| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 8.0.705911761.1 |
$x^{8} - x^{7} + x^{6} - 4 x^{5} + 5 x^{4} - 8 x^{3} + 4 x^{2} - 8 x + 16$ |
$8$ |
[0,4] |
$163^{4}$ |
$1$ |
$12.7671453348$ |
$29.839513369337443$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$62.8368450498$ |
| 8.8.5887339441.1 |
$x^{8} - x^{7} - 11 x^{6} + 13 x^{5} + 32 x^{4} - 41 x^{3} - 23 x^{2} + 32 x - 1$ |
$8$ |
[8,0] |
$277^{4}$ |
$1$ |
$16.6433169771$ |
$42.49323998594522$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$171.868819788$ |
| 8.0.10093618089.1 |
$x^{8} + x^{6} - 3 x^{5} - 3 x^{4} - 6 x^{3} + 4 x^{2} + 16$ |
$8$ |
[0,4] |
$3^{6}\cdot 61^{4}$ |
$2$ |
$17.8035192528$ |
$35.3232643150687$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[2]$ |
$2$ |
$3$ |
$127.369589756$ |
| 8.8.10093618089.1 |
$x^{8} - 4 x^{7} - 4 x^{6} + 23 x^{5} + 4 x^{4} - 38 x^{3} - x^{2} + 16 x + 4$ |
$8$ |
[8,0] |
$3^{6}\cdot 61^{4}$ |
$2$ |
$17.8035192528$ |
$35.3232643150687$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$246.700109046$ |
| 8.0.14835483601.1 |
$x^{8} - 4 x^{7} + 5 x^{6} + x^{5} - 6 x^{4} + 7 x^{3} + 31 x^{2} + 34 x + 12$ |
$8$ |
[0,4] |
$349^{4}$ |
$1$ |
$18.6815416923$ |
$49.56977542044145$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$166.768783691$ |
| 8.0.24840596881.1 |
$x^{8} - x^{6} - 2 x^{5} - 5 x^{4} - 6 x^{3} - 9 x^{2} + 81$ |
$8$ |
[0,4] |
$397^{4}$ |
$1$ |
$19.9248588452$ |
$54.016570132056195$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$155.330581721$ |
| 8.8.57178852641.1 |
$x^{8} - 2 x^{7} - 13 x^{6} + 24 x^{5} + 48 x^{4} - 73 x^{3} - 38 x^{2} + 9 x + 3$ |
$8$ |
[8,0] |
$3^{4}\cdot 163^{4}$ |
$2$ |
$22.1133443875$ |
$51.68355322882323$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$751.205508883$ |
| 8.0.89526025681.1 |
$x^{8} - 5 x^{6} - 3 x^{5} + 28 x^{4} - 12 x^{3} - 80 x^{2} + 256$ |
$8$ |
[0,4] |
$547^{4}$ |
$1$ |
$23.3880311271$ |
$66.88440750411058$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[3]$ |
$2$ |
$3$ |
$235.83141838$ |
| 8.8.135754665601.1 |
$x^{8} - 15 x^{6} + 47 x^{4} - 38 x^{2} + 9$ |
$8$ |
[8,0] |
$607^{4}$ |
$1$ |
$24.6373699895$ |
$71.69009029420101$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$1200.81327796$ |
| 8.8.180713410816.1 |
$x^{8} - 9 x^{6} + 23 x^{4} - 14 x^{2} + 1$ |
$8$ |
[8,0] |
$2^{8}\cdot 163^{4}$ |
$2$ |
$25.5342906696$ |
$59.679026738674885$ |
|
|
✓ |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$2065.34504661$ |
| 8.0.212558803681.1 |
$x^{8} + 15 x^{6} + 60 x^{4} + 35 x^{2} + 1$ |
$8$ |
[0,4] |
$7^{4}\cdot 97^{4}$ |
$2$ |
$26.0576284416$ |
$77.25261386965467$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$255.648044055$ |
| 8.8.244242535681.1 |
$x^{8} - 2 x^{7} - 14 x^{6} + 17 x^{5} + 74 x^{4} - 26 x^{3} - 145 x^{2} - 43 x + 29$ |
$8$ |
[8,0] |
$19^{4}\cdot 37^{4}$ |
$2$ |
$26.5141471671$ |
$79.06244062028483$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$1318.94368647$ |
| 8.0.252688187761.1 |
$x^{8} + 19 x^{6} + 106 x^{4} + 215 x^{2} + 144$ |
$8$ |
[0,4] |
$709^{4}$ |
$1$ |
$26.6270539114$ |
$79.51166053927216$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[7]$ |
$2$ |
$3$ |
$372.443892625$ |
| 8.8.255551481441.1 |
$x^{8} - x^{7} - 16 x^{6} + 7 x^{5} + 71 x^{4} - 31 x^{3} - 100 x^{2} + 61 x + 1$ |
$8$ |
[8,0] |
$3^{8}\cdot 79^{4}$ |
$2$ |
$26.6645832519$ |
$79.66111860276087$ |
|
|
✓ |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$1498.64402143$ |
| 8.8.338920744561.1 |
$x^{8} - 19 x^{6} + 79 x^{4} - 98 x^{2} + 9$ |
$8$ |
[8,0] |
$7^{4}\cdot 109^{4}$ |
$2$ |
$27.6224546339$ |
$83.49933665075943$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$2009.54817518$ |
| 8.0.441194850625.1 |
$x^{8} - 2 x^{7} + 15 x^{6} - 22 x^{5} + 68 x^{4} - 37 x^{3} + 188 x^{2} - 269 x + 599$ |
$8$ |
[0,4] |
$5^{4}\cdot 163^{4}$ |
$2$ |
$28.5482048472$ |
$66.7231803093523$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[2]$ |
$2$ |
$3$ |
$125.6736901$ |
| 8.0.476874494721.1 |
$x^{8} - 3 x^{7} + 7 x^{6} - 5 x^{5} + 16 x^{4} - 31 x^{3} + 289 x^{2} - 180 x + 69$ |
$8$ |
[0,4] |
$3^{4}\cdot 277^{4}$ |
$2$ |
$28.8270706108$ |
$73.60045063387453$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[4]$ |
$2$ |
$3$ |
$101.705491954$ |
| 8.0.529414856881.1 |
$x^{8} - x^{7} - 10 x^{6} + 32 x^{5} + 43 x^{4} - 245 x^{3} + 393 x^{2} - 192 x + 68$ |
$8$ |
[0,4] |
$853^{4}$ |
$1$ |
$29.206163733$ |
$89.94272075480275$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$282.299934222$ |
| 8.0.770829564961.1 |
$x^{8} - 3 x^{7} + 6 x^{5} - 6 x^{4} + 8 x^{3} + 162 x^{2} + 284 x + 173$ |
$8$ |
[0,4] |
$937^{4}$ |
$1$ |
$30.61045573$ |
$95.75461782408576$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$512.768829357$ |
| 8.0.811082161201.1 |
$x^{8} + 19 x^{6} + 116 x^{4} + 255 x^{2} + 169$ |
$8$ |
[0,4] |
$13^{4}\cdot 73^{4}$ |
$2$ |
$30.8058436015$ |
$96.57042475710601$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$425.20130162$ |
| 8.8.1036488922561.1 |
$x^{8} - 3 x^{7} - 20 x^{6} + 49 x^{5} + 86 x^{4} - 188 x^{3} - 91 x^{2} + 190 x - 53$ |
$8$ |
[8,0] |
$1009^{4}$ |
$1$ |
$31.7647603485$ |
$100.59910358121267$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$3982.13151887$ |
| 8.8.1201674171681.1 |
$x^{8} - 4 x^{7} - 13 x^{6} + 36 x^{5} + 76 x^{4} - 34 x^{3} - 69 x^{2} + 10 x + 16$ |
$8$ |
[8,0] |
$3^{4}\cdot 349^{4}$ |
$2$ |
$32.3573793747$ |
$85.85736954798351$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$12037.554856$ |
| 8.0.1507158896896.1 |
$x^{8} + 13 x^{6} + 52 x^{4} + 65 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 277^{4}$ |
$2$ |
$33.2866339542$ |
$84.98647997189045$ |
✓ |
|
|
$\SL(2,3)$ (as 8T12) |
$[2, 14]$ |
$2$ |
$3$ |
$101.705491954$ |
| 8.8.1616465588409.1 |
$x^{8} - 17 x^{6} - 15 x^{5} + 36 x^{4} + 15 x^{3} - 17 x^{2} + 1$ |
$8$ |
[8,0] |
$3^{6}\cdot 7^{4}\cdot 31^{4}$ |
$3$ |
$33.5792357824$ |
$82.31533758230549$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$3526.469394$ |
| 8.0.1616465588409.2 |
$x^{8} - 4 x^{7} + 17 x^{6} - 13 x^{5} + 73 x^{4} + 88 x^{3} + 248 x^{2} + 304 x + 208$ |
$8$ |
[0,4] |
$3^{6}\cdot 7^{4}\cdot 31^{4}$ |
$3$ |
$33.5792357824$ |
$82.31533758230549$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[6]$ |
$2$ |
$3$ |
$505.296367936$ |
| 8.8.1694894138161.1 |
$x^{8} - x^{7} - 26 x^{6} + 6 x^{5} + 101 x^{4} + 53 x^{3} - 33 x^{2} - 17 x + 2$ |
$8$ |
[8,0] |
$7^{4}\cdot 163^{4}$ |
$2$ |
$33.7786915081$ |
$78.94793161845391$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$11338.955448$ |
| 8.8.1706808989601.1 |
$x^{8} - 17 x^{6} + 78 x^{4} - 53 x^{2} + 4$ |
$8$ |
[8,0] |
$3^{8}\cdot 127^{4}$ |
$2$ |
$33.8082830088$ |
$109.31946230762344$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$4890.61405464$ |
| 8.0.1730827040881.1 |
$x^{8} + 17 x^{6} + 59 x^{4} + 46 x^{2} + 1$ |
$8$ |
[0,4] |
$31^{4}\cdot 37^{4}$ |
$2$ |
$33.8673884438$ |
$109.57436064430937$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$450.031440224$ |
| 8.8.2012088347361.1 |
$x^{8} - x^{7} - 22 x^{6} + 16 x^{5} + 156 x^{4} - 61 x^{3} - 422 x^{2} + 30 x + 319$ |
$8$ |
[8,0] |
$3^{4}\cdot 397^{4}$ |
$2$ |
$34.5108678535$ |
$93.55944391932883$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$4575.92530631$ |
| 8.0.2052941630481.1 |
$x^{8} - 2 x^{7} - 6 x^{6} + 3 x^{5} + 9 x^{4} - 78 x^{3} + 704 x^{2} - 544 x + 336$ |
$8$ |
[0,4] |
$3^{8}\cdot 7^{4}\cdot 19^{4}$ |
$3$ |
$34.597687784$ |
$112.7360377530179$ |
✓ |
|
|
$\SL(2,3)$ (as 8T12) |
$[7]$ |
$2$ |
$3$ |
$747.270122433$ |
| 8.0.2299963332969.1 |
$x^{8} - x^{7} + x^{6} + 4 x^{5} - 19 x^{4} + 226 x^{3} + 310 x^{2} - 214 x + 241$ |
$8$ |
[0,4] |
$3^{10}\cdot 79^{4}$ |
$2$ |
$35.0925650841$ |
$95.66798122071407$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[4]$ |
$2$ |
$3$ |
$345.716432417$ |
| 8.0.2576952773521.1 |
$x^{8} - x^{7} - 8 x^{6} + 12 x^{5} - 4 x^{4} + 13 x^{3} + 642 x^{2} - 440 x + 281$ |
$8$ |
[0,4] |
$7^{4}\cdot 181^{4}$ |
$2$ |
$35.5949434611$ |
$117.08944386520729$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$3$ |
$474.774181023$ |
| 8.0.2583966230784.1 |
$x^{8} + 15 x^{6} + 63 x^{4} + 54 x^{2} + 9$ |
$8$ |
[0,4] |
$2^{8}\cdot 3^{6}\cdot 61^{4}$ |
$3$ |
$35.6070385056$ |
$70.6465286301374$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[2, 4]$ |
$2$ |
$3$ |
$127.369589756$ |
| 8.8.2583966230784.1 |
$x^{8} - 18 x^{6} + 63 x^{4} - 45 x^{2} + 9$ |
$8$ |
[8,0] |
$2^{8}\cdot 3^{6}\cdot 61^{4}$ |
$3$ |
$35.6070385056$ |
$70.6465286301374$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
$[2]$ |
$2$ |
$7$ |
$4691.17451885$ |
| 8.8.2713409501049.1 |
$x^{8} - 21 x^{6} + 108 x^{4} - 81 x^{2} + 9$ |
$8$ |
[8,0] |
$3^{6}\cdot 13^{4}\cdot 19^{4}$ |
$3$ |
$35.8252655037$ |
$89.73714395375625$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$6151.46735611$ |
| 8.0.2713409501049.2 |
$x^{8} - x^{7} - 4 x^{6} - 13 x^{5} + 7 x^{4} + 127 x^{3} + 182 x^{2} + 67 x + 13$ |
$8$ |
[0,4] |
$3^{6}\cdot 13^{4}\cdot 19^{4}$ |
$3$ |
$35.8252655037$ |
$89.73714395375625$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[2]$ |
$2$ |
$3$ |
$507.260828694$ |
| 8.0.2891414573056.1 |
$x^{8} + 18 x^{6} + 92 x^{4} + 112 x^{2} + 16$ |
$8$ |
[0,4] |
$2^{12}\cdot 163^{4}$ |
$2$ |
$36.1109401705$ |
$84.3988890030606$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[2, 4]$ |
$2$ |
$3$ |
$125.6736901$ |
| 8.8.2891414573056.1 |
$x^{8} - 18 x^{6} + 92 x^{4} - 112 x^{2} + 16$ |
$8$ |
[8,0] |
$2^{12}\cdot 163^{4}$ |
$2$ |
$36.1109401705$ |
$84.3988890030606$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$15042.1876928$ |
| 8.8.3157334518321.1 |
$x^{8} - 19 x^{6} + 113 x^{4} - 204 x^{2} + 16$ |
$8$ |
[8,0] |
$31^{4}\cdot 43^{4}$ |
$2$ |
$36.5102725271$ |
$121.12118178531371$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$7495.41180062$ |
| 8.8.3320190535321.1 |
$x^{8} - x^{7} - 21 x^{6} + 6 x^{5} + 109 x^{4} + 36 x^{3} - 85 x^{2} - 18 x + 20$ |
$8$ |
[8,0] |
$11^{6}\cdot 37^{4}$ |
$2$ |
$36.7405265296$ |
$67.06753273569937$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$7270.0625309$ |
| 8.0.3320190535321.2 |
$x^{8} - 2 x^{7} + 13 x^{6} + 18 x^{5} + 5 x^{4} + 126 x^{3} + 142 x^{2} - 70 x + 47$ |
$8$ |
[0,4] |
$11^{6}\cdot 37^{4}$ |
$2$ |
$36.7405265296$ |
$67.06753273569937$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[14]$ |
$2$ |
$3$ |
$396.703867611$ |
| 8.0.3341024655409.1 |
$x^{8} - x^{7} + 8 x^{6} + 8 x^{5} + 32 x^{4} + 66 x^{3} + 128 x^{2} + 204 x + 179$ |
$8$ |
[0,4] |
$7^{6}\cdot 73^{4}$ |
$2$ |
$36.7692659697$ |
$75.16899954665448$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[2]$ |
$2$ |
$3$ |
$393.657283234$ |
| 8.8.3341024655409.1 |
$x^{8} - 2 x^{7} - 26 x^{6} + 25 x^{5} + 160 x^{4} + 60 x^{3} - 145 x^{2} - 107 x - 13$ |
$8$ |
[8,0] |
$7^{6}\cdot 73^{4}$ |
$2$ |
$36.7692659697$ |
$75.16899954665448$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$4505.33153315$ |
| 8.8.3679587150625.1 |
$x^{8} - 3 x^{7} - 23 x^{6} + 53 x^{5} + 132 x^{4} - 173 x^{3} + 29 x^{2} + 6 x - 1$ |
$8$ |
[8,0] |
$5^{4}\cdot 277^{4}$ |
$2$ |
$37.2155881319$ |
$95.01777319278573$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
$[2]$ |
$2$ |
$7$ |
$5687.94563401$ |
| 8.8.3797883801856.1 |
$x^{8} - 15 x^{6} + 74 x^{4} - 131 x^{2} + 64$ |
$8$ |
[8,0] |
$2^{8}\cdot 349^{4}$ |
$2$ |
$37.3630833845$ |
$99.1395508408829$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$14077.7203941$ |
| 8.8.3830635754401.1 |
$x^{8} - 3 x^{7} - 19 x^{6} + 68 x^{5} + 61 x^{4} - 358 x^{3} + 126 x^{2} + 346 x - 139$ |
$8$ |
[8,0] |
$1399^{4}$ |
$1$ |
$37.4032084185$ |
$125.08689424778738$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$3947.29543206$ |
| 8.8.3873527824384.1 |
$x^{8} - 12 x^{6} + 42 x^{4} - 40 x^{2} + 4$ |
$8$ |
[8,0] |
$2^{22}\cdot 31^{4}$ |
$2$ |
$37.4553047494$ |
$66.38555910891195$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$5750.25732435$ |
| 8.0.3873527824384.1 |
$x^{8} + 20 x^{6} + 42 x^{4} + 24 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{22}\cdot 31^{4}$ |
$2$ |
$37.4553047494$ |
$66.38555910891195$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[6]$ |
$2$ |
$3$ |
$153.831959383$ |
| 8.8.3873527824384.2 |
$x^{8} - 20 x^{6} + 42 x^{4} - 24 x^{2} + 4$ |
$8$ |
[8,0] |
$2^{22}\cdot 31^{4}$ |
$2$ |
$37.4553047494$ |
$66.38555910891195$ |
|
|
? |
$\SL(2,3)$ (as 8T12) |
trivial |
$2$ |
$7$ |
$11513.8676242$ |
| 8.0.3873527824384.2 |
$x^{8} + 12 x^{6} + 42 x^{4} + 40 x^{2} + 4$ |
$8$ |
[0,4] |
$2^{22}\cdot 31^{4}$ |
$2$ |
$37.4553047494$ |
$66.38555910891195$ |
✓ |
|
? |
$\SL(2,3)$ (as 8T12) |
$[26]$ |
$2$ |
$3$ |
$153.831959383$ |
