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Label Polynomial Discriminant Galois group Class group Regulator
8.6.65106259.1 $x^{8} - 5 x^{6} - x^{5} + 7 x^{4} + 4 x^{3} - 4 x^{2} - 2 x + 1$ $-\,89\cdot 731531$ $S_8$ (as 8T50) trivial $7.13506329205$
8.6.68494627.1 $x^{8} - 2 x^{7} - 3 x^{6} + 10 x^{5} - 2 x^{4} - 11 x^{3} + 5 x^{2} + 2 x - 1$ $-\,811\cdot 84457$ $S_8$ (as 8T50) trivial $7.38088275852$
8.6.68856875.1 $x^{8} - 2 x^{7} - 2 x^{6} + x^{5} + x^{4} + 5 x^{3} - x^{2} - 3 x + 1$ $-\,5^{4}\cdot 29^{2}\cdot 131$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $7.41473348387$
8.6.69367411.1 $x^{8} - x^{6} - 3 x^{5} - 3 x^{4} + 6 x^{3} + 4 x^{2} - 2 x - 1$ $-\,69367411$ $S_8$ (as 8T50) trivial $7.43035213338$
8.6.73061875.1 $x^{8} - 4 x^{6} - 3 x^{4} - 5 x^{3} + 4 x^{2} + 5 x + 1$ $-\,5^{4}\cdot 29^{2}\cdot 139$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $7.66924336082$
8.6.74671875.1 $x^{8} - 4 x^{7} + 5 x^{6} - x^{5} - 6 x^{4} + 9 x^{3} - 4 x + 1$ $-\,3^{4}\cdot 5^{6}\cdot 59$ $((C_8 : C_2):C_2):C_2$ (as 8T27) trivial $7.76874863093$
8.6.74906875.1 $x^{8} - 3 x^{6} - 3 x^{5} + 3 x^{4} + 7 x^{3} - 2 x^{2} - 3 x + 1$ $-\,5^{4}\cdot 119851$ $S_4\wr C_2$ (as 8T47) trivial $7.80639541536$
8.6.75272867.1 $x^{8} - 2 x^{7} - 3 x^{6} + 9 x^{5} - x^{4} - 10 x^{3} + 3 x^{2} + 3 x - 1$ $-\,31\cdot 2428157$ $S_8$ (as 8T50) trivial $7.82545816415$
8.6.83260171.1 $x^{8} - 2 x^{7} - 3 x^{6} + 4 x^{5} + 3 x^{4} + x^{3} - x^{2} - 3 x - 1$ $-\,47\cdot 1771493$ $S_8$ (as 8T50) trivial $8.34345597927$
8.6.84356875.1 $x^{8} - 3 x^{6} - x^{5} + 4 x^{3} + 3 x^{2} - 2 x - 1$ $-\,5^{4}\cdot 71\cdot 1901$ $S_4\wr C_2$ (as 8T47) trivial $8.3932670464$
8.6.86606875.1 $x^{8} - x^{7} - 3 x^{6} + 2 x^{5} - x^{4} + 6 x^{3} + 3 x^{2} - 7 x - 1$ $-\,5^{4}\cdot 138571$ $S_4\wr C_2$ (as 8T47) trivial $8.61675807033$
8.6.93594547.1 $x^{8} - x^{7} - 6 x^{6} + 4 x^{5} + 11 x^{4} - 3 x^{3} - 7 x^{2} + x + 1$ $-\,1117\cdot 83791$ $S_8$ (as 8T50) trivial $8.97005663928$
8.6.94086875.1 $x^{8} - 2 x^{7} + x^{6} + 4 x^{5} - 12 x^{4} + 3 x^{3} + 9 x^{2} - 6 x + 1$ $-\,5^{4}\cdot 29^{2}\cdot 179$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $8.98090007444$
8.6.94156147.1 $x^{8} - 5 x^{6} - x^{5} + 7 x^{4} + 4 x^{3} - 3 x^{2} - 3 x + 1$ $-\,94156147$ $S_8$ (as 8T50) trivial $9.0269732907$
8.6.94856875.1 $x^{8} - x^{7} - x^{6} + 3 x^{5} - 5 x^{4} - 2 x^{3} + 6 x^{2} + x - 1$ $-\,5^{4}\cdot 151771$ $S_4\wr C_2$ (as 8T47) trivial $9.1297954509$
8.6.95029219.1 $x^{8} - x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 2 x^{3} + 4 x^{2} + x - 1$ $-\,1291\cdot 73609$ $S_8$ (as 8T50) trivial $9.10258386395$
8.6.96530491.1 $x^{8} - 2 x^{7} - 3 x^{6} + 7 x^{5} - 6 x^{3} + 4 x^{2} + x - 1$ $-\,96530491$ $S_8$ (as 8T50) trivial $9.17845856742$
8.6.96598171.1 $x^{8} - 3 x^{7} + x^{6} + 4 x^{5} - 7 x^{4} + 5 x^{3} + 5 x^{2} - 6 x + 1$ $-\,53\cdot 1229\cdot 1483$ $S_8$ (as 8T50) trivial $9.13243508284$
8.6.97161811.1 $x^{8} - 5 x^{6} - x^{5} + 6 x^{4} + 3 x^{3} - 2 x - 1$ $-\,43\cdot 521\cdot 4337$ $S_8$ (as 8T50) trivial $9.26321506754$
8.6.98070859.1 $x^{8} - 2 x^{7} - x^{6} + 3 x^{5} - 5 x^{4} + 10 x^{3} - 4 x^{2} - 2 x + 1$ $-\,61\cdot 263\cdot 6113$ $S_8$ (as 8T50) trivial $9.27226479393$
8.6.98151947.1 $x^{8} - 4 x^{6} - x^{5} + 3 x^{4} + 3 x^{3} + 2 x^{2} - 2 x - 1$ $-\,7297\cdot 13451$ $S_8$ (as 8T50) trivial $9.2719804595$
8.6.98915419.1 $x^{8} - 4 x^{6} - x^{5} + 2 x^{4} + x^{3} + 3 x^{2} - 1$ $-\,151\cdot 655069$ $S_8$ (as 8T50) trivial $9.3162069083$
8.6.103405923.1 $x^{8} - x^{7} + x^{5} - 8 x^{4} + x^{3} + 8 x^{2} - 2 x - 1$ $-\,3^{3}\cdot 19^{2}\cdot 103^{2}$ $C_2 \wr S_4$ (as 8T44) trivial $9.68622718301$
8.6.104081867.1 $x^{8} - 3 x^{7} - x^{6} + 10 x^{5} - 5 x^{4} - 10 x^{3} + 7 x^{2} + 3 x - 1$ $-\,19\cdot 73\cdot 75041$ $S_8$ (as 8T50) trivial $9.59842021162$
8.6.104429827.1 $x^{8} - x^{7} - 2 x^{6} + x^{5} - 2 x^{4} + 5 x^{3} + 2 x^{2} - 4 x + 1$ $-\,17\cdot 199\cdot 30869$ $S_8$ (as 8T50) trivial $9.62967810582$
8.6.106143931.1 $x^{8} - 4 x^{7} + 3 x^{6} + 5 x^{5} - 8 x^{4} + 2 x^{3} + 5 x^{2} - 2 x - 1$ $-\,3659\cdot 29009$ $S_8$ (as 8T50) trivial $10.048074566$
8.6.106899371.1 $x^{8} - 3 x^{7} + 3 x^{5} + 3 x^{4} - 6 x^{2} + 1$ $-\,67\cdot 1595513$ $S_8$ (as 8T50) trivial $10.081255108$
8.6.107555299.1 $x^{8} - 3 x^{7} - x^{6} + 9 x^{5} - 5 x^{4} - 5 x^{3} + 6 x^{2} - 1$ $-\,1153\cdot 93283$ $S_8$ (as 8T50) trivial $10.1197503358$
8.6.107781875.1 $x^{8} - 2 x^{7} - x^{6} + 4 x^{5} - 5 x^{4} - 3 x^{3} + 5 x^{2} + x - 1$ $-\,5^{4}\cdot 331\cdot 521$ $S_4\wr C_2$ (as 8T47) trivial $9.85579681337$
8.6.108493747.1 $x^{8} - x^{7} - 5 x^{6} + 5 x^{5} + 7 x^{4} - 8 x^{3} - 3 x^{2} + 4 x + 1$ $-\,108493747$ $S_8$ (as 8T50) trivial $9.96053466815$
8.6.108714131.1 $x^{8} - x^{7} - 4 x^{6} + 5 x^{5} + 3 x^{4} - 9 x^{3} + x^{2} + 4 x - 1$ $-\,103\cdot 971\cdot 1087$ $S_8$ (as 8T50) trivial $10.0232921526$
8.6.109020787.1 $x^{8} - 5 x^{6} - 3 x^{5} + 8 x^{4} + 9 x^{3} - 4 x^{2} - 6 x - 1$ $-\,109020787$ $S_8$ (as 8T50) trivial $9.9328123712$
8.6.109380619.1 $x^{8} - 2 x^{7} - 2 x^{6} + 2 x^{5} + x^{4} + 5 x^{3} + x^{2} - 4 x - 1$ $-\,109380619$ $S_8$ (as 8T50) trivial $9.90248579451$
8.6.110906875.1 $x^{8} - 2 x^{7} - 4 x^{6} + 9 x^{5} - 9 x^{3} + 4 x^{2} + 3 x - 1$ $-\,5^{4}\cdot 29^{2}\cdot 211$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $9.94997062$
8.6.111219379.1 $x^{8} - 2 x^{7} - 2 x^{6} + 7 x^{5} - 3 x^{4} - 7 x^{3} + 4 x^{2} + 2 x - 1$ $-\,29\cdot 389\cdot 9859$ $S_8$ (as 8T50) trivial $10.034952344$
8.6.112129379.1 $x^{8} - x^{7} - 4 x^{6} + 2 x^{5} + 4 x^{4} + 3 x^{3} - x^{2} - 4 x - 1$ $-\,1427\cdot 78577$ $S_8$ (as 8T50) trivial $10.1802489898$
8.6.114655339.1 $x^{8} - 4 x^{7} + 3 x^{6} + 4 x^{5} - 5 x^{4} + 3 x^{3} - x^{2} - 3 x + 1$ $-\,233\cdot 492083$ $S_8$ (as 8T50) trivial $10.1164006344$
8.6.118871243.1 $x^{8} - 2 x^{6} - 2 x^{5} - 3 x^{4} + 5 x^{3} + 5 x^{2} - 2 x - 1$ $-\,101\cdot 1176943$ $S_8$ (as 8T50) trivial $10.6488116417$
8.6.119649419.1 $x^{8} - x^{7} - 4 x^{6} + 6 x^{5} + 6 x^{4} - 9 x^{3} - 4 x^{2} + 3 x + 1$ $-\,119649419$ $S_8$ (as 8T50) trivial $10.444006294$
8.6.121587131.1 $x^{8} - 2 x^{7} - x^{6} + 7 x^{5} - 7 x^{4} - 5 x^{3} + 8 x^{2} + x - 1$ $-\,23\cdot 271\cdot 19507$ $S_8$ (as 8T50) trivial $10.9088684379$
8.6.123531875.1 $x^{8} - 5 x^{6} - 3 x^{5} + 8 x^{4} + 10 x^{3} - 4 x^{2} - 7 x + 1$ $-\,5^{4}\cdot 197651$ $S_4\wr C_2$ (as 8T47) trivial $10.8492896616$
8.6.128782547.1 $x^{8} - 2 x^{7} + 5 x^{5} - 8 x^{4} - 3 x^{3} + 8 x^{2} - x - 1$ $-\,157\cdot 820271$ $S_8$ (as 8T50) trivial $11.1025063692$
8.6.129062827.1 $x^{8} - 2 x^{7} - 4 x^{6} + 5 x^{5} + 8 x^{4} - 3 x^{3} - 6 x^{2} + x + 1$ $-\,17\cdot 31\cdot 244901$ $S_8$ (as 8T50) trivial $10.9881510415$
8.6.131931875.1 $x^{8} - x^{7} - 5 x^{6} + 5 x^{5} + 3 x^{4} - 3 x + 1$ $-\,5^{4}\cdot 29^{2}\cdot 251$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $11.2866336082$
8.6.132655867.1 $x^{8} - 2 x^{6} - 2 x^{5} - 3 x^{4} + 3 x^{3} + 4 x^{2} - x - 1$ $-\,137\cdot 968291$ $S_8$ (as 8T50) trivial $11.5180770626$
8.6.132761875.1 $x^{8} - x^{7} - 5 x^{6} + 2 x^{5} + 11 x^{4} - x^{3} - 9 x^{2} + 1$ $-\,5^{4}\cdot 212419$ $S_4\wr C_2$ (as 8T47) trivial $12.0204012295$
8.6.134560000.1 $x^{8} - 3 x^{6} + 4 x^{2} - 1$ $-\,2^{8}\cdot 5^{4}\cdot 29^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $11.4855032762$
8.6.134560000.2 $x^{8} - 6 x^{4} + 5 x^{2} - 1$ $-\,2^{8}\cdot 5^{4}\cdot 29^{2}$ $C_2 \wr C_2\wr C_2$ (as 8T35) trivial $11.1552211117$
8.6.135123147.1 $x^{8} - 4 x^{6} - 4 x^{5} + 9 x^{4} + 5 x^{3} - 6 x^{2} - x + 1$ $-\,3^{4}\cdot 257\cdot 6491$ $S_8$ (as 8T50) trivial $11.2672389878$
8.6.136128151.1 $x^{8} - 2 x^{7} + x^{6} + 2 x^{5} - 7 x^{4} + 2 x^{3} + 6 x^{2} - x - 1$ $-\,97\cdot 1403383$ $S_8$ (as 8T50) trivial $11.5512184196$
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