| 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 |
| 7.3.2007889.1 |
$x^{7} - x^{6} - 3 x^{5} + x^{4} + 4 x^{3} - x^{2} - x + 1$ |
$7$ |
[3,2] |
$13^{2}\cdot 109^{2}$ |
$2$ |
$7.95044405252$ |
$37.64306044943742$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2.21765243914$ |
| 7.3.2007889.2 |
$x^{7} - 2 x^{6} - x^{5} + 4 x^{4} - 3 x^{2} - x + 1$ |
$7$ |
[3,2] |
$13^{2}\cdot 109^{2}$ |
$2$ |
$7.95044405252$ |
$37.64306044943742$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$2.21765243914$ |
| 7.3.6431296.1 |
$x^{7} - 2 x^{6} + 2 x^{4} - 2 x^{3} + 2 x^{2} - 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 317^{2}$ |
$2$ |
$9.38888611504$ |
$32.251902756545775$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$6.93508051031$ |
| 7.3.6431296.2 |
$x^{7} - 3 x^{6} + 3 x^{5} - x^{4} - 5 x^{3} + 5 x^{2} + 3 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 317^{2}$ |
$2$ |
$9.38888611504$ |
$32.251902756545775$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$6.93508051031$ |
| 7.3.7513081.1 |
$x^{7} - x^{6} - 4 x^{5} + x^{4} + 4 x^{3} - 3 x + 1$ |
$7$ |
[3,2] |
$2741^{2}$ |
$1$ |
$9.59974560788$ |
$52.354560450833695$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$6.19684249891$ |
| 7.3.7513081.2 |
$x^{7} - x^{6} + 2 x^{5} - 3 x^{4} - 4 x^{3} + 2 x^{2} + 3 x + 1$ |
$7$ |
[3,2] |
$2741^{2}$ |
$1$ |
$9.59974560788$ |
$52.354560450833695$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$6.19684249891$ |
| 7.3.9388096.1 |
$x^{7} - x^{6} + 2 x^{5} + 2 x^{4} - 5 x^{3} + 7 x^{2} - 5 x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 383^{2}$ |
$2$ |
$9.91020191594$ |
$55.35341001239219$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$9.62702271378$ |
| 7.3.9388096.2 |
$x^{7} - x^{6} - x^{5} - 5 x^{4} + 2 x^{3} + 4 x^{2} + 6 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 383^{2}$ |
$2$ |
$9.91020191594$ |
$55.35341001239219$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$9.62702271378$ |
| 7.3.12559936.1 |
$x^{7} - 3 x^{6} + 3 x^{5} + x^{4} - 3 x^{3} + x^{2} - x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 443^{2}$ |
$2$ |
$10.3309690607$ |
$38.12655571705284$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.5831141711$ |
| 7.3.12559936.2 |
$x^{7} - 3 x^{6} + x^{5} + 3 x^{4} - x^{3} + x^{2} - 3 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 443^{2}$ |
$2$ |
$10.3309690607$ |
$38.12655571705284$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.5831141711$ |
| 7.3.13366336.1 |
$x^{7} - 2 x^{6} + 2 x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} - 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 457^{2}$ |
$2$ |
$10.42321672$ |
$38.72432092086267$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.0103307877$ |
| 7.3.13366336.2 |
$x^{7} - 2 x^{6} - 2 x^{5} + 6 x^{4} - 4 x^{3} - 2 x^{2} + 4 x - 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 457^{2}$ |
$2$ |
$10.42321672$ |
$38.72432092086267$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.0103307877$ |
| 7.3.14462809.1 |
$x^{7} - 3 x^{6} + 3 x^{5} + 3 x^{4} - 13 x^{3} + 17 x^{2} - 10 x + 1$ |
$7$ |
[3,2] |
$3803^{2}$ |
$1$ |
$10.5412772454$ |
$61.66846844214635$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$7.61729812148$ |
| 7.3.14462809.2 |
$x^{7} - 2 x^{5} - 4 x^{4} - x^{3} + 5 x^{2} + 5 x + 1$ |
$7$ |
[3,2] |
$3803^{2}$ |
$1$ |
$10.5412772454$ |
$61.66846844214635$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$7.61729812148$ |
| 7.3.15429184.1 |
$x^{7} - 3 x^{6} + 7 x^{5} - 5 x^{4} + x^{3} + 7 x^{2} - 3 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 491^{2}$ |
$2$ |
$10.6391305219$ |
$49.74419505825309$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$18.7523072477$ |
| 7.3.15429184.2 |
$x^{7} - 3 x^{6} - x^{5} + 9 x^{4} - 12 x^{2} + 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 491^{2}$ |
$2$ |
$10.6391305219$ |
$49.74419505825309$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$18.7523072477$ |
| 7.3.15864289.1 |
$x^{7} - x^{6} + x^{5} - 4 x^{4} + 4 x^{3} - 5 x^{2} + 2 x + 1$ |
$7$ |
[3,2] |
$7^{2}\cdot 569^{2}$ |
$2$ |
$10.6814820774$ |
$63.111013301958636$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$8.28712673096$ |
| 7.3.15864289.2 |
$x^{7} - x^{6} - 3 x^{5} - x^{4} + 2 x^{3} + 4 x^{2} + 4 x + 1$ |
$7$ |
[3,2] |
$7^{2}\cdot 569^{2}$ |
$2$ |
$10.6814820774$ |
$63.111013301958636$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$8.28712673096$ |
| 7.3.17280649.1 |
$x^{7} - x^{6} - 4 x^{5} + x^{4} + 8 x^{3} + x^{2} - 4 x - 1$ |
$7$ |
[3,2] |
$4157^{2}$ |
$1$ |
$10.8127745988$ |
$64.47480127925948$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$6.78801046429$ |
| 7.3.17280649.2 |
$x^{7} - 2 x^{6} + 4 x^{4} - 3 x^{3} - 4 x^{2} + 2 x + 1$ |
$7$ |
[3,2] |
$4157^{2}$ |
$1$ |
$10.8127745988$ |
$64.47480127925948$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$6.78801046429$ |
| 7.3.17372224.1 |
$x^{7} - 2 x^{5} - 4 x^{4} - 2 x^{3} - 2 x^{2} + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 521^{2}$ |
$2$ |
$10.820941772$ |
$41.347054089982244$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$13.5280236844$ |
| 7.3.17372224.2 |
$x^{7} - 3 x^{6} + 5 x^{5} - 7 x^{4} + 5 x^{3} - 3 x^{2} - x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 521^{2}$ |
$2$ |
$10.820941772$ |
$41.347054089982244$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$13.5280236844$ |
| 7.3.19456921.1 |
$x^{7} - 3 x^{6} + 5 x^{4} - 2 x^{3} - 2 x^{2} + 4 x - 1$ |
$7$ |
[3,2] |
$11^{2}\cdot 401^{2}$ |
$2$ |
$10.9975590418$ |
$66.41535966928132$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$15.4322144182$ |
| 7.3.19456921.2 |
$x^{7} - 5 x^{5} - 4 x^{4} + 3 x^{3} + 3 x^{2} + 2 x + 4$ |
$7$ |
[3,2] |
$11^{2}\cdot 401^{2}$ |
$2$ |
$10.9975590418$ |
$66.41535966928132$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$15.4322144182$ |
| 7.3.23785129.1 |
$x^{7} - 3 x^{6} + 5 x^{5} - 3 x^{4} + 2 x^{2} - 5 x + 1$ |
$7$ |
[3,2] |
$4877^{2}$ |
$1$ |
$11.3176935457$ |
$69.83552104767315$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$16.0818297281$ |
| 7.3.23785129.2 |
$x^{7} - 4 x^{5} - 6 x^{4} + 3 x^{3} + 12 x^{2} + 9 x + 4$ |
$7$ |
[3,2] |
$4877^{2}$ |
$1$ |
$11.3176935457$ |
$69.83552104767315$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$16.0818297281$ |
| 7.3.25806400.1 |
$x^{7} - 3 x^{6} + x^{5} + 7 x^{4} - 9 x^{3} - x^{2} + 7 x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 5^{2}\cdot 127^{2}$ |
$3$ |
$11.4503352791$ |
$45.6470349996514$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$17.8803848057$ |
| 7.3.25806400.2 |
$x^{7} - x^{6} - 3 x^{5} + 7 x^{4} - 7 x^{3} - x^{2} + 3 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 5^{2}\cdot 127^{2}$ |
$3$ |
$11.4503352791$ |
$45.6470349996514$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$17.8803848057$ |
| 7.3.27290176.1 |
$x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{3} + 5 x^{2} + 3 x - 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 653^{2}$ |
$2$ |
$11.5421474877$ |
$72.27724399837061$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$19.1946803596$ |
| 7.3.27290176.2 |
$x^{7} - 2 x^{6} + x^{5} - 3 x^{4} + 2 x^{3} + 6 x^{2} - 6 x + 2$ |
$7$ |
[3,2] |
$2^{6}\cdot 653^{2}$ |
$2$ |
$11.5421474877$ |
$72.27724399837061$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$19.1946803596$ |
| 7.3.27962944.1 |
$x^{7} - 2 x^{6} - 2 x^{5} + 4 x^{4} + 8 x^{2} - 12 x + 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 661^{2}$ |
$2$ |
$11.5823732466$ |
$46.57216637954686$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$21.5365674329$ |
| 7.3.27962944.2 |
$x^{7} - x^{6} + x^{5} + 3 x^{4} - 5 x^{3} + 7 x^{2} - 5 x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 661^{2}$ |
$2$ |
$11.5823732466$ |
$46.57216637954686$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$21.5365674329$ |
| 7.3.28291761.1 |
$x^{7} - 6 x^{5} - 6 x^{4} + 3 x^{3} + 6 x^{2} + 2 x - 3$ |
$7$ |
[3,2] |
$3^{6}\cdot 197^{2}$ |
$2$ |
$11.6017326767$ |
$50.567860229151826$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$20.6177124051$ |
| 7.3.28291761.2 |
$x^{7} - 2 x^{6} + 3 x^{5} - 6 x^{4} + 3 x^{3} - 6 x^{2} + 5 x - 1$ |
$7$ |
[3,2] |
$3^{6}\cdot 197^{2}$ |
$2$ |
$11.6017326767$ |
$50.567860229151826$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$20.6177124051$ |
| 7.3.28912129.1 |
$x^{7} + x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 2 x - 1$ |
$7$ |
[3,2] |
$19^{2}\cdot 283^{2}$ |
$2$ |
$11.6377381645$ |
$73.32803011127464$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.3445591408$ |
| 7.3.28912129.2 |
$x^{7} - x^{5} - 5 x^{4} - 7 x^{3} - 5 x^{2} - 3 x + 1$ |
$7$ |
[3,2] |
$19^{2}\cdot 283^{2}$ |
$2$ |
$11.6377381645$ |
$73.32803011127464$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.3445591408$ |
| 7.3.30063289.1 |
$x^{7} - 2 x^{6} - x^{5} + 9 x^{4} - 11 x^{3} + 4 x^{2} + 3 x - 2$ |
$7$ |
[3,2] |
$5483^{2}$ |
$1$ |
$11.7028308368$ |
$74.04728219185361$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$19.9691007387$ |
| 7.3.30063289.2 |
$x^{7} - x^{6} - 4 x^{5} + 3 x^{4} + 8 x^{3} - 6 x + 1$ |
$7$ |
[3,2] |
$5483^{2}$ |
$1$ |
$11.7028308368$ |
$74.04728219185361$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$19.9691007387$ |
| 7.3.30558784.1 |
$x^{7} - 3 x^{6} + 4 x^{5} - 5 x^{4} + 3 x^{3} - x^{2} - 2 x + 1$ |
$7$ |
[3,2] |
$2^{6}\cdot 691^{2}$ |
$2$ |
$11.7301928633$ |
$74.35052118176442$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$18.3119129313$ |
| 7.3.30558784.2 |
$x^{7} - x^{5} - 2 x^{4} - 2 x^{3} + 2 x^{2} - x + 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 691^{2}$ |
$2$ |
$11.7301928633$ |
$74.35052118176442$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$18.3119129313$ |
| 7.3.32684089.1 |
$x^{7} - x^{6} - 2 x^{5} + 4 x^{4} - x^{3} - 2 x^{2} - x + 1$ |
$7$ |
[3,2] |
$5717^{2}$ |
$1$ |
$11.8434062428$ |
$75.61084578286372$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.777791792$ |
| 7.3.32684089.2 |
$x^{7} - x^{6} - x^{5} - 2 x^{4} - 7 x^{3} - x^{2} + 3 x + 1$ |
$7$ |
[3,2] |
$5717^{2}$ |
$1$ |
$11.8434062428$ |
$75.61084578286372$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$11.777791792$ |
| 7.3.32913169.1 |
$x^{7} - x^{6} - 2 x^{4} - 9 x^{3} + 2 x^{2} - 3 x - 1$ |
$7$ |
[3,2] |
$5737^{2}$ |
$1$ |
$11.8552292654$ |
$75.7429864739964$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$13.6434515247$ |
| 7.3.32913169.2 |
$x^{7} - 2 x^{6} + 3 x^{5} - 4 x^{3} + 5 x^{2} - x - 1$ |
$7$ |
[3,2] |
$5737^{2}$ |
$1$ |
$11.8552292654$ |
$75.7429864739964$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$13.6434515247$ |
| 7.3.35331136.1 |
$x^{7} - 2 x^{6} - 3 x^{5} + 4 x^{4} + 5 x^{3} - 3 x - 4$ |
$7$ |
[3,2] |
$2^{6}\cdot 743^{2}$ |
$2$ |
$11.9759018707$ |
$61.19220015890557$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$30.7244086365$ |
| 7.3.35331136.2 |
$x^{7} - x^{6} + x^{5} + 5 x^{4} - 6 x^{3} + 4 x^{2} + 8 x - 8$ |
$7$ |
[3,2] |
$2^{6}\cdot 743^{2}$ |
$2$ |
$11.9759018707$ |
$61.19220015890557$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$30.7244086365$ |
| 7.3.36445369.1 |
$x^{7} - x^{6} + 4 x^{5} - x^{4} + 4 x^{3} - 4 x^{2} - x + 1$ |
$7$ |
[3,2] |
$6037^{2}$ |
$1$ |
$12.0291411706$ |
$77.69813382572325$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$14.4640725247$ |
| 7.3.36445369.2 |
$x^{7} - x^{6} - 2 x^{5} - x^{4} + 6 x^{2} + 5 x + 1$ |
$7$ |
[3,2] |
$6037^{2}$ |
$1$ |
$12.0291411706$ |
$77.69813382572325$ |
|
|
✓ |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$14.4640725247$ |
| 7.3.37884025.1 |
$x^{7} - 3 x^{5} - 6 x^{4} + x^{3} + 6 x^{2} + 7 x + 1$ |
$7$ |
[3,2] |
$5^{2}\cdot 1231^{2}$ |
$2$ |
$12.0958554384$ |
$78.45380806563821$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$16.4245593853$ |
| 7.3.37884025.2 |
$x^{7} - 3 x^{6} + 5 x^{5} - 3 x^{4} - 8 x^{3} + 18 x^{2} - 22 x + 13$ |
$7$ |
[3,2] |
$5^{2}\cdot 1231^{2}$ |
$2$ |
$12.0958554384$ |
$78.45380806563821$ |
|
|
? |
$\GL(3,2)$ (as 7T5) |
trivial |
$2$ |
$4$ |
$16.4245593853$ |
