| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 8.2.482643651365691219.1 |
$x^{8} - 2 x^{7} - 31 x^{6} - 443 x^{5} + 1342 x^{4} + 6989 x^{3} - 47788 x^{2} - 151204 x + 93232$ |
$8$ |
[2,3] |
$-\,3^{6}\cdot 131^{7}$ |
$2$ |
$162.350385704$ |
$162.35038570399587$ |
|
|
|
$QD_{16}$ (as 8T8) |
$[9]$ |
$[18]$ |
$2$ |
$4$ |
$367777.882275$ |
| 8.2.433...696.1 |
$x^{8} + 2358 x^{4} - 81875$ |
$8$ |
[2,3] |
$-\,2^{16}\cdot 131^{7}$ |
$2$ |
$284.88683149$ |
$284.88683149045704$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$4830924.57066$ |
| 8.2.778...339.1 |
$x^{8} - 2 x^{7} - 31 x^{6} + 736 x^{5} - 2981 x^{4} - 1395 x^{3} - 47395 x^{2} + 616849 x - 1108693$ |
$8$ |
[2,3] |
$-\,7^{6}\cdot 131^{7}$ |
$2$ |
$306.503835631$ |
$306.5038356312733$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$4349431.55376$ |
| 8.2.173...784.1 |
$x^{8} - 2358 x^{4} - 81875$ |
$8$ |
[2,3] |
$-\,2^{18}\cdot 131^{7}$ |
$2$ |
$338.789446979$ |
$338.7894469790328$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$12864785.215$ |
| 8.2.694...136.1 |
$x^{8} - 8384$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 131^{7}$ |
$2$ |
$402.890820835$ |
$522.484752665034$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$[2]$ |
$2$ |
$4$ |
$22579255.1539$ |
| 8.2.694...136.2 |
$x^{8} - 524$ |
$8$ |
[2,3] |
$-\,2^{20}\cdot 131^{7}$ |
$2$ |
$402.890820835$ |
$522.484752665034$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$[2]$ |
$2$ |
$4$ |
$22579255.1539$ |
| 8.2.117...971.1 |
$x^{8} - 2 x^{7} - 31 x^{6} + 2570 x^{5} - 25251 x^{4} + 272002 x^{3} - 1136136 x^{2} + 624840 x - 107984$ |
$8$ |
[2,3] |
$-\,11^{6}\cdot 131^{7}$ |
$2$ |
$430.186619081$ |
$430.1866190806643$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$207207858.999$ |
| 8.0.138...272.1 |
$x^{8} + 262 x^{6} + 23056 x^{4} + 848880 x^{2} + 11226438$ |
$8$ |
[0,4] |
$2^{21}\cdot 131^{7}$ |
$2$ |
$439.355555541$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$16809415.3591$ |
| 8.4.138...272.1 |
$x^{8} - 262 x^{6} + 23056 x^{4} - 848880 x^{2} + 11226438$ |
$8$ |
[4,2] |
$2^{21}\cdot 131^{7}$ |
$2$ |
$439.355555541$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$98266329.2098$ |
| 8.0.138...272.2 |
$x^{8} + 262 x^{6} + 25676 x^{4} + 1184764 x^{2} + 13500598$ |
$8$ |
[0,4] |
$2^{21}\cdot 131^{7}$ |
$2$ |
$439.355555541$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$17455899.3184$ |
| 8.4.138...272.2 |
$x^{8} - 262 x^{6} + 25676 x^{4} - 1184764 x^{2} + 13500598$ |
$8$ |
[4,2] |
$2^{21}\cdot 131^{7}$ |
$2$ |
$439.355555541$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$75914290.7528$ |
| 8.6.111...176.1 |
$x^{8} - 42706 x^{4} + 311256 x^{2} - 553475$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$868461304.397$ |
| 8.2.111...176.1 |
$x^{8} - 131$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$621.3425853496952$ |
|
|
✓ |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$[2]$ |
$2$ |
$4$ |
$329472794.154$ |
| 8.2.111...176.2 |
$x^{8} - 42706 x^{4} - 311256 x^{2} - 553475$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$297117576.413$ |
| 8.6.111...176.2 |
$x^{8} - 524 x^{6} - 3144 x^{5} + 66286 x^{4} + 748272 x^{3} + 1707192 x^{2} - 2461752 x + 106110$ |
$8$ |
[6,1] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$670917744.661$ |
| 8.2.111...176.3 |
$x^{8} - 4716 x^{4} - 327500$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$569.7736629809141$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$929333711.477$ |
| 8.2.111...176.4 |
$x^{8} + 4716 x^{4} - 327500$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$569.7736629809141$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$100277741.875$ |
| 8.2.111...176.5 |
$x^{8} - 2096$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$621.3425853496952$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$[2]$ |
$2$ |
$4$ |
$329472794.154$ |
| 8.2.111...176.6 |
$x^{8} - 3144 x^{5} + 10742 x^{4} - 150912 x^{3} + 4951800 x^{2} - 35410872 x + 116526334$ |
$8$ |
[2,3] |
$-\,2^{24}\cdot 131^{7}$ |
$2$ |
$569.773662981$ |
$788.515402682017$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$308544609.60$ |
| 8.0.222...352.1 |
$x^{8} - 262 x^{4} + 4716 x^{2} + 6550$ |
$8$ |
[0,4] |
$2^{25}\cdot 131^{7}$ |
$2$ |
$621.34258535$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[62]$ |
$[62]$ |
$2$ |
$3$ |
$7734509.93374$ |
| 8.4.222...352.1 |
$x^{8} - 262 x^{4} - 4716 x^{2} + 6550$ |
$8$ |
[4,2] |
$2^{25}\cdot 131^{7}$ |
$2$ |
$621.34258535$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$665383517.715$ |
| 8.0.222...352.2 |
$x^{8} - 1048 x^{4} + 37728 x^{2} + 104800$ |
$8$ |
[0,4] |
$2^{25}\cdot 131^{7}$ |
$2$ |
$621.34258535$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[2]$ |
$[2]$ |
$2$ |
$3$ |
$327528279.213$ |
| 8.4.222...352.2 |
$x^{8} - 1048 x^{4} - 37728 x^{2} + 104800$ |
$8$ |
[4,2] |
$2^{25}\cdot 131^{7}$ |
$2$ |
$621.34258535$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1501915155.77$ |
| 8.2.444...704.1 |
$x^{8} - 524 x^{4} - 4716 x^{2} - 10611$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 131^{7}$ |
$2$ |
$677.578893958$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$4$ |
$945857268.15$ |
| 8.6.444...704.1 |
$x^{8} - 524 x^{4} + 4716 x^{2} - 10611$ |
$8$ |
[6,1] |
$-\,2^{26}\cdot 131^{7}$ |
$2$ |
$677.578893958$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$2168663679.43$ |
| 8.2.444...704.2 |
$x^{8} - 2096 x^{4} - 37728 x^{2} - 169776$ |
$8$ |
[2,3] |
$-\,2^{26}\cdot 131^{7}$ |
$2$ |
$677.578893958$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$[31]$ |
$[62]$ |
$2$ |
$4$ |
$22336216.1399$ |
| 8.6.444...704.2 |
$x^{8} - 2096 x^{4} + 37728 x^{2} - 169776$ |
$8$ |
[6,1] |
$-\,2^{26}\cdot 131^{7}$ |
$2$ |
$677.578893958$ |
$1022.5779636496085$ |
|
|
|
$C_2 \wr C_2\wr C_2$ (as 8T35) |
trivial |
$[2]$ |
$2$ |
$6$ |
$960768697.364$ |
| 8.0.888...408.1 |
$x^{8} + 4716 x^{4} + 1048$ |
$8$ |
[0,4] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[70]$ |
$[70]$ |
$2$ |
$3$ |
$4669129.58118$ |
| 8.8.888...408.1 |
$x^{8} - 524 x^{6} + 32750 x^{4} - 655000 x^{2} + 4093750$ |
$8$ |
[8,0] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$878.7111110815015$ |
|
|
? |
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$7$ |
$2449411395.79$ |
| 8.4.888...408.1 |
$x^{8} - 4716 x^{4} + 1048$ |
$8$ |
[4,2] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$5$ |
$642626337.133$ |
| 8.0.888...408.2 |
$x^{8} + 7074 x^{4} + 163750$ |
$8$ |
[0,4] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[70]$ |
$[70]$ |
$2$ |
$3$ |
$4898489.54665$ |
| 8.4.888...408.2 |
$x^{8} - 1572 x^{4} - 18864 x^{2} + 26200$ |
$8$ |
[4,2] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$878.7111110815015$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$[2]$ |
$2$ |
$5$ |
$996813447.58$ |
| 8.4.888...408.3 |
$x^{8} - 1572 x^{4} + 18864 x^{2} + 26200$ |
$8$ |
[4,2] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$878.7111110815015$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
trivial |
$[2]$ |
$2$ |
$5$ |
$996813447.58$ |
| 8.0.888...408.3 |
$x^{8} + 14148 x^{4} + 655000$ |
$8$ |
[0,4] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[70]$ |
$[70]$ |
$2$ |
$3$ |
$2703111.59246$ |
| 8.0.888...408.4 |
$x^{8} + 524 x^{6} + 32750 x^{4} + 655000 x^{2} + 4093750$ |
$8$ |
[0,4] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$878.7111110815015$ |
✓ |
|
? |
$QD_{16}$ (as 8T8) |
$[8466]$ |
$[8466]$ |
$2$ |
$3$ |
$37895.8415043$ |
| 8.4.888...408.4 |
$x^{8} - 7074 x^{4} + 163750$ |
$8$ |
[4,2] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$5$ |
$633404107.502$ |
| 8.0.888...408.5 |
$x^{8} + 2358 x^{4} + 262$ |
$8$ |
[0,4] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[70]$ |
$[70]$ |
$2$ |
$3$ |
$2664319.66256$ |
| 8.4.888...408.5 |
$x^{8} - 14148 x^{4} + 655000$ |
$8$ |
[4,2] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1110019153.01$ |
| 8.4.888...408.6 |
$x^{8} - 2358 x^{4} + 262$ |
$8$ |
[4,2] |
$2^{27}\cdot 131^{7}$ |
$2$ |
$738.905023352$ |
$1091.2342578523335$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
trivial |
$[2]$ |
$2$ |
$5$ |
$1164546222.82$ |
| 8.0.142...528.1 |
$x^{8} + 1048$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1139.5473259618282$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$157129080.844$ |
| 8.0.142...528.2 |
$x^{8} + 4192$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1139.5473259618282$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$127345870.924$ |
| 8.0.142...528.3 |
$x^{8} + 16768$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1139.5473259618282$ |
|
|
? |
$Z_8 : Z_8^\times$ (as 8T15) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$157129080.844$ |
| 8.0.142...528.4 |
$x^{8} + 262$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1139.5473259618282$ |
|
|
✓ |
$Z_8 : Z_8^\times$ (as 8T15) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$127345870.924$ |
| 8.0.142...528.5 |
$x^{8} + 50304 x^{4} - 3885984 x^{2} + 1432155928$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1297.7035435727091$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$106656516.058$ |
| 8.0.142...528.6 |
$x^{8} + 50304 x^{4} + 3885984 x^{2} + 1432155928$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1297.7035435727091$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$193203632.782$ |
| 8.0.142...528.7 |
$x^{8} - 44016 x^{4} - 3885984 x^{2} + 1481579608$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1297.7035435727091$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$186605463.141$ |
| 8.0.142...528.8 |
$x^{8} - 44016 x^{4} + 3885984 x^{2} + 1481579608$ |
$8$ |
[0,4] |
$2^{31}\cdot 131^{7}$ |
$2$ |
$1044.96950533$ |
$1297.7035435727091$ |
|
|
? |
$(C_4^2 : C_2):C_2$ (as 8T26) |
$[6]$ |
$[6]$ |
$2$ |
$3$ |
$103014049.423$ |
| 8.2.418...739.1 |
$x^{8} - 2 x^{7} - 293 x^{6} + 15932 x^{5} + 26494 x^{4} - 3789522 x^{3} - 34109229 x^{2} + 698077224 x - 468700093$ |
$8$ |
[2,3] |
$-\,43^{6}\cdot 131^{7}$ |
$2$ |
$1195.9519338$ |
$1195.9519337983759$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$8319256249.79$ |
| 8.2.279...851.1 |
$x^{8} - 2 x^{7} - 162 x^{6} - 36468 x^{5} + 36712 x^{4} + 8821586 x^{3} + 325224819 x^{2} - 4417819926 x - 19267076560$ |
$8$ |
[2,3] |
$-\,59^{6}\cdot 131^{7}$ |
$2$ |
$1516.18219553$ |
$1516.1821955318298$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$126678536292$ |
| 8.2.993...539.1 |
$x^{8} - 2 x^{7} - 31 x^{6} + 10561 x^{5} - 192800 x^{4} + 2396953 x^{3} - 27426526 x^{2} + 701868 x - 188379088$ |
$8$ |
[2,3] |
$-\,107^{6}\cdot 131^{7}$ |
$2$ |
$2369.46455785$ |
$2369.464557852261$ |
|
|
|
$QD_{16}$ (as 8T8) |
trivial |
$[2]$ |
$2$ |
$4$ |
$101660823654$ |
