| 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 |
| 7.7.13841287201.1 |
$x^{7} - 21 x^{5} - 21 x^{4} + 91 x^{3} + 112 x^{2} - 84 x - 97$ |
$7$ |
[7,0] |
$7^{12}$ |
$1$ |
$28.1021467385$ |
$28.102146738487733$ |
|
✓ |
|
$C_7$ (as 7T1) |
trivial |
$2$ |
$6$ |
$550.88577714$ |
| 7.3.3543369523456.3 |
$x^{7} - 21 x^{5} - 28 x^{4} - 7 x^{3} - 112 x^{2} + 259 x + 244$ |
$7$ |
[3,2] |
$2^{8}\cdot 7^{12}$ |
$2$ |
$62.0545710514$ |
$112.40858695395093$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
$[7]$ |
$2$ |
$4$ |
$12405.1123243$ |
| 7.3.3543369523456.4 |
$x^{7} - 21 x^{5} - 70 x^{4} + 238 x^{3} + 1092 x^{2} - 2240 x + 736$ |
$7$ |
[3,2] |
$2^{8}\cdot 7^{12}$ |
$2$ |
$62.0545710514$ |
$112.40858695395093$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
$[14]$ |
$2$ |
$4$ |
$6202.55616215$ |
| 7.3.645779095649856.3 |
$x^{7} - 21 x^{5} - 70 x^{4} - 105 x^{3} - 84 x^{2} - 35 x + 40818$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$130.53479252$ |
$365.55514436199405$ |
|
|
? |
$A_7$ (as 7T6) |
$[7]$ |
$2$ |
$4$ |
$58386.9611144$ |
| 7.3.1148051725599744.1 |
$x^{7} - 42 x^{5} - 28 x^{4} + 609 x^{3} + 756 x^{2} - 3024 x + 864$ |
$7$ |
[3,2] |
$2^{10}\cdot 3^{4}\cdot 7^{12}$ |
$3$ |
$141.717363809$ |
$287.6153731130211$ |
|
|
? |
$A_7$ (as 7T6) |
$[7]$ |
$2$ |
$4$ |
$105789.61343$ |
| 7.3.13841287201000000.2 |
$x^{7} - 2744 x^{2} + 27440$ |
$7$ |
[3,2] |
$2^{6}\cdot 5^{6}\cdot 7^{12}$ |
$3$ |
$202.247123883$ |
$324.0266365133118$ |
|
|
? |
$A_7$ (as 7T6) |
$[7]$ |
$2$ |
$4$ |
$63284.5358524$ |
| 7.3.52308106747638336.4 |
$x^{7} - 84 x^{5} - 420 x^{4} + 5376 x^{3} - 3780 x^{2} - 16156 x + 27900$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{10}\cdot 7^{12}$ |
$3$ |
$244.549624435$ |
$381.493820923204$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
$[7]$ |
$2$ |
$4$ |
$539181.587994$ |
| 7.3.52308106747638336.6 |
$x^{7} - 84 x^{5} - 364 x^{4} - 1680 x^{3} + 6720 x^{2} + 77728 x + 391638$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{10}\cdot 7^{12}$ |
$3$ |
$244.549624435$ |
$381.493820923204$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
$[7]$ |
$2$ |
$4$ |
$539181.587994$ |
| 7.1.247979172729544704.1 |
$x^{7} - 882 x^{4} + 882 x^{3} - 15876$ |
$7$ |
[1,3] |
$-\,2^{13}\cdot 3^{7}\cdot 7^{12}$ |
$3$ |
$305.433351812$ |
$1784.9975216126422$ |
|
|
? |
$S_7$ (as 7T7) |
$[7]$ |
$2$ |
$3$ |
$1346046.93683$ |
| 7.1.1313840933532421875.2 |
$x^{7} - 35 x^{5} - 70 x^{4} + 280 x^{3} + 1232 x^{2} + 1680 x - 117325$ |
$7$ |
[1,3] |
$-\,3^{5}\cdot 5^{8}\cdot 7^{12}$ |
$3$ |
$387.581693052$ |
$991.9747858827791$ |
|
|
? |
$S_7$ (as 7T7) |
$[7]$ |
$2$ |
$3$ |
$620527.310781$ |
| 7.7.874...849.1 |
$x^{7} - 903 x^{5} - 11739 x^{4} - 4515 x^{3} + 484008 x^{2} + 1555568 x - 609267$ |
$7$ |
[7,0] |
$7^{12}\cdot 43^{6}$ |
$2$ |
$706.082286107$ |
$706.0822861068045$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$80239711.6814$ |
| 7.7.874...849.2 |
$x^{7} - 903 x^{5} - 3311 x^{4} + 256753 x^{3} + 1655500 x^{2} - 20129676 x - 154845881$ |
$7$ |
[7,0] |
$7^{12}\cdot 43^{6}$ |
$2$ |
$706.082286107$ |
$706.0822861068045$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$3504328.2978067407$ |
| 7.7.874...849.3 |
$x^{7} - 903 x^{5} - 1204 x^{4} + 218827 x^{3} + 753704 x^{2} - 16141125 x - 86614900$ |
$7$ |
[7,0] |
$7^{12}\cdot 43^{6}$ |
$2$ |
$706.082286107$ |
$706.0822861068045$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$2429511482.583454$ |
| 7.7.874...849.4 |
$x^{7} - 903 x^{5} - 15953 x^{4} - 97223 x^{3} - 177590 x^{2} + 46956 x + 94471$ |
$7$ |
[7,0] |
$7^{12}\cdot 43^{6}$ |
$2$ |
$706.082286107$ |
$706.0822861068045$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$8351632.841147239$ |
| 7.7.874...849.5 |
$x^{7} - 903 x^{5} - 3311 x^{4} + 206185 x^{3} + 1491154 x^{2} - 1773492 x + 461089$ |
$7$ |
[7,0] |
$7^{12}\cdot 43^{6}$ |
$2$ |
$706.082286107$ |
$706.0822861068045$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$4703614.757954623$ |
| 7.7.874...849.6 |
$x^{7} - 903 x^{5} - 7525 x^{4} + 105049 x^{3} + 905408 x^{2} - 1520652 x + 545369$ |
$7$ |
[7,0] |
$7^{12}\cdot 43^{6}$ |
$2$ |
$706.082286107$ |
$706.0822861068045$ |
|
✓ |
|
$C_7$ (as 7T1) |
$[7]$ |
$2$ |
$6$ |
$12027627.652134134$ |
| 8.4.3543369523456.1 |
$x^{8} - 7 x^{6} - 14 x^{5} + 7 x^{4} + 28 x^{2} + 48 x + 14$ |
$8$ |
[4,2] |
$2^{8}\cdot 7^{12}$ |
$2$ |
$37.0405183549$ |
$112.40858695395093$ |
|
|
|
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$7262.24637552$ |
| 8.0.14173478093824.1 |
$x^{8} + 7 x^{6} + 21 x^{4} - 14 x^{3} + 42 x^{2} - 48 x + 28$ |
$8$ |
[0,4] |
$2^{10}\cdot 7^{12}$ |
$2$ |
$44.048847971$ |
$133.6770913930405$ |
|
|
|
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$1447.05229669$ |
| 8.0.226775649501184.4 |
$x^{8} - 2 x^{7} + 14 x^{6} - 14 x^{5} - 126 x^{4} + 630 x^{3} + 658 x^{2} - 5130 x + 10267$ |
$8$ |
[0,4] |
$2^{14}\cdot 7^{12}$ |
$2$ |
$62.2944782076$ |
$94.52397781331281$ |
|
|
? |
$C_2^3:C_7$ (as 8T25) |
trivial |
$2$ |
$3$ |
$24239.5513308$ |
| 8.0.226775649501184.5 |
$x^{8} - 2 x^{7} + 14 x^{6} + 84 x^{4} - 112 x^{3} + 28 x^{2} + 188 x + 310$ |
$8$ |
[0,4] |
$2^{14}\cdot 7^{12}$ |
$2$ |
$62.2944782076$ |
$94.52397781331281$ |
|
|
? |
$C_2^3:C_7$ (as 8T25) |
trivial |
$2$ |
$3$ |
$26620.3609911$ |
| 8.0.907102598004736.3 |
$x^{8} - 56 x^{5} + 7 x^{4} - 84 x^{3} + 770 x^{2} - 116 x + 2394$ |
$8$ |
[0,4] |
$2^{16}\cdot 7^{12}$ |
$2$ |
$74.0810367098$ |
$112.40858695395093$ |
|
|
? |
$\PSL(2,7)$ (as 8T37) |
$[2, 6]$ |
$2$ |
$3$ |
$10627.578275$ |
| 8.0.907102598004736.6 |
$x^{8} - 56 x^{5} - 70 x^{4} + 224 x^{3} + 672 x^{2} + 264 x + 329$ |
$8$ |
[0,4] |
$2^{16}\cdot 7^{12}$ |
$2$ |
$74.0810367098$ |
$112.40858695395093$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 2]$ |
$2$ |
$3$ |
$25714.4903521$ |
| 8.0.907102598004736.7 |
$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} + 70 x^{4} - 84 x^{3} + 378 x^{2} - 124 x + 517$ |
$8$ |
[0,4] |
$2^{16}\cdot 7^{12}$ |
$2$ |
$74.0810367098$ |
$158.96974819747277$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 2]$ |
$2$ |
$3$ |
$8070.98128542$ |
| 8.4.907102598004736.7 |
$x^{8} - 28 x^{6} - 84 x^{5} + 133 x^{4} + 1204 x^{3} + 2310 x^{2} + 1224 x + 189$ |
$8$ |
[4,2] |
$2^{16}\cdot 7^{12}$ |
$2$ |
$74.0810367098$ |
$158.96974819747277$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$5$ |
$44501.4858602$ |
| 8.0.1803810389321521.1 |
$x^{8} - 2 x^{7} - 28 x^{6} + 154 x^{5} + 189 x^{4} - 2016 x^{3} + 5278 x^{2} + 2701 x + 2949$ |
$8$ |
[0,4] |
$7^{12}\cdot 19^{4}$ |
$2$ |
$80.7279381627$ |
$122.49441772961917$ |
|
|
? |
$C_2^3:C_7$ (as 8T25) |
$[2, 4]$ |
$2$ |
$3$ |
$7631.3442133$ |
| 8.0.1803810389321521.2 |
$x^{8} - 4 x^{7} + 35 x^{6} - 42 x^{5} + 329 x^{4} - 14 x^{3} + 2611 x^{2} - 6607 x + 3692$ |
$8$ |
[0,4] |
$7^{12}\cdot 19^{4}$ |
$2$ |
$80.7279381627$ |
$122.49441772961917$ |
|
|
? |
$C_2^3:C_7$ (as 8T25) |
$[2, 4]$ |
$2$ |
$3$ |
$7306.25989421$ |
| 8.0.2296103451199488.1 |
$x^{8} - 3 x^{7} + 28 x^{6} - 161 x^{5} + 392 x^{4} + 371 x^{3} + 672 x^{2} + 353 x + 187$ |
$8$ |
[0,4] |
$2^{11}\cdot 3^{4}\cdot 7^{12}$ |
$3$ |
$83.2001159276$ |
$173.45564966273548$ |
|
|
? |
$\PGL(2,7)$ (as 8T43) |
$[2]$ |
$2$ |
$3$ |
$91728.6569631$ |
| 8.4.3628410392018944.1 |
$x^{8} - 4 x^{7} + 28 x^{6} - 196 x^{4} - 784 x^{2} + 2016 x - 1008$ |
$8$ |
[4,2] |
$2^{18}\cdot 7^{12}$ |
$2$ |
$88.0976959421$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$118573.087895$ |
| 8.0.3628410392018944.1 |
$x^{8} - 4 x^{7} - 56 x^{5} + 196 x^{4} - 224 x^{3} + 1792 x^{2} + 1408 x + 1088$ |
$8$ |
[0,4] |
$2^{18}\cdot 7^{12}$ |
$2$ |
$88.0976959421$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$131688.580848$ |
| 8.4.3628410392018944.3 |
$x^{8} - 4 x^{7} - 28 x^{6} - 28 x^{5} + 70 x^{4} + 588 x^{3} + 1764 x^{2} + 1940 x + 661$ |
$8$ |
[4,2] |
$2^{18}\cdot 7^{12}$ |
$2$ |
$88.0976959421$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
trivial |
$2$ |
$5$ |
$146393.854072$ |
| 8.0.3628410392018944.3 |
$x^{8} - 4 x^{7} + 28 x^{6} - 56 x^{5} + 301 x^{4} - 280 x^{3} + 2128 x^{2} + 320 x + 6672$ |
$8$ |
[0,4] |
$2^{18}\cdot 7^{12}$ |
$2$ |
$88.0976959421$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$3$ |
$181346.72701$ |
| 8.4.3628410392018944.4 |
$x^{8} - 4 x^{7} - 14 x^{6} + 56 x^{5} + 84 x^{4} - 28 x^{3} - 112 x^{2} - 16 x + 50$ |
$8$ |
[4,2] |
$2^{18}\cdot 7^{12}$ |
$2$ |
$88.0976959421$ |
$133.6770913930405$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 2]$ |
$2$ |
$5$ |
$51933.9162826$ |
| 8.8.12782719397154721.1 |
$x^{8} - x^{7} - 42 x^{6} + 77 x^{5} + 420 x^{4} - 854 x^{3} - 987 x^{2} + 1577 x + 733$ |
$8$ |
[8,0] |
$7^{12}\cdot 31^{4}$ |
$2$ |
$103.116439039$ |
$156.46613112957195$ |
|
|
? |
$C_2^3:C_7$ (as 8T25) |
trivial |
$2$ |
$7$ |
$942691.948946$ |
| 8.0.12782719397154721.1 |
$x^{8} - 3 x^{7} - 56 x^{6} + 28 x^{5} + 1043 x^{4} - 567 x^{3} + 4704 x^{2} + 46853 x + 57555$ |
$8$ |
[0,4] |
$7^{12}\cdot 31^{4}$ |
$2$ |
$103.116439039$ |
$156.46613112957195$ |
|
|
? |
$C_2^3:C_7$ (as 8T25) |
$[2, 2, 2]$ |
$2$ |
$3$ |
$20731.5393723$ |
| 8.4.14513641568075776.1 |
$x^{8} - 4 x^{7} + 14 x^{6} - 28 x^{5} - 273 x^{4} - 84 x^{3} + 2534 x^{2} + 4384 x - 9381$ |
$8$ |
[4,2] |
$2^{20}\cdot 7^{12}$ |
$2$ |
$104.76640683$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$5$ |
$208750.585146$ |
| 8.0.14513641568075776.2 |
$x^{8} - 4 x^{7} + 28 x^{6} - 56 x^{5} + 252 x^{4} - 280 x^{3} + 952 x^{2} - 464 x + 1380$ |
$8$ |
[0,4] |
$2^{20}\cdot 7^{12}$ |
$2$ |
$104.76640683$ |
$158.96974819747277$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 12]$ |
$2$ |
$3$ |
$15171.4047761$ |
| 8.0.14513641568075776.3 |
$x^{8} - 56 x^{5} + 126 x^{4} + 224 x^{3} - 112 x^{2} + 1048 x + 1505$ |
$8$ |
[0,4] |
$2^{20}\cdot 7^{12}$ |
$2$ |
$104.76640683$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 2]$ |
$2$ |
$3$ |
$32642.9044999$ |
| 8.4.14513641568075776.5 |
$x^{8} - 28 x^{6} - 84 x^{5} + 210 x^{4} + 5096 x^{3} + 13552 x^{2} + 6008 x - 2002$ |
$8$ |
[4,2] |
$2^{20}\cdot 7^{12}$ |
$2$ |
$104.76640683$ |
$158.96974819747277$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$5$ |
$144495.61499$ |
| 8.0.14513641568075776.7 |
$x^{8} - 4 x^{7} - 56 x^{5} + 490 x^{4} - 1008 x^{3} + 1400 x^{2} - 3296 x + 4616$ |
$8$ |
[0,4] |
$2^{20}\cdot 7^{12}$ |
$2$ |
$104.76640683$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 2]$ |
$2$ |
$3$ |
$44578.5697838$ |
| 8.4.14513641568075776.11 |
$x^{8} - 4 x^{7} - 28 x^{6} + 56 x^{5} + 686 x^{4} - 4256 x^{3} + 14112 x^{2} - 16672 x + 4080$ |
$8$ |
[4,2] |
$2^{20}\cdot 7^{12}$ |
$2$ |
$104.76640683$ |
$189.04795562662562$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2]$ |
$2$ |
$5$ |
$896141.00032$ |
| 8.0.470772960728745024.2 |
$x^{8} - 2 x^{7} + 28 x^{6} - 13608 x + 27216$ |
$8$ |
[0,4] |
$2^{6}\cdot 3^{12}\cdot 7^{12}$ |
$3$ |
$161.84580193$ |
$381.493820923204$ |
|
|
? |
$\PSL(2,7)$ (as 8T37) |
$[4]$ |
$2$ |
$3$ |
$747394.855325$ |
| 8.0.928873060356849664.4 |
$x^{8} + 56 x^{6} + 952 x^{4} - 896 x^{3} + 7392 x^{2} + 2304 x + 15120$ |
$8$ |
[0,4] |
$2^{26}\cdot 7^{12}$ |
$2$ |
$176.195391884$ |
$291.55180368862204$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 4]$ |
$2$ |
$3$ |
$258306.421026$ |
| 8.4.928873060356849664.7 |
$x^{8} - 56 x^{6} - 112 x^{5} + 350 x^{4} + 3528 x^{3} + 11592 x^{2} + 16120 x + 6727$ |
$8$ |
[4,2] |
$2^{26}\cdot 7^{12}$ |
$2$ |
$176.195391884$ |
$291.55180368862204$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[4]$ |
$2$ |
$5$ |
$719098.828771$ |
| 8.4.928873060356849664.8 |
$x^{8} - 28 x^{6} - 224 x^{5} - 1176 x^{4} - 1064 x^{3} - 6104 x^{2} - 7920 x + 8442$ |
$8$ |
[4,2] |
$2^{26}\cdot 7^{12}$ |
$2$ |
$176.195391884$ |
$291.55180368862204$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 2]$ |
$2$ |
$5$ |
$1034710.48001$ |
| 8.0.928873060356849664.12 |
$x^{8} - 28 x^{6} - 112 x^{5} + 1386 x^{4} + 6272 x^{3} + 18060 x^{2} - 49520 x + 426209$ |
$8$ |
[0,4] |
$2^{26}\cdot 7^{12}$ |
$2$ |
$176.195391884$ |
$291.55180368862204$ |
|
|
? |
$C_2^3:\GL(3,2)$ (as 8T48) |
$[2, 4]$ |
$2$ |
$3$ |
$121607.01614$ |
| 8.0.3715492241427398656.1 |
$x^{8} - 896 x + 1568$ |
$8$ |
[0,4] |
$2^{28}\cdot 7^{12}$ |
$2$ |
$209.532813659$ |
$394.83564736477246$ |
|
|
? |
$A_8$ (as 8T49) |
$[2, 2]$ |
$2$ |
$3$ |
$468980.925517$ |
| 8.2.650...376.1 |
$x^{8} - 3528 x^{2} - 6048 x - 2646$ |
$8$ |
[2,3] |
$-\,2^{31}\cdot 3^{7}\cdot 7^{12}$ |
$3$ |
$710.590490282$ |
$2146.813805316912$ |
|
|
? |
$S_8$ (as 8T50) |
trivial |
$2$ |
$4$ |
$683277868.793$ |
| 8.2.131...864.1 |
$x^{8} - 56 x^{5} - 1050 x^{4} - 8400 x^{3} - 35000 x^{2} - 75000 x - 65625$ |
$8$ |
[2,3] |
$-\,2^{29}\cdot 3^{11}\cdot 7^{12}$ |
$3$ |
$1034.95750826$ |
$5227.251692600439$ |
|
|
? |
$S_8$ (as 8T50) |
$[2]$ |
$2$ |
$4$ |
$1754817880.49$ |
| 8.2.186...216.1 |
$x^{8} - 5824 x - 5096$ |
$8$ |
[2,3] |
$-\,2^{31}\cdot 7^{12}\cdot 13^{7}$ |
$3$ |
$2563.53190246$ |
$4830.621803680782$ |
|
|
? |
$S_8$ (as 8T50) |
$[2, 2]$ |
$2$ |
$4$ |
$16760064929.9$ |
| 9.3.203...368.1 |
$x^{9} - 3 x^{8} + 756 x^{2} - 2268 x + 1764$ |
$9$ |
[3,3] |
$-\,2^{10}\cdot 3^{15}\cdot 7^{12}$ |
$3$ |
$180.500018538$ |
$491.70169406493306$ |
|
|
? |
$S_9$ (as 9T34) |
trivial |
$2$ |
$5$ |
$38577167.6361$ |
