276 x + 2969$ $5^{4}\cdot 67^{6}$ $S_4$ (as 8T14) trivial $2765.40207537$
8.0.208416112517376.1 $x^{8} - 66 x^{6} + 1131 x^{4} - 314 x^{2} + 441$ $2^{8}\cdot 3^{2}\cdot 67^{6}$ $D_4\times C_2$ (as 8T9) $[5]$ $4529.5790978$
8.4.208416112517376.1 $x^{8} - 13 x^{6} + 189 x^{4} - 1180 x^{2} + 4$ $2^{8}\cdot 3^{2}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $551473.840168$
8.0.208416112517376.3 $x^{8} + 17 x^{6} + 100 x^{4} + 1065 x^{2} + 1521$ $2^{8}\cdot 3^{2}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) $[2]$ $14282.6985267$
8.0.208416112517376.4 $x^{8} - 8 x^{6} + 91 x^{4} - 268 x^{3} + 370 x^{2} - 268 x + 83$ $2^{8}\cdot 3^{2}\cdot 67^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $10423.2415769$
8.0.217190575587769.3 $x^{8} + 16 x^{6} + 163 x^{4} + 323 x^{2} - 1407 x + 1395$ $7^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[6]$ $2727.06777786$
8.0.370517533364224.2 $x^{8} - 4 x^{7} + 8 x^{6} - 10 x^{5} - 25 x^{4} + 62 x^{3} + 2 x^{2} - 34 x + 289$ $2^{12}\cdot 67^{6}$ $D_4$ (as 8T4) trivial $37956.223286$
8.0.370517533364224.3 $x^{8} - 2 x^{7} + 2 x^{6} + 116 x^{5} + 212 x^{4} + 1388 x^{3} + 3528 x^{2} - 1848 x + 484$ $2^{12}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) $[2]$ $9547.44020548$
8.4.468936253164096.1 $x^{8} - 32 x^{6} + 116 x^{4} + 2240 x^{2} + 4096$ $2^{6}\cdot 3^{4}\cdot 67^{6}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $247462.645628$
8.0.508828399700625.1 $x^{8} + 49 x^{6} + 1227 x^{4} + 1411 x^{2} + 10816$ $3^{2}\cdot 5^{4}\cdot 67^{6}$ $D_4\times C_2$ (as 8T9) $[9]$ $2900.87120677$
8.0.593497445410809.1 $x^{8} - 4 x^{7} + 28 x^{6} - 70 x^{5} + 148 x^{4} - 184 x^{3} + 713 x^{2} - 632 x + 668$ $3^{8}\cdot 67^{6}$ $S_4$ (as 8T14) trivial $29771.8818436$
8.0.904583821690000.1 $x^{8} - 3 x^{7} + 30 x^{6} - 93 x^{5} + 474 x^{4} - 797 x^{3} + 1585 x^{2} + 598 x + 76$ $2^{4}\cdot 5^{4}\cdot 67^{6}$ $V_4^2:S_3$ (as 8T34) $[2, 4]$ $2690.27856622$
8.4.904583821690000.1 $x^{8} - 2 x^{7} - 20 x^{6} - 52 x^{5} + 419 x^{4} + 112 x^{3} + 1160 x^{2} - 10908 x + 12141$ $2^{4}\cdot 5^{4}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $59733.4279922$
8.4.904583821690000.2 $x^{8} - x^{7} - 25 x^{6} - 92 x^{5} + 6 x^{4} + 3138 x^{3} - 3856 x^{2} + 2360 x + 24100$ $2^{4}\cdot 5^{4}\cdot 67^{6}$ $(A_4\wr C_2):C_2$ (as 8T45) trivial $70089.2192108$
8.0.904583821690000.3 $x^{8} - 4 x^{7} + 16 x^{6} - 34 x^{5} + 35 x^{4} - 18 x^{3} - 34 x^{2} + 38 x + 127$ $2^{4}\cdot 5^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[2, 2]$ $4048.70862136$
8.0.904583821690000.4 $x^{8} - 3 x^{7} - 2 x^{6} - 21 x^{5} + 232 x^{4} - 669 x^{3} + 895 x^{2} - 576 x + 144$ $2^{4}\cdot 5^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[10]$ $3016.95213717$
8.0.904583821690000.5 $x^{8} + 39 x^{6} + 160 x^{4} + 504 x^{2} + 324$ $2^{4}\cdot 5^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[2, 4]$ $3219.2156152$
8.0.1055106569619216.1 $x^{8} - 4 x^{7} + 42 x^{6} - 112 x^{5} + 595 x^{4} - 1008 x^{3} + 3402 x^{2} - 2916 x + 3345$ $2^{4}\cdot 3^{6}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[10]$ $9543.13005455$
8.4.1055106569619216.1 $x^{8} - 32 x^{6} + 183 x^{4} - 1608 x^{3} - 6872 x^{2} - 6432 x + 880$ $2^{4}\cdot 3^{6}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) trivial $470281.436754$
8.0.1055106569619216.2 $x^{8} + 35 x^{6} + 384 x^{4} + 2240 x^{2} + 4096$ $2^{4}\cdot 3^{6}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[10]$ $11923.9744146$
8.4.1055106569619216.2 $x^{8} - 4 x^{7} - 25 x^{6} - 112 x^{5} + 595 x^{4} + 3280 x^{3} - 12343 x^{2} - 21140 x + 196$ $2^{4}\cdot 3^{6}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) trivial $587608.445811$
8.4.1413412221390625.1 $x^{8} - x^{7} - 25 x^{6} - 25 x^{5} + 140 x^{4} + 659 x^{3} - 1109 x^{2} + 1020 x - 355$ $5^{6}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $41237.9539683$
8.0.1648604015030025.1 $x^{8} - 2 x^{7} + 62 x^{6} + 160 x^{5} - 146 x^{4} - 1198 x^{3} - 433 x^{2} + 3608 x + 3568$ $3^{6}\cdot 5^{2}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[18]$ $4072.35699302$
8.4.1648604015030025.1 $x^{8} - 3 x^{7} + 7 x^{6} - 192 x^{5} - 636 x^{4} + 1032 x^{3} + 11587 x^{2} + 100419 x - 277835$ $3^{6}\cdot 5^{2}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) trivial $173532.758349$
8.0.1648604015030025.2 $x^{8} + 35 x^{6} + 384 x^{4} - 373 x^{2} + 18769$ $3^{6}\cdot 5^{2}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[18]$ $48373.9177595$
8.4.1648604015030025.2 $x^{8} - 4 x^{7} + 42 x^{6} - 112 x^{5} - 8 x^{4} + 198 x^{3} - 3633 x^{2} + 3516 x + 1536$ $3^{6}\cdot 5^{2}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) trivial $2061326.98959$
8.8.1875745012656384.1 $x^{8} - 51 x^{6} + 632 x^{4} - 816 x^{2} + 256$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $D_4$ (as 8T4) trivial $2035015.20519$
8.4.1875745012656384.2 $x^{8} - 2 x^{7} - 27 x^{6} - 8 x^{5} + 277 x^{4} - 144 x^{3} + 900 x^{2} - 2016 x - 1152$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) $[4]$ $117724.584417$
8.4.1875745012656384.3 $x^{8} - 30 x^{6} - 134 x^{5} - 98 x^{4} + 88 x^{2} + 2144 x + 1912$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $130419.671462$
8.4.1875745012656384.5 $x^{8} - 4 x^{7} - 4 x^{6} + 26 x^{5} - 25 x^{4} + 2 x^{3} - 92 x^{2} + 96 x + 60$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $667831.094125$
8.0.1875745012656384.9 $x^{8} - 4 x^{7} + 62 x^{6} - 172 x^{5} + 1211 x^{4} - 2140 x^{3} - 4598 x^{2} + 5640 x + 13425$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $D_4$ (as 8T4) $[5, 10]$ $1675.96006677$
8.0.1875745012656384.10 $x^{8} + 49 x^{6} + 892 x^{4} + 7977 x^{2} + 29241$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[2, 6]$ $18731.551058$
8.0.1875745012656384.13 $x^{8} + 17 x^{6} + 904 x^{4} + 7497 x^{2} + 194481$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $D_4\times C_2$ (as 8T9) $[30]$ $10916.6125854$
8.0.1875745012656384.16 $x^{8} - 20 x^{6} + 150 x^{4} + 1912 x^{2} + 625$ $2^{8}\cdot 3^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[2, 2]$ $7068.28872035$
8.6.2500993350208512.1 $x^{8} - 32 x^{6} + 116 x^{4} + 96 x^{2} - 192$ $-\,2^{10}\cdot 3^{3}\cdot 67^{6}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $1179457.99819$
8.0.3334657800278016.2 $x^{8} + 16 x^{6} + 230 x^{4} + 1328 x^{2} + 2601$ $2^{12}\cdot 3^{2}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) $[10]$ $20222.9131574$
8.4.3334657800278016.2 $x^{8} + 16 x^{6} - 172 x^{4} + 256 x^{2} + 256$ $2^{12}\cdot 3^{2}\cdot 67^{6}$ $C_2^2 \wr C_2$ (as 8T18) trivial $996576.65783$
8.0.3334657800278016.3 $x^{8} - 4 x^{7} - 62 x^{6} + 200 x^{5} + 1531 x^{4} - 3400 x^{3} - 17650 x^{2} + 19384 x + 83588$ $2^{12}\cdot 3^{2}\cdot 67^{6}$ $D_4\times C_2$ (as 8T9) $[7, 21]$ $384.984432894$
8.4.3475049209404304.1 $x^{8} - 4 x^{7} - 24 x^{6} + 86 x^{5} + 215 x^{4} - 578 x^{3} - 1350 x^{2} + 1654 x + 1443$ $2^{4}\cdot 7^{4}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) $[3]$ $226076.711964$
8.0.3475049209404304.3 $x^{8} + 33 x^{6} + 199 x^{4} - 681 x^{2} + 484$ $2^{4}\cdot 7^{4}\cdot 67^{6}$ $S_4$ (as 8T14) $[2]$ $25829.0474619$
8.4.4579455597305625.1 $x^{8} - 2 x^{7} - 20 x^{6} - 320 x^{5} + 1089 x^{4} + 1184 x^{3} + 29032 x^{2} - 116902 x + 64669$ $3^{4}\cdot 5^{4}\cdot 67^{6}$ $D_4\times C_2$ (as 8T9) trivial $301201.561089$
8.0.4579455597305625.13 $x^{8} + 82 x^{6} + 2689 x^{4} + 21228 x^{2} + 254016$ $3^{4}\cdot 5^{4}\cdot 67^{6}$ $D_4$ (as 8T4) $[18]$ $991421.876225$
8.0.4579455597305625.16 $x^{8} - 13 x^{6} + 256 x^{4} + 12555 x^{2} + 540225$ $3^{4}\cdot 5^{4}\cdot 67^{6}$ $D_4$ (as 8T4) $[18]$ $7026.31568723$
8.0.5928280533827584.1 $x^{8} + 4 x^{6} - 128 x^{4} + 808 x^{2} + 4356$ $2^{16}\cdot 67^{6}$ $D_4$ (as 8T4) $[3, 3]$ $12209.3527086$
8.4.5928280533827584.1 $x^{8} + 4 x^{6} + 6 x^{4} - 130 x^{2} + 1$ $2^{16}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $82392.6959166$
8.4.5928280533827584.2 $x^{8} - 34 x^{6} + 132 x^{4} - 4232 x^{2} + 484$ $2^{16}\cdot 67^{6}$ $S_4\times C_2$ (as 8T24) trivial $98578.0191311$
8.0.5928280533827584.3 $x^{8} - 8 x^{6} + 24 x^{4} - 1072 x^{3} + 772 x^{2} + 2680 x + 18575$ $2^{16}\cdot 67^{6}$ $S_4$ (as 8T14) $[5]$ $8156.2349541$
8.0.5928280533827584.7 $x^{8} - 2 x^{6} + 35 x^{4} + 100 x^{2} + 289$ $2^{16}\cdot 67^{6}$ $D_4\times C_2$ (as 8T9) $[21]$ $3302.75969775$
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