| 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 |
| 6.0.10051.1 |
$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,19\cdot 23^{2}$ |
$2$ |
$4.64552582629$ |
$20.904544960366874$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.205216461048$ |
| 6.0.10571.1 |
$x^{6} - x^{5} - x^{4} + 2 x^{3} - x + 1$ |
$6$ |
[0,3] |
$-\,11\cdot 31^{2}$ |
$2$ |
$4.68474560175$ |
$18.466185312619388$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.21320935989$ |
| 6.0.18515.1 |
$x^{6} + 2 x^{4} - x^{3} + 2 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 7\cdot 23^{2}$ |
$3$ |
$5.14344325363$ |
$28.372521918222215$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.328780614749$ |
| 6.0.22747.1 |
$x^{6} - x^{5} - 2 x^{3} + x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 43$ |
$2$ |
$5.32297003373$ |
$31.448370387032774$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.388951542699$ |
| 6.0.27556.1 |
$x^{6} - x^{5} + 2 x^{3} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 83^{2}$ |
$2$ |
$5.4958646601$ |
$18.2208671582886$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.594769419961$ |
| 6.0.27848.1 |
$x^{6} - x^{5} + 2 x^{4} + 2 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{3}\cdot 59^{2}$ |
$2$ |
$5.5055283296$ |
$21.72556098240043$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.599228830431$ |
| 6.2.28037.1 |
$x^{6} - 2 x^{5} + 3 x^{3} - 2 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 53$ |
$2$ |
$5.51173831771$ |
$34.91418050019218$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.478924705547$ |
| 6.0.29095.1 |
$x^{6} - x^{5} + 3 x^{4} - x^{3} + 3 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 11\cdot 23^{2}$ |
$3$ |
$5.54587053377$ |
$35.566838487557476$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.446620658377$ |
| 6.0.31211.1 |
$x^{6} - x^{4} - x^{3} + 2 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 59$ |
$2$ |
$5.61114227353$ |
$36.837480912787726$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.482550424804$ |
| 6.2.32269.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 61$ |
$2$ |
$5.64240494139$ |
$37.456641600656084$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.529910039105$ |
| 6.0.33856.1 |
$x^{6} - x^{4} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{2}$ |
$2$ |
$5.6877339597$ |
$16.131190144457708$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.480272990261$ |
| 6.2.35557.1 |
$x^{6} - 2 x^{4} - x^{3} + 2 x^{2} - 1$ |
$6$ |
[2,2] |
$31^{2}\cdot 37$ |
$2$ |
$5.73439385986$ |
$33.8673884437522$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.567960387605$ |
| 6.0.37479.1 |
$x^{6} - x^{5} + 3 x^{4} - 3 x^{3} + 3 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,3\cdot 13\cdot 31^{2}$ |
$3$ |
$5.78492854723$ |
$34.77067730142742$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.594386436128$ |
| 6.2.40733.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 3 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$7\cdot 11\cdot 23^{2}$ |
$3$ |
$5.86576148388$ |
$42.08325082500163$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.628987885726$ |
| 6.0.41791.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} - x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 79$ |
$2$ |
$5.89088385918$ |
$42.62628297189423$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.551815988703$ |
| 6.2.44965.1 |
$x^{6} - 2 x^{4} - 3 x - 1$ |
$6$ |
[2,2] |
$5\cdot 17\cdot 23^{2}$ |
$3$ |
$5.96319621326$ |
$44.21538193886829$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.690763980612$ |
| 6.0.45167.1 |
$x^{6} - x^{5} + x^{4} - x^{3} + 3 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,31^{2}\cdot 47$ |
$2$ |
$5.9676527056$ |
$38.17066936798463$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.562471666434$ |
| 6.2.47081.1 |
$x^{6} - x^{5} - 3 x^{4} + 3 x^{3} + 3 x^{2} - x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 89$ |
$2$ |
$6.00907484204$ |
$45.24378410345447$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.694306844279$ |
| 6.0.49011.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 3 x^{3} + 4 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3\cdot 17\cdot 31^{2}$ |
$3$ |
$6.0494458549$ |
$39.761790704142086$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.70402948966$ |
| 6.2.50933.1 |
$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 3 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$31^{2}\cdot 53$ |
$2$ |
$6.08835372223$ |
$40.53393639902249$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.730388860061$ |
| 6.2.53429.1 |
$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} + x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 101$ |
$2$ |
$6.13709492811$ |
$48.19751030914356$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.765009894688$ |
| 6.0.54208.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 3 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7\cdot 11^{2}$ |
$3$ |
$6.15191836841$ |
$19.699129000227927$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.956984205134$ |
| 6.0.55696.1 |
$x^{6} + 2 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 59^{2}$ |
$2$ |
$6.17974660587$ |
$21.72556098240043$ |
|
|
|
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.759839555864$ |
| 6.2.56144.1 |
$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 3 x + 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 11^{2}\cdot 29$ |
$3$ |
$6.18800361127$ |
$28.351889352086026$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.832028349165$ |
| 6.0.56603.1 |
$x^{6} - 2 x^{5} + 3 x^{4} + x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 107$ |
$2$ |
$6.19640660621$ |
$49.60846701924985$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.735797593925$ |
| 6.2.57661.1 |
$x^{6} - x^{5} + 4 x^{3} - 3 x^{2} + x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 109$ |
$2$ |
$6.21556141005$ |
$50.06995106848019$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.804738209577$ |
| 6.2.59177.1 |
$x^{6} - x^{4} - x^{3} + x^{2} - 1$ |
$6$ |
[2,2] |
$17\cdot 59^{2}$ |
$2$ |
$6.24250392532$ |
$31.670175244226233$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.862058499217$ |
| 6.0.60835.1 |
$x^{6} - x^{5} + 4 x^{4} + 3 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,5\cdot 23^{3}$ |
$2$ |
$6.27131938061$ |
$23.48447625945622$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.725411195117$ |
| 6.0.61504.1 |
$x^{6} + x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 31^{2}$ |
$2$ |
$6.28276130478$ |
$18.727652374724588$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.966786014018$ |
| 6.0.62951.1 |
$x^{6} - x^{5} + 2 x^{4} - x^{3} + 4 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,7\cdot 17\cdot 23^{2}$ |
$3$ |
$6.30715889518$ |
$52.316345438113316$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.6933695847$ |
| 6.0.64387.1 |
$x^{6} - 2 x^{5} - 2 x^{3} + 4 x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,31^{2}\cdot 67$ |
$2$ |
$6.33091328593$ |
$45.574115460423364$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.98574296608$ |
| 6.0.64387.2 |
$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + x^{2} + 1$ |
$6$ |
[0,3] |
$-\,31^{2}\cdot 67$ |
$2$ |
$6.33091328593$ |
$45.574115460423364$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.682828118648$ |
| 6.0.64387.3 |
$x^{6} - 2 x^{5} + 4 x^{4} - 6 x^{3} + 6 x^{2} - 5 x + 3$ |
$6$ |
[0,3] |
$-\,31^{2}\cdot 67$ |
$2$ |
$6.33091328593$ |
$45.574115460423364$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.98999267824$ |
| 6.2.66309.1 |
$x^{6} + x^{4} - x^{3} - 2 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$3\cdot 23\cdot 31^{2}$ |
$3$ |
$6.36202561092$ |
$46.24932431938871$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.00714192637$ |
| 6.0.69312.1 |
$x^{6} + x^{4} - 2 x^{3} + x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3\cdot 19^{2}$ |
$3$ |
$6.40916430241$ |
$16.948805249221287$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$1.30201062094$ |
| 6.2.70153.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + 3 x^{2} - x - 1$ |
$6$ |
[2,2] |
$31^{2}\cdot 73$ |
$2$ |
$6.42206023448$ |
$47.57099956906519$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.907852321232$ |
| 6.2.72473.1 |
$x^{6} - 2 x^{5} - 2 x^{3} + 5 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 137$ |
$2$ |
$6.45697898876$ |
$56.133768802744754$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$0.925119739279$ |
| 6.2.75088.1 |
$x^{6} - x^{5} + x^{3} - x - 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 13\cdot 19^{2}$ |
$3$ |
$6.495238303$ |
$24.947965821847426$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.01738805374$ |
| 6.2.78821.1 |
$x^{6} - x^{5} + 2 x^{4} - 4 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 149$ |
$2$ |
$6.54797466011$ |
$58.540584213005594$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.0562023024$ |
| 6.0.79763.1 |
$x^{6} - x^{5} - 2 x^{4} + 4 x^{3} - 4 x + 3$ |
$6$ |
[0,3] |
$-\,31^{2}\cdot 83$ |
$2$ |
$6.56095279879$ |
$50.724747411889595$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$1.15043495705$ |
| 6.0.80143.1 |
$x^{6} - 2 x^{5} + x^{4} + x^{3} + x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,7\cdot 107^{2}$ |
$2$ |
$6.56615200849$ |
$27.367864366808018$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.997137782636$ |
| 6.2.83053.1 |
$x^{6} - 2 x^{5} - x^{4} + x^{3} + 4 x^{2} + x - 5$ |
$6$ |
[2,2] |
$23^{2}\cdot 157$ |
$2$ |
$6.60530010429$ |
$60.091596750294464$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.09315347136$ |
| 6.0.83248.1 |
$x^{6} - x^{5} + x^{3} + 2 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{2}\cdot 43$ |
$3$ |
$6.60788234144$ |
$34.52369205633357$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.9213154377$ |
| 6.0.83607.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 3 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3\cdot 29\cdot 31^{2}$ |
$3$ |
$6.61262315292$ |
$51.93264869039514$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.992474020399$ |
| 6.2.85169.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 6 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$7\cdot 23^{3}$ |
$2$ |
$6.63305489226$ |
$27.787207043050365$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.04071919564$ |
| 6.0.88343.1 |
$x^{6} - 2 x^{5} + 4 x^{3} - 3 x^{2} - 4 x + 5$ |
$6$ |
[0,3] |
$-\,23^{2}\cdot 167$ |
$2$ |
$6.67362844907$ |
$61.97580172938467$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$0.949693349042$ |
| 6.2.89373.1 |
$x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 3 x^{2} - 5 x + 1$ |
$6$ |
[2,2] |
$3\cdot 31^{3}$ |
$2$ |
$6.68653398103$ |
$22.755265011491122$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.23553129297$ |
| 6.0.90992.1 |
$x^{6} - x^{5} + x^{4} + x^{3} + 2$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{2}\cdot 47$ |
$3$ |
$6.70657113107$ |
$36.0937441337318$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$2$ |
$1.96673851282$ |
| 6.2.91517.1 |
$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - x^{2} - 5 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 173$ |
$2$ |
$6.71300487433$ |
$63.079315151640635$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.16462402103$ |
| 6.2.91592.1 |
$x^{6} - x^{5} - x - 1$ |
$6$ |
[2,2] |
$2^{3}\cdot 107^{2}$ |
$2$ |
$6.71392146821$ |
$29.257477676655586$ |
|
|
✓ |
$S_4\times C_2$ (as 6T11) |
trivial |
$2$ |
$3$ |
$1.57248453398$ |
