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Label Polynomial Discriminant Galois group Class group Regulator
8.0.339738624.9 $x^{8} - 4 x^{6} + 10 x^{4} - 24 x^{2} + 36$ $2^{22}\cdot 3^{4}$ $D_4$ (as 8T4) trivial $30.1437202202$
8.0.2151677952.3 $x^{8} - 8 x^{5} + 20 x^{4} - 24 x^{3} + 12 x^{2} + 3$ $2^{22}\cdot 3^{3}\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $32.9889234401$
8.0.2621440000.14 $x^{8} + 4 x^{6} - 8 x^{5} + 24 x^{2} + 16 x + 12$ $2^{22}\cdot 5^{4}$ $S_4$ (as 8T14) trivial $50.9500558475$
8.0.4567597056.11 $x^{8} + 4 x^{6} + 2 x^{4} - 8 x^{2} + 4$ $2^{22}\cdot 3^{2}\cdot 11^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $82.0190483211$
8.2.7813988352.4 $x^{8} - 4 x^{7} - 2 x^{6} + 16 x^{5} + 21 x^{4} - 64 x^{3} - 14 x^{2} + 52 x + 19$ $-\,2^{22}\cdot 3^{4}\cdot 23$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $119.499011807$
8.0.10909384704.14 $x^{8} - 4 x^{7} + 14 x^{6} - 16 x^{5} + 43 x^{4} - 40 x^{3} + 54 x^{2} - 108 x + 83$ $2^{22}\cdot 3^{2}\cdot 17^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $125.846288551$
8.0.10909384704.16 $x^{8} - 4 x^{7} + 14 x^{6} - 24 x^{5} + 39 x^{4} + 24 x^{3} - 38 x^{2} + 44 x + 107$ $2^{22}\cdot 3^{2}\cdot 17^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $49.4581707379$
8.0.13627293696.15 $x^{8} - 12 x^{6} + 34 x^{4} + 24 x^{2} + 4$ $2^{22}\cdot 3^{2}\cdot 19^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $157.294925806$
8.0.16043212800.3 $x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} + 3 x^{4} - 24 x^{3} + 34 x^{2} - 20 x + 19$ $2^{22}\cdot 3^{2}\cdot 5^{2}\cdot 17$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $139.188646372$
8.2.18350080000.2 $x^{8} + 4 x^{6} - 16 x^{5} + 20 x^{4} - 32 x^{3} + 16 x^{2} + 16$ $-\,2^{22}\cdot 5^{4}\cdot 7$ $C_2 \wr S_4$ (as 8T44) trivial $311.061840906$
8.0.21143486464.9 $x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 5 x^{4} - 8 x^{3} + 10 x^{2} - 4 x + 3$ $2^{22}\cdot 71^{2}$ $S_4\times C_2$ (as 8T24) trivial $150.335798937$
8.0.23592960000.11 $x^{8} + 12 x^{6} + 58 x^{4} + 72 x^{2} + 36$ $2^{22}\cdot 3^{2}\cdot 5^{4}$ $D_4\times C_2$ (as 8T9) trivial $124.709200996$
8.0.24868028416.3 $x^{8} - 4 x^{7} + 14 x^{6} - 24 x^{5} + 39 x^{4} - 56 x^{3} + 42 x^{2} - 36 x + 27$ $2^{22}\cdot 7^{2}\cdot 11^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $356.236387958$
8.0.27518828544.15 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 19 x^{4} - 16 x^{3} + 18 x^{2} - 12 x + 3$ $2^{22}\cdot 3^{8}$ $S_4$ (as 8T14) trivial $329.860958867$
8.2.27644657664.1 $x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 9 x^{4} - 10 x^{2} + 12 x - 7$ $-\,2^{22}\cdot 3\cdot 13^{3}$ $C_2 \wr S_4$ (as 8T44) trivial $299.814225915$
8.2.27644657664.3 $x^{8} - 4 x^{7} + 2 x^{6} + 8 x^{5} - 11 x^{4} + 14 x^{2} - 12 x + 3$ $-\,2^{22}\cdot 3\cdot 13^{3}$ $C_2 \wr S_4$ (as 8T44) trivial $173.074242255$
8.0.30236737536.4 $x^{8} - 4 x^{7} + 6 x^{6} - 41 x^{4} + 72 x^{3} + 42 x^{2} - 164 x + 121$ $2^{22}\cdot 3^{4}\cdot 89$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $101.918396357$
8.0.31142707200.5 $x^{8} + 8 x^{6} - 8 x^{5} + 20 x^{4} - 24 x^{3} + 36 x^{2} + 3$ $2^{22}\cdot 3^{3}\cdot 5^{2}\cdot 11$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $159.592880183$
8.2.32275169280.1 $x^{8} - 4 x^{7} - 2 x^{6} + 8 x^{5} + 15 x^{4} - 8 x^{3} - 14 x^{2} - 20 x - 5$ $-\,2^{22}\cdot 3^{4}\cdot 5\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $193.393074371$
8.2.32275169280.3 $x^{8} + 8 x^{6} + 20 x^{4} - 24 x^{3} - 20 x^{2} - 72 x - 29$ $-\,2^{22}\cdot 3^{4}\cdot 5\cdot 19$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $159.505005358$
8.0.38390464512.4 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} - 3 x^{4} + 16 x^{3} + 10 x^{2} + 4 x + 1$ $2^{22}\cdot 3^{4}\cdot 113$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $53.7641927741$
8.4.41108373504.6 $x^{8} - 8 x^{6} - 8 x^{5} - 28 x^{4} - 40 x^{3} - 12 x^{2} - 16 x + 19$ $2^{22}\cdot 3^{4}\cdot 11^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $343.354645327$
8.0.41108373504.12 $x^{8} - 4 x^{7} + 22 x^{6} - 40 x^{5} + 99 x^{4} - 128 x^{3} + 142 x^{2} - 68 x + 19$ $2^{22}\cdot 3^{4}\cdot 11^{2}$ $C_2^2 \wr C_2$ (as 8T18) $[2]$ $74.1367711994$
8.0.41108373504.35 $x^{8} - 4 x^{6} - 6 x^{4} - 88 x^{2} + 484$ $2^{22}\cdot 3^{4}\cdot 11^{2}$ $D_4\times C_2$ (as 8T9) $[2]$ $526.985001981$
8.0.43826282496.2 $x^{8} - 4 x^{7} - 2 x^{6} + 8 x^{5} + 37 x^{4} + 8 x^{3} - 2 x^{2} - 4 x + 1$ $2^{22}\cdot 3^{5}\cdot 43$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $85.8803263819$
8.0.49262100480.1 $x^{8} - 8 x^{5} + 4 x^{4} + 24 x^{3} - 20 x^{2} - 16 x + 19$ $2^{22}\cdot 3^{4}\cdot 5\cdot 29$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $40.63163724345047$
8.4.57415827456.8 $x^{8} - 12 x^{6} - 8 x^{5} + 32 x^{4} - 8 x^{2} + 16 x - 20$ $2^{22}\cdot 3^{4}\cdot 13^{2}$ $S_4\times C_2$ (as 8T24) trivial $466.104948559$
8.0.57415827456.19 $x^{8} + 8 x^{6} - 16 x^{5} + 62 x^{4} - 64 x^{3} + 80 x^{2} + 16 x + 4$ $2^{22}\cdot 3^{4}\cdot 13^{2}$ $S_4\times C_2$ (as 8T24) $[4]$ $166.804564313$
8.0.60133736448.6 $x^{8} + 8 x^{6} + 4 x^{4} - 24 x^{3} + 12 x^{2} + 24 x + 51$ $2^{22}\cdot 3^{5}\cdot 59$ $C_2 \wr C_2\wr C_2$ (as 8T35) $[2]$ $101.932001999$
8.0.61408804864.10 $x^{8} + 12 x^{6} + 90 x^{4} + 104 x^{2} + 36$ $2^{22}\cdot 11^{4}$ $D_4$ (as 8T4) trivial $1519.91232067$
8.0.63455625216.6 $x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 111 x^{4} - 160 x^{3} + 126 x^{2} - 52 x + 11$ $2^{22}\cdot 3^{2}\cdot 41^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $181.759691971$
8.0.63455625216.13 $x^{8} - 4 x^{7} + 18 x^{6} - 40 x^{5} + 63 x^{4} - 64 x^{3} - 34 x^{2} + 60 x + 75$ $2^{22}\cdot 3^{2}\cdot 41^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $306.035234755$
8.4.65536000000.5 $x^{8} - 8 x^{6} - 8 x^{5} - 10 x^{4} + 32 x^{3} + 40 x^{2} - 96 x + 44$ $2^{22}\cdot 5^{6}$ $S_4\times C_2$ (as 8T24) trivial $405.380108206$
8.0.69797412864.6 $x^{8} - 4 x^{6} + 26 x^{4} - 56 x^{2} + 36$ $2^{22}\cdot 3^{2}\cdot 43^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $294.240898169$
8.0.76441190400.7 $x^{8} - 12 x^{6} + 114 x^{4} - 360 x^{2} + 900$ $2^{22}\cdot 3^{6}\cdot 5^{2}$ $D_4\times C_2$ (as 8T9) $[2]$ $289.896295837$
8.0.76441190400.15 $x^{8} + 12 x^{6} + 42 x^{4} + 72 x^{2} + 36$ $2^{22}\cdot 3^{6}\cdot 5^{2}$ $C_2^2 \wr C_2$ (as 8T18) $[2]$ $75.8813316477$
8.4.76441190400.16 $x^{8} - 8 x^{6} + 60 x^{4} - 176 x^{2} + 100$ $2^{22}\cdot 3^{6}\cdot 5^{2}$ $C_2^2 \wr C_2$ (as 8T18) trivial $599.737531436$
8.0.78722891776.11 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 11 x^{4} + 18 x^{2} - 20 x + 17$ $2^{22}\cdot 137^{2}$ $S_4\times C_2$ (as 8T24) trivial $129.921384946$
8.0.78722891776.15 $x^{8} - 4 x^{7} - 2 x^{6} + 16 x^{5} + 5 x^{4} - 16 x^{3} + 2 x^{2} + 4 x + 3$ $2^{22}\cdot 137^{2}$ $V_4^2:(S_3\times C_2)$ (as 8T41) trivial $315.045736677$
8.0.83386957824.3 $x^{8} - 4 x^{7} + 6 x^{6} - 25 x^{4} + 122 x^{2} - 108 x + 27$ $2^{22}\cdot 3^{2}\cdot 47^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $366.895251535$
8.4.90030735360.1 $x^{8} - 4 x^{7} + 6 x^{6} - 63 x^{4} + 224 x^{3} - 322 x^{2} + 212 x - 53$ $2^{22}\cdot 3^{4}\cdot 5\cdot 53$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $362.4231972246938$
8.2.95693045760.1 $x^{8} - 4 x^{6} + 26 x^{4} - 48 x^{3} - 40 x^{2} + 32 x + 36$ $-\,2^{22}\cdot 3^{3}\cdot 5\cdot 13^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $674.436016102$
8.2.95693045760.2 $x^{8} - 4 x^{7} + 2 x^{6} + 21 x^{4} - 8 x^{3} + 22 x^{2} - 20 x + 3$ $-\,2^{22}\cdot 3^{3}\cdot 5\cdot 13^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $598.806699131$
8.0.98184462336.20 $x^{8} - 20 x^{6} + 298 x^{4} - 2040 x^{2} + 10404$ $2^{22}\cdot 3^{4}\cdot 17^{2}$ $D_4\times C_2$ (as 8T9) $[2]$ $389.677571348$
8.4.119793516544.3 $x^{8} - 16 x^{5} - 10 x^{4} + 64 x^{2} + 80 x - 92$ $2^{22}\cdot 13^{4}$ $S_4\times C_2$ (as 8T24) trivial $804.485315395$
8.0.119793516544.13 $x^{8} - 4 x^{7} + 6 x^{6} + 8 x^{5} + 5 x^{4} + 8 x^{3} + 38 x^{2} + 12 x + 1$ $2^{22}\cdot 13^{4}$ $S_4$ (as 8T14) $[6]$ $109.817350908$
8.4.122645643264.8 $x^{8} - 4 x^{7} + 6 x^{6} - 3 x^{4} - 16 x^{3} - 10 x^{2} + 20 x + 1$ $2^{22}\cdot 3^{4}\cdot 19^{2}$ $(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) trivial $517.010926393$
8.0.122645643264.12 $x^{8} + 12 x^{6} + 106 x^{4} + 456 x^{2} + 1444$ $2^{22}\cdot 3^{4}\cdot 19^{2}$ $D_4\times C_2$ (as 8T9) $[2]$ $372.569157808$
8.0.122645643264.41 $x^{8} - 4 x^{7} + 10 x^{6} - 16 x^{5} + 71 x^{4} - 120 x^{3} + 118 x^{2} - 60 x + 123$ $2^{22}\cdot 3^{4}\cdot 19^{2}$ $C_2^2 \wr C_2$ (as 8T18) $[2]$ $125.048431294$
8.0.128450560000.20 $x^{8} - 4 x^{7} - 6 x^{6} + 32 x^{5} + 19 x^{4} - 96 x^{3} + 146 x^{2} - 92 x + 131$ $2^{22}\cdot 5^{4}\cdot 7^{2}$ $D_4\times C_2$ (as 8T9) trivial $275.288450439$
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