| 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 |
| 7.3.1475789056.1 |
$x^{7} - 14 x^{3} - 14 x^{2} + 7 x + 22$ |
$7$ |
[3,2] |
$2^{8}\cdot 7^{8}$ |
$2$ |
$20.4108274941$ |
$44.50121314235103$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$326.439203548$ |
| 7.3.1475789056.2 |
$x^{7} - 7 x^{5} - 14 x^{4} - 7 x^{3} - 7 x + 2$ |
$7$ |
[3,2] |
$2^{8}\cdot 7^{8}$ |
$2$ |
$20.4108274941$ |
$44.50121314235103$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$326.439203548$ |
| 7.3.3320525376.2 |
$x^{7} - 14 x^{4} - 7 x^{3} + 21 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{2}\cdot 7^{8}$ |
$3$ |
$22.9177723177$ |
$54.502632566798404$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$633.574083388$ |
| 7.3.3320525376.4 |
$x^{7} - 7 x^{5} - 7 x^{4} + 7 x^{3} + 14 x^{2} + 7 x + 3$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{2}\cdot 7^{8}$ |
$3$ |
$22.9177723177$ |
$54.502632566798404$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$633.574083388$ |
| 7.3.8768262321.1 |
$x^{7} - 7 x^{5} - 21 x^{4} - 35 x^{3} - 35 x^{2} - 21 x - 3$ |
$7$ |
[3,2] |
$3^{2}\cdot 7^{8}\cdot 13^{2}$ |
$3$ |
$26.3278999659$ |
$106.53722684884416$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$408.509773441$ |
| 7.1.9961576128.3 |
$x^{7} + 7 x^{5} - 7 x^{4} + 7 x^{3} - 21 x^{2} - 21$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{3}\cdot 7^{8}$ |
$3$ |
$26.8122079943$ |
$113.37004431593924$ |
|
|
|
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$764.107877578$ |
| 7.3.12734445409.1 |
$x^{7} - 21 x^{3} + 7 x - 27$ |
$7$ |
[3,2] |
$7^{8}\cdot 47^{2}$ |
$2$ |
$27.7695330182$ |
$76.27123665069657$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$919.504522754$ |
| 7.3.12734445409.2 |
$x^{7} - 14 x^{4} - 70 x^{3} - 91 x^{2} - 28 x + 16$ |
$7$ |
[3,2] |
$7^{8}\cdot 47^{2}$ |
$2$ |
$27.7695330182$ |
$76.27123665069657$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$919.504522754$ |
| 7.3.16810159716.1 |
$x^{7} - 14 x^{4} - 42 x^{3} - 63 x^{2} - 77 x - 39$ |
$7$ |
[3,2] |
$2^{2}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$28.893222175$ |
$81.22073815911318$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$921.282525828$ |
| 7.3.16810159716.2 |
$x^{7} - 28 x^{4} + 224 x - 192$ |
$7$ |
[3,2] |
$2^{2}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$28.893222175$ |
$81.22073815911318$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$1090.2242225$ |
| 7.1.17709468672.2 |
$x^{7} + 7 x^{5} - 7 x^{3} - 28 x^{2} - 35 x - 24$ |
$7$ |
[1,3] |
$-\,2^{10}\cdot 3\cdot 7^{8}$ |
$3$ |
$29.1091391153$ |
$86.51753627157204$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$1412.7595346$ |
| 7.3.18447363200.2 |
$x^{7} - 7 x^{5} - 14 x^{4} - 28 x^{3} - 40$ |
$7$ |
[3,2] |
$2^{7}\cdot 5^{2}\cdot 7^{8}$ |
$3$ |
$29.2793912232$ |
$121.40843298386821$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$4$ |
$1395.04473233$ |
| 7.1.19185257728.2 |
$x^{7} - 14 x^{4} + 28 x^{3} + 56 x^{2} + 104$ |
$7$ |
[1,3] |
$-\,2^{8}\cdot 7^{8}\cdot 13$ |
$3$ |
$29.4439028981$ |
$180.1006136141094$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$723.678230124$ |
| 7.1.22413546288.1 |
$x^{7} + 7 x^{5} - 14 x^{4} + 42 x^{3} - 14 x^{2} + 42$ |
$7$ |
[1,3] |
$-\,2^{4}\cdot 3^{5}\cdot 7^{8}$ |
$3$ |
$30.1053976536$ |
$100.65091739580683$ |
|
|
|
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$3236.45436697$ |
| 7.3.23612624896.1 |
$x^{7} + 7 x^{5} - 14 x^{4} - 21 x^{3} - 28 x^{2} - 91 x + 50$ |
$7$ |
[3,2] |
$2^{12}\cdot 7^{8}$ |
$2$ |
$30.3303730927$ |
$74.84182121168894$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$3297.77111247$ |
| 7.3.23612624896.2 |
$x^{7} - 14 x^{5} + 77 x^{3} - 56 x^{2} - 84 x + 80$ |
$7$ |
[3,2] |
$2^{12}\cdot 7^{8}$ |
$2$ |
$30.3303730927$ |
$74.84182121168894$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2471.08321775$ |
| 7.3.23612624896.3 |
$x^{7} - 7 x^{5} + 14 x^{3} - 14 x - 8$ |
$7$ |
[3,2] |
$2^{12}\cdot 7^{8}$ |
$2$ |
$30.3303730927$ |
$74.84182121168894$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2471.08321775$ |
| 7.3.23612624896.4 |
$x^{7} - 7 x^{5} - 14 x^{3} - 56 x^{2} - 14 x - 8$ |
$7$ |
[3,2] |
$2^{12}\cdot 7^{8}$ |
$2$ |
$30.3303730927$ |
$74.84182121168894$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$3297.77111247$ |
| 7.3.29884728384.3 |
$x^{7} - 14 x^{4} - 42 x^{3} - 54$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$31.3684282906$ |
$45.93867985553893$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2048.78265387$ |
| 7.3.29884728384.4 |
$x^{7} - 14 x^{5} - 14 x^{4} + 28 x^{3} + 70 x^{2} + 42 x + 10$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$31.3684282906$ |
$45.93867985553893$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2048.78265387$ |
| 7.3.33620319432.1 |
$x^{7} - 63 x^{3} + 126 x - 144$ |
$7$ |
[3,2] |
$2^{3}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$31.9007036197$ |
$80.6896679038271$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$4$ |
$2797.00782182$ |
| 7.1.35021166075.1 |
$x^{7} - 7 x^{5} - 14 x^{4} + 28 x^{3} + 56 x^{2} - 125$ |
$7$ |
[1,3] |
$-\,3^{5}\cdot 5^{2}\cdot 7^{8}$ |
$3$ |
$32.0872828934$ |
$89.62688961814845$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$742.415757818$ |
| 7.3.35049990080.1 |
$x^{7} - 7 x - 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 5\cdot 7^{8}\cdot 19$ |
$4$ |
$32.0910543185$ |
$216.8720862965027$ |
|
|
✓ |
$S_7$ (as 7T7) |
trivial |
$2$ |
$4$ |
$2540.5156797$ |
| 7.3.37822859361.1 |
$x^{7} - 14 x^{4} - 105 x^{3} - 147 x^{2} - 315 x - 192$ |
$7$ |
[3,2] |
$3^{8}\cdot 7^{8}$ |
$2$ |
$32.4420108653$ |
$91.36803059355806$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$3068.95702139$ |
| 7.1.39846304512.3 |
$x^{7} + 7 x^{5} - 28 x^{4} - 56 x^{2} - 28 x - 32$ |
$7$ |
[1,3] |
$-\,2^{8}\cdot 3^{3}\cdot 7^{8}$ |
$3$ |
$32.6844476444$ |
$86.51753627157204$ |
|
|
|
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$4481.27430614$ |
| 7.3.44642618944.1 |
$x^{7} - 56 x^{3} + 28 x - 44$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 11^{2}$ |
$3$ |
$33.2194784126$ |
$66.83961077471815$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$1228.2892712$ |
| 7.3.44642618944.2 |
$x^{7} - 14 x^{4} - 56 x^{3} - 28 x^{2} + 196 x + 364$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 11^{2}$ |
$3$ |
$33.2194784126$ |
$66.83961077471815$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$1228.2892712$ |
| 7.3.67240638864.2 |
$x^{7} - 35 x^{4} - 84 x^{3} + 84 x^{2} + 462 x + 726$ |
$7$ |
[3,2] |
$2^{4}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$35.2212323453$ |
$98.6086672406947$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$5207.02804573$ |
| 7.3.68491600681.1 |
$x^{7} - 7 x^{5} + 7 x^{3} - 28 x^{2} - 35 x - 1$ |
$7$ |
[3,2] |
$7^{8}\cdot 109^{2}$ |
$2$ |
$35.3141037009$ |
$116.15157630612579$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$1025.43829025$ |
| 7.3.68491600681.2 |
$x^{7} - 28 x^{3} + 35 x - 33$ |
$7$ |
[3,2] |
$7^{8}\cdot 109^{2}$ |
$2$ |
$35.3141037009$ |
$116.15157630612579$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$1025.43829025$ |
| 7.3.73789452800.1 |
$x^{7} - 14 x^{5} + 28 x^{3} + 56 x - 256$ |
$7$ |
[3,2] |
$2^{9}\cdot 5^{2}\cdot 7^{8}$ |
$3$ |
$35.6919776878$ |
$154.74240850576766$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$4$ |
$1996.82770242$ |
| 7.3.77571162256.3 |
$x^{7} + 7 x^{5} - 21 x^{4} + 7 x^{3} - 21 x^{2} + 14 x + 3$ |
$7$ |
[3,2] |
$2^{4}\cdot 7^{8}\cdot 29^{2}$ |
$3$ |
$35.9477300114$ |
$119.82318344449011$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$3022.74774168$ |
| 7.3.77571162256.4 |
$x^{7} + 7 x^{5} - 7 x^{4} - 49 x^{3} - 63 x^{2} - 378 x - 351$ |
$7$ |
[3,2] |
$2^{4}\cdot 7^{8}\cdot 29^{2}$ |
$3$ |
$35.9477300114$ |
$119.82318344449011$ |
|
|
|
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$3022.74774168$ |
| 7.1.79692609024.2 |
$x^{7} + 14 x^{5} - 21 x^{4} + 42 x^{3} - 70 x^{2} + 56 x - 18$ |
$7$ |
[1,3] |
$-\,2^{9}\cdot 3^{3}\cdot 7^{8}$ |
$3$ |
$36.0865559044$ |
$269.64092665737746$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$4606.82536274$ |
| 7.1.89654185152.4 |
$x^{7} + 7 x^{5} - 7 x^{4} - 14 x^{3} + 14 x^{2} + 8$ |
$7$ |
[1,3] |
$-\,2^{6}\cdot 3^{5}\cdot 7^{8}$ |
$3$ |
$36.698890805$ |
$113.37004431593924$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$4199.65524279$ |
| 7.1.100860958296.1 |
$x^{7} - 21 x^{4} + 63 x^{3} - 63 x^{2} + 14 x + 12$ |
$7$ |
[1,3] |
$-\,2^{3}\cdot 3^{7}\cdot 7^{8}$ |
$3$ |
$37.3216161133$ |
$208.72077570277946$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$2900.77019146$ |
| 7.3.106625759296.1 |
$x^{7} - 14 x^{5} - 14 x^{4} - 49 x^{3} - 70 x^{2} - 35 x - 6$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 17^{2}$ |
$3$ |
$37.6191411818$ |
$129.74221654765316$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2280.92270691$ |
| 7.3.106625759296.2 |
$x^{7} - 7 x^{5} - 7 x^{4} + 14 x^{3} + 14 x^{2} + 14 x - 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 17^{2}$ |
$3$ |
$37.6191411818$ |
$129.74221654765316$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2280.92270691$ |
| 7.1.113468578083.2 |
$x^{7} - 7 x^{4} - 21 x^{3} - 63 x^{2} - 35 x - 75$ |
$7$ |
[1,3] |
$-\,3^{9}\cdot 7^{8}$ |
$2$ |
$37.9549081391$ |
$57.80877162075288$ |
|
|
? |
$F_7$ (as 7T4) |
trivial |
$2$ |
$3$ |
$2287.03197439$ |
| 7.3.133189962304.3 |
$x^{7} - 7 x^{5} - 7 x^{4} + 14 x^{3} + 14 x^{2} - 14 x + 6$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 19^{2}$ |
$3$ |
$38.8338289817$ |
$137.16195072190786$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2817.08585099$ |
| 7.3.133189962304.4 |
$x^{7} - 14 x^{5} - 14 x^{4} + 77 x^{3} - 14 x^{2} + 35 x + 18$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 19^{2}$ |
$3$ |
$38.8338289817$ |
$137.16195072190786$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2817.08585099$ |
| 7.3.134481277728.2 |
$x^{7} - 21 x^{4} - 63 x^{3} - 105 x^{2} - 168 x - 72$ |
$7$ |
[3,2] |
$2^{5}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$38.8873932911$ |
$165.2976511693965$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$4$ |
$6744.78426757$ |
| 7.3.195173102656.2 |
$x^{7} - 21 x^{4} + 28 x^{3} - 56 x^{2} + 84 x - 26$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 23^{2}$ |
$3$ |
$41.0125844838$ |
$150.9109560904078$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$7387.66846376$ |
| 7.3.195173102656.3 |
$x^{7} - 7 x^{5} + 7 x^{3} - 14 x^{2} - 14 x - 8$ |
$7$ |
[3,2] |
$2^{6}\cdot 7^{8}\cdot 23^{2}$ |
$3$ |
$41.0125844838$ |
$150.9109560904078$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$7387.66846376$ |
| 7.1.201721916592.2 |
$x^{7} + 21 x^{5} - 42 x^{3} - 126 x^{2} + 126 x + 72$ |
$7$ |
[1,3] |
$-\,2^{4}\cdot 3^{7}\cdot 7^{8}$ |
$3$ |
$41.2064049841$ |
$142.21830795647816$ |
|
|
|
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$19043.3312019$ |
| 7.3.268962555456.6 |
$x^{7} - 14 x^{4} - 63 x^{3} - 42 x^{2} + 42 x + 54$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$42.9351631468$ |
$89.98186380440167$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$13240.5203949$ |
| 7.3.268962555456.9 |
$x^{7} - 28 x^{4} - 84 x^{3} + 420 x^{2} - 420 x + 144$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$42.9351631468$ |
$89.98186380440167$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$13240.5203949$ |
| 7.3.268962555456.11 |
$x^{7} - 28 x^{4} - 84 x^{3} - 168 x^{2} - 28 x + 144$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$42.9351631468$ |
$114.86346945057184$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$5817.28843737$ |
| 7.3.268962555456.13 |
$x^{7} - 7 x^{5} - 28 x^{4} + 49 x^{3} - 56 x^{2} + 294 x - 244$ |
$7$ |
[3,2] |
$2^{6}\cdot 3^{6}\cdot 7^{8}$ |
$3$ |
$42.9351631468$ |
$163.5078977003952$ |
|
|
? |
$A_7$ (as 7T6) |
trivial |
$2$ |
$4$ |
$8748.34383568$ |
| 7.1.270225046875.1 |
$x^{7} - 35 x^{4} + 105 x^{3} - 35 x^{2} - 175 x + 235$ |
$7$ |
[1,3] |
$-\,3\cdot 5^{6}\cdot 7^{8}$ |
$3$ |
$42.9638960614$ |
$76.55783316475387$ |
|
|
? |
$S_7$ (as 7T7) |
trivial |
$2$ |
$3$ |
$2881.68102645$ |
