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Label Polynomial Discriminant Galois group Class group Regulator
8.0.705911761.1 $x^{8} - x^{7} + x^{6} - 4 x^{5} + 5 x^{4} - 8 x^{3} + 4 x^{2} - 8 x + 16$ $163^{4}$ $\SL(2,3)$ (as 8T12) trivial $62.8368450498$
8.8.5887339441.1 $x^{8} - x^{7} - 11 x^{6} + 13 x^{5} + 32 x^{4} - 41 x^{3} - 23 x^{2} + 32 x - 1$ $277^{4}$ $\SL(2,3)$ (as 8T12) trivial $171.868819788$
8.0.10093618089.1 $x^{8} + x^{6} - 3 x^{5} - 3 x^{4} - 6 x^{3} + 4 x^{2} + 16$ $3^{6}\cdot 61^{4}$ $\SL(2,3)$ (as 8T12) $[2]$ $127.369589756$
8.8.10093618089.1 $x^{8} - 4 x^{7} - 4 x^{6} + 23 x^{5} + 4 x^{4} - 38 x^{3} - x^{2} + 16 x + 4$ $3^{6}\cdot 61^{4}$ $\SL(2,3)$ (as 8T12) trivial $246.700109046$
8.0.14835483601.1 $x^{8} - 4 x^{7} + 5 x^{6} + x^{5} - 6 x^{4} + 7 x^{3} + 31 x^{2} + 34 x + 12$ $349^{4}$ $\SL(2,3)$ (as 8T12) trivial $166.768783691$
8.0.24840596881.1 $x^{8} - x^{6} - 2 x^{5} - 5 x^{4} - 6 x^{3} - 9 x^{2} + 81$ $397^{4}$ $\SL(2,3)$ (as 8T12) trivial $155.330581721$
8.8.57178852641.1 $x^{8} - 2 x^{7} - 13 x^{6} + 24 x^{5} + 48 x^{4} - 73 x^{3} - 38 x^{2} + 9 x + 3$ $3^{4}\cdot 163^{4}$ $\SL(2,3)$ (as 8T12) trivial $751.205508883$
8.0.89526025681.1 $x^{8} - 5 x^{6} - 3 x^{5} + 28 x^{4} - 12 x^{3} - 80 x^{2} + 256$ $547^{4}$ $\SL(2,3)$ (as 8T12) $[3]$ $235.83141838$
8.8.135754665601.1 $x^{8} - 15 x^{6} + 47 x^{4} - 38 x^{2} + 9$ $607^{4}$ $\SL(2,3)$ (as 8T12) trivial $1200.81327796$
8.8.180713410816.1 $x^{8} - 9 x^{6} + 23 x^{4} - 14 x^{2} + 1$ $2^{8}\cdot 163^{4}$ $\SL(2,3)$ (as 8T12) trivial $2065.34504661$
8.0.212558803681.1 $x^{8} + 15 x^{6} + 60 x^{4} + 35 x^{2} + 1$ $7^{4}\cdot 97^{4}$ $\SL(2,3)$ (as 8T12) trivial $255.648044055$
8.8.244242535681.1 $x^{8} - 2 x^{7} - 14 x^{6} + 17 x^{5} + 74 x^{4} - 26 x^{3} - 145 x^{2} - 43 x + 29$ $19^{4}\cdot 37^{4}$ $\SL(2,3)$ (as 8T12) trivial $1318.94368647$
8.0.252688187761.1 $x^{8} + 19 x^{6} + 106 x^{4} + 215 x^{2} + 144$ $709^{4}$ $\SL(2,3)$ (as 8T12) $[7]$ $372.443892625$
8.8.255551481441.1 $x^{8} - x^{7} - 16 x^{6} + 7 x^{5} + 71 x^{4} - 31 x^{3} - 100 x^{2} + 61 x + 1$ $3^{8}\cdot 79^{4}$ $\SL(2,3)$ (as 8T12) trivial $1498.64402143$
8.8.338920744561.1 $x^{8} - 19 x^{6} + 79 x^{4} - 98 x^{2} + 9$ $7^{4}\cdot 109^{4}$ $\SL(2,3)$ (as 8T12) trivial $2009.54817518$
8.0.441194850625.1 $x^{8} - 2 x^{7} + 15 x^{6} - 22 x^{5} + 68 x^{4} - 37 x^{3} + 188 x^{2} - 269 x + 599$ $5^{4}\cdot 163^{4}$ $\SL(2,3)$ (as 8T12) $[2]$ $125.6736901$
8.0.476874494721.1 $x^{8} - 3 x^{7} + 7 x^{6} - 5 x^{5} + 16 x^{4} - 31 x^{3} + 289 x^{2} - 180 x + 69$ $3^{4}\cdot 277^{4}$ $\SL(2,3)$ (as 8T12) $[4]$ $101.705491954$
8.0.529414856881.1 $x^{8} - x^{7} - 10 x^{6} + 32 x^{5} + 43 x^{4} - 245 x^{3} + 393 x^{2} - 192 x + 68$ $853^{4}$ $\SL(2,3)$ (as 8T12) trivial $282.299934222$
8.0.770829564961.1 $x^{8} - 3 x^{7} + 6 x^{5} - 6 x^{4} + 8 x^{3} + 162 x^{2} + 284 x + 173$ $937^{4}$ $\SL(2,3)$ (as 8T12) trivial $512.768829357$
8.0.811082161201.1 $x^{8} + 19 x^{6} + 116 x^{4} + 255 x^{2} + 169$ $13^{4}\cdot 73^{4}$ $\SL(2,3)$ (as 8T12) trivial $425.20130162$
8.8.1036488922561.1 $x^{8} - 3 x^{7} - 20 x^{6} + 49 x^{5} + 86 x^{4} - 188 x^{3} - 91 x^{2} + 190 x - 53$ $1009^{4}$ $\SL(2,3)$ (as 8T12) trivial $3982.13151887$
8.8.1201674171681.1 $x^{8} - 4 x^{7} - 13 x^{6} + 36 x^{5} + 76 x^{4} - 34 x^{3} - 69 x^{2} + 10 x + 16$ $3^{4}\cdot 349^{4}$ $\SL(2,3)$ (as 8T12) trivial $12037.554856$
8.0.1507158896896.1 $x^{8} + 13 x^{6} + 52 x^{4} + 65 x^{2} + 9$ $2^{8}\cdot 277^{4}$ $\SL(2,3)$ (as 8T12) $[2, 14]$ $101.705491954$
8.8.1616465588409.1 $x^{8} - 17 x^{6} - 15 x^{5} + 36 x^{4} + 15 x^{3} - 17 x^{2} + 1$ $3^{6}\cdot 7^{4}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) trivial $3526.469394$
8.0.1616465588409.2 $x^{8} - 4 x^{7} + 17 x^{6} - 13 x^{5} + 73 x^{4} + 88 x^{3} + 248 x^{2} + 304 x + 208$ $3^{6}\cdot 7^{4}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) $[6]$ $505.296367936$
8.8.1694894138161.1 $x^{8} - x^{7} - 26 x^{6} + 6 x^{5} + 101 x^{4} + 53 x^{3} - 33 x^{2} - 17 x + 2$ $7^{4}\cdot 163^{4}$ $\SL(2,3)$ (as 8T12) trivial $11338.955448$
8.8.1706808989601.1 $x^{8} - 17 x^{6} + 78 x^{4} - 53 x^{2} + 4$ $3^{8}\cdot 127^{4}$ $\SL(2,3)$ (as 8T12) trivial $4890.61405464$
8.0.1730827040881.1 $x^{8} + 17 x^{6} + 59 x^{4} + 46 x^{2} + 1$ $31^{4}\cdot 37^{4}$ $\SL(2,3)$ (as 8T12) trivial $450.031440224$
8.8.2012088347361.1 $x^{8} - x^{7} - 22 x^{6} + 16 x^{5} + 156 x^{4} - 61 x^{3} - 422 x^{2} + 30 x + 319$ $3^{4}\cdot 397^{4}$ $\SL(2,3)$ (as 8T12) trivial $4575.92530631$
8.0.2052941630481.1 $x^{8} - 2 x^{7} - 6 x^{6} + 3 x^{5} + 9 x^{4} - 78 x^{3} + 704 x^{2} - 544 x + 336$ $3^{8}\cdot 7^{4}\cdot 19^{4}$ $\SL(2,3)$ (as 8T12) $[7]$ $747.270122433$
8.0.2299963332969.1 $x^{8} - x^{7} + x^{6} + 4 x^{5} - 19 x^{4} + 226 x^{3} + 310 x^{2} - 214 x + 241$ $3^{10}\cdot 79^{4}$ $\SL(2,3)$ (as 8T12) $[4]$ $345.716432417$
8.0.2576952773521.1 $x^{8} - x^{7} - 8 x^{6} + 12 x^{5} - 4 x^{4} + 13 x^{3} + 642 x^{2} - 440 x + 281$ $7^{4}\cdot 181^{4}$ $\SL(2,3)$ (as 8T12) trivial $474.774181023$
8.0.2583966230784.1 $x^{8} + 15 x^{6} + 63 x^{4} + 54 x^{2} + 9$ $2^{8}\cdot 3^{6}\cdot 61^{4}$ $\SL(2,3)$ (as 8T12) $[2, 4]$ $127.369589756$
8.8.2583966230784.1 $x^{8} - 18 x^{6} + 63 x^{4} - 45 x^{2} + 9$ $2^{8}\cdot 3^{6}\cdot 61^{4}$ $\SL(2,3)$ (as 8T12) $[2]$ $4691.17451885$
8.8.2713409501049.1 $x^{8} - 21 x^{6} + 108 x^{4} - 81 x^{2} + 9$ $3^{6}\cdot 13^{4}\cdot 19^{4}$ $\SL(2,3)$ (as 8T12) trivial $6151.46735611$
8.0.2713409501049.2 $x^{8} - x^{7} - 4 x^{6} - 13 x^{5} + 7 x^{4} + 127 x^{3} + 182 x^{2} + 67 x + 13$ $3^{6}\cdot 13^{4}\cdot 19^{4}$ $\SL(2,3)$ (as 8T12) $[2]$ $507.260828694$
8.0.2891414573056.1 $x^{8} + 18 x^{6} + 92 x^{4} + 112 x^{2} + 16$ $2^{12}\cdot 163^{4}$ $\SL(2,3)$ (as 8T12) $[2, 4]$ $125.6736901$
8.8.2891414573056.1 $x^{8} - 18 x^{6} + 92 x^{4} - 112 x^{2} + 16$ $2^{12}\cdot 163^{4}$ $\SL(2,3)$ (as 8T12) trivial $15042.1876928$
8.8.3157334518321.1 $x^{8} - 19 x^{6} + 113 x^{4} - 204 x^{2} + 16$ $31^{4}\cdot 43^{4}$ $\SL(2,3)$ (as 8T12) trivial $7495.41180062$
8.8.3320190535321.1 $x^{8} - x^{7} - 21 x^{6} + 6 x^{5} + 109 x^{4} + 36 x^{3} - 85 x^{2} - 18 x + 20$ $11^{6}\cdot 37^{4}$ $\SL(2,3)$ (as 8T12) trivial $7270.0625309$
8.0.3320190535321.2 $x^{8} - 2 x^{7} + 13 x^{6} + 18 x^{5} + 5 x^{4} + 126 x^{3} + 142 x^{2} - 70 x + 47$ $11^{6}\cdot 37^{4}$ $\SL(2,3)$ (as 8T12) $[14]$ $396.703867611$
8.0.3341024655409.1 $x^{8} - x^{7} + 8 x^{6} + 8 x^{5} + 32 x^{4} + 66 x^{3} + 128 x^{2} + 204 x + 179$ $7^{6}\cdot 73^{4}$ $\SL(2,3)$ (as 8T12) $[2]$ $393.657283234$
8.8.3341024655409.1 $x^{8} - 2 x^{7} - 26 x^{6} + 25 x^{5} + 160 x^{4} + 60 x^{3} - 145 x^{2} - 107 x - 13$ $7^{6}\cdot 73^{4}$ $\SL(2,3)$ (as 8T12) trivial $4505.33153315$
8.8.3679587150625.1 $x^{8} - 3 x^{7} - 23 x^{6} + 53 x^{5} + 132 x^{4} - 173 x^{3} + 29 x^{2} + 6 x - 1$ $5^{4}\cdot 277^{4}$ $\SL(2,3)$ (as 8T12) $[2]$ $5687.94563401$
8.8.3797883801856.1 $x^{8} - 15 x^{6} + 74 x^{4} - 131 x^{2} + 64$ $2^{8}\cdot 349^{4}$ $\SL(2,3)$ (as 8T12) trivial $14077.7203941$
8.8.3830635754401.1 $x^{8} - 3 x^{7} - 19 x^{6} + 68 x^{5} + 61 x^{4} - 358 x^{3} + 126 x^{2} + 346 x - 139$ $1399^{4}$ $\SL(2,3)$ (as 8T12) trivial $3947.29543206$
8.0.3873527824384.1 $x^{8} + 20 x^{6} + 42 x^{4} + 24 x^{2} + 4$ $2^{22}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) $[6]$ $153.831959383$
8.8.3873527824384.1 $x^{8} - 12 x^{6} + 42 x^{4} - 40 x^{2} + 4$ $2^{22}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) trivial $5750.25732435$
8.0.3873527824384.2 $x^{8} + 12 x^{6} + 42 x^{4} + 40 x^{2} + 4$ $2^{22}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) $[26]$ $153.831959383$
8.8.3873527824384.2 $x^{8} - 20 x^{6} + 42 x^{4} - 24 x^{2} + 4$ $2^{22}\cdot 31^{4}$ $\SL(2,3)$ (as 8T12) trivial $11513.8676242$
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