| 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 |
| 6.2.31213.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 13$ |
$2$ |
$5.6112021989$ |
$13.193814370085985$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$0.517040346258$ |
| 6.2.69629.1 |
$x^{6} - 2 x^{5} + x^{4} + 3 x^{3} - 4 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 29$ |
$2$ |
$6.41404042819$ |
$19.705964328162043$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$0.91219234994$ |
| 6.2.98441.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + x^{2} + x - 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 41$ |
$2$ |
$6.79510235307$ |
$23.430989084024507$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$1.11979910776$ |
| 6.4.103243.1 |
$x^{6} - x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x - 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 43$ |
$2$ |
$6.84925658504$ |
$23.99567223510292$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$1.35989705552$ |
| 6.2.111537.1 |
$x^{6} - 3 x^{5} + 3 x^{4} + x^{3} - 3 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$3^{8}\cdot 17$ |
$2$ |
$6.93803510882$ |
$17.839641950637386$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$1.21307108981$ |
| 6.4.124659.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 3 x^{2} + 3 x - 1$ |
$6$ |
[4,1] |
$-\,3^{8}\cdot 19$ |
$2$ |
$7.06784917257$ |
$18.859860385004858$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$1.54949123381$ |
| 6.2.142805.1 |
$x^{6} - 2 x^{5} + x^{3} - 2 x + 1$ |
$6$ |
[2,2] |
$5\cdot 13^{4}$ |
$2$ |
$7.22976035991$ |
$12.362716315674692$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$1.65144736754$ |
| 6.4.153664.1 |
$x^{6} - x^{4} - 2 x^{2} + 1$ |
$6$ |
[4,1] |
$-\,2^{6}\cdot 7^{4}$ |
$2$ |
$7.31861142005$ |
$12.308388215503062$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$1.79006336385$ |
| 6.4.170471.1 |
$x^{6} - 3 x^{5} + x^{4} + 3 x^{3} - 3 x^{2} + x + 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 71$ |
$2$ |
$7.44632095503$ |
$30.833857978493015$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$1.93594594089$ |
| 6.4.199283.1 |
$x^{6} - 2 x^{5} + x^{4} - 4 x^{3} + 3 x^{2} + 3 x - 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 83$ |
$2$ |
$7.6426688442$ |
$33.33786161694775$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$2.17772456899$ |
| 6.4.218491.1 |
$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + 2 x + 1$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 13$ |
$2$ |
$7.76078392578$ |
$18.248200448594663$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$2.26526479968$ |
| 6.2.232897.1 |
$x^{6} - 3 x^{5} + 7 x^{4} - 9 x^{3} + 7 x^{2} - 3 x - 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 97$ |
$2$ |
$7.84381452391$ |
$36.039981591316774$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$1.86153378443$ |
| 6.2.242757.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - 3 x - 1$ |
$6$ |
[2,2] |
$3^{8}\cdot 37$ |
$2$ |
$7.89820909548$ |
$26.318584936813835$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$2.80685792821$ |
| 6.2.271313.1 |
$x^{6} - x^{5} + 2 x^{4} + 3 x^{3} - 2 x^{2} + 6 x - 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 113$ |
$2$ |
$8.04597046288$ |
$38.898953270916685$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$2.2078591254$ |
| 6.4.304927.1 |
$x^{6} - 2 x^{5} + 2 x^{3} - 7 x^{2} + 6 x - 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 127$ |
$2$ |
$8.2041321421$ |
$41.23828102000196$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$2.80736740928$ |
| 6.4.333739.1 |
$x^{6} - x^{5} - 4 x^{4} - 2 x^{2} - 2 x + 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 139$ |
$2$ |
$8.32851987979$ |
$43.14257805043105$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$3.03235730888$ |
| 6.4.334611.1 |
$x^{6} - 3 x^{4} - 5 x^{3} + 3 x + 1$ |
$6$ |
[4,1] |
$-\,3^{9}\cdot 17$ |
$2$ |
$8.33214275848$ |
$21.42428528562855$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$3.48815660412$ |
| 6.2.347733.1 |
$x^{6} - 3 x^{5} + 6 x^{4} - 7 x^{3} + 3 x^{2} - 1$ |
$6$ |
[2,2] |
$3^{8}\cdot 53$ |
$2$ |
$8.38573211408$ |
$31.499206078816627$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$2.17658370696$ |
| 6.2.373977.1 |
$x^{6} - 3 x^{5} + 3 x^{4} + 3 x^{3} - 9 x^{2} + 9 x - 3$ |
$6$ |
[2,2] |
$3^{9}\cdot 19$ |
$2$ |
$8.48804126495$ |
$22.64950330581225$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.07919997975$ |
| 6.0.400967.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 7 x^{3} + 10 x^{2} - 8 x + 8$ |
$6$ |
[0,3] |
$-\,7^{4}\cdot 167$ |
$2$ |
$8.5871972435$ |
$47.28865141512203$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.419904.1 |
$x^{6} - 3 x^{2} + 1$ |
$6$ |
[4,1] |
$-\,2^{6}\cdot 3^{8}$ |
$2$ |
$8.65349742184$ |
$14.553389922872519$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$3.36087216518$ |
| 6.6.434581.1 |
$x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1$ |
$6$ |
[6,0] |
$7^{4}\cdot 181$ |
$2$ |
$8.70318982123$ |
$49.23092329595919$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$4.18794361412$ |
| 6.0.465831.1 |
$x^{6} - 3 x^{5} + 9 x^{4} - 13 x^{3} + 15 x^{2} - 9 x + 3$ |
$6$ |
[0,3] |
$-\,3^{8}\cdot 71$ |
$2$ |
$8.80450067483$ |
$36.45783266912841$ |
✓ |
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$2$ |
$3.39714980258$ |
| 6.2.472997.1 |
$x^{6} - x^{5} + 2 x^{4} - 4 x^{3} - 2 x^{2} - 8 x - 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 197$ |
$2$ |
$8.82693098597$ |
$51.36080315808082$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$2.8515360014$ |
| 6.2.478953.1 |
$x^{6} - 2 x^{3} + 3 x^{2} - 3$ |
$6$ |
[2,2] |
$3^{8}\cdot 73$ |
$2$ |
$8.84535938676$ |
$36.967757191167294$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$4.47997610813$ |
| 6.4.487403.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 6 x^{3} - 5 x^{2} + 3 x + 1$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 29$ |
$2$ |
$8.87117948881$ |
$27.255074007139722$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$3.69839946438$ |
| 6.4.506611.1 |
$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 6 x^{2} + 3 x + 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 211$ |
$2$ |
$8.92851232694$ |
$53.154485765124456$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$3.66672738576$ |
| 6.4.535423.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 3 x^{2} + 6 x + 1$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 223$ |
$2$ |
$9.01120432398$ |
$54.645087394089686$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$4.23647185387$ |
| 6.0.573839.1 |
$x^{6} - x^{5} + 4 x^{4} - 3 x^{3} + 8 x^{2} - 4 x + 8$ |
$6$ |
[0,3] |
$-\,7^{4}\cdot 239$ |
$2$ |
$9.11587462525$ |
$56.571493428918835$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.583929.1 |
$x^{6} - 5 x^{3} - 3 x - 1$ |
$6$ |
[2,2] |
$3^{8}\cdot 89$ |
$2$ |
$9.14239555184$ |
$40.818465701990505$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.11318797866$ |
| 6.0.602651.1 |
$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 21 x^{2} - 14 x + 7$ |
$6$ |
[0,3] |
$-\,7^{4}\cdot 251$ |
$2$ |
$9.19060949664$ |
$57.97430541309734$ |
✓ |
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.674681.1 |
$x^{6} - 2 x^{5} + x^{4} + 3 x^{3} - 4 x^{2} - 4 x - 8$ |
$6$ |
[2,2] |
$7^{4}\cdot 281$ |
$2$ |
$9.3651861315$ |
$61.34114146731612$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.86646287532$ |
| 6.4.689087.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 13 x^{3} - 12 x^{2} - 4 x + 8$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 41$ |
$2$ |
$9.39822149451$ |
$32.407109386315106$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$4.78391581904$ |
| 6.4.702027.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - 9 x^{2} + 6 x - 1$ |
$6$ |
[4,1] |
$-\,3^{8}\cdot 107$ |
$2$ |
$9.42740799261$ |
$44.75623667824389$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$6.7913976674$ |
| 6.6.703493.1 |
$x^{6} - 2 x^{5} - 5 x^{4} + 11 x^{3} + 2 x^{2} - 9 x + 1$ |
$6$ |
[6,0] |
$7^{4}\cdot 293$ |
$2$ |
$9.4306862545$ |
$62.637224203074084$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$5.70730462791$ |
| 6.2.715149.1 |
$x^{6} - 2 x^{3} - 6 x^{2} - 9 x - 3$ |
$6$ |
[2,2] |
$3^{8}\cdot 109$ |
$2$ |
$9.45655071392$ |
$45.17258272906164$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$5.38613194077$ |
| 6.2.722701.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 8 x^{3} + 2 x^{2} - 11 x + 1$ |
$6$ |
[2,2] |
$7^{5}\cdot 43$ |
$2$ |
$9.47312153875$ |
$33.18811562467677$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.31543456345$ |
| 6.4.728271.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} - 3 x^{2} + 3 x + 1$ |
$6$ |
[4,1] |
$-\,3^{9}\cdot 37$ |
$2$ |
$9.48525118246$ |
$31.606961258558215$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$5.91431201806$ |
| 6.4.737107.1 |
$x^{6} - 2 x^{5} - x^{4} + 8 x^{3} - 7 x^{2} - 7 x + 7$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 307$ |
$2$ |
$9.50433544657$ |
$64.1162156695002$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$4.95319808061$ |
| 6.2.809137.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - x^{3} - 7 x^{2} + 7 x - 7$ |
$6$ |
[2,2] |
$7^{4}\cdot 337$ |
$2$ |
$9.6531786455$ |
$67.17592321777249$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$4.14038097011$ |
| 6.4.833247.1 |
$x^{6} - 3 x^{4} - 2 x^{3} - 6 x^{2} - 6 x - 1$ |
$6$ |
[4,1] |
$-\,3^{8}\cdot 127$ |
$2$ |
$9.70053364845$ |
$48.75998164220662$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$5.17267609621$ |
| 6.2.837949.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 9 x^{3} + 4 x^{2} - 9 x - 1$ |
$6$ |
[2,2] |
$7^{4}\cdot 349$ |
$2$ |
$9.70963559799$ |
$68.36147218655364$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.26724753988$ |
| 6.4.842751.1 |
$x^{6} - 2 x^{5} - 4 x^{4} + 12 x^{3} - 3 x^{2} - 16 x + 13$ |
$6$ |
[4,1] |
$-\,3^{3}\cdot 7^{4}\cdot 13$ |
$3$ |
$9.71888730004$ |
$22.852356834621286$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$5.14793885149$ |
| 6.4.885391.1 |
$x^{6} - x^{5} - 3 x^{4} + 7 x^{3} - x^{2} - 3 x + 1$ |
$6$ |
[4,1] |
$-\,13^{4}\cdot 31$ |
$2$ |
$9.79916755847$ |
$30.78291537771342$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$6.29028885334$ |
| 6.2.905177.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{3} + 2 x^{2} + 5 x - 13$ |
$6$ |
[2,2] |
$7^{4}\cdot 13\cdot 29$ |
$3$ |
$9.83532959706$ |
$71.05086481765254$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.99839895103$ |
| 6.6.905177.1 |
$x^{6} - x^{5} - 7 x^{4} + 9 x^{3} + 7 x^{2} - 9 x - 1$ |
$6$ |
[6,0] |
$7^{4}\cdot 13\cdot 29$ |
$3$ |
$9.83532959706$ |
$71.05086481765254$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$6.90930178248$ |
| 6.2.905177.2 |
$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} - 6 x^{2} + 8 x - 8$ |
$6$ |
[2,2] |
$7^{4}\cdot 13\cdot 29$ |
$3$ |
$9.83532959706$ |
$71.05086481765254$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$3.81198034409$ |
| 6.0.909979.1 |
$x^{6} - 2 x^{5} + 7 x^{4} - 12 x^{3} + 21 x^{2} - 15 x + 13$ |
$6$ |
[0,3] |
$-\,7^{4}\cdot 379$ |
$2$ |
$9.84400657273$ |
$71.23907935884031$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.912247.1 |
$x^{6} - x^{5} - 3 x^{4} + 5 x^{3} - 3 x^{2} - x + 1$ |
$6$ |
[4,1] |
$-\,7\cdot 19^{4}$ |
$2$ |
$9.84809147592$ |
$18.838721275076466$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$5.71881021969$ |
| 6.4.1006019.1 |
$x^{6} - x^{5} - 2 x^{4} + 8 x^{3} - 7 x^{2} - 7 x + 7$ |
$6$ |
[4,1] |
$-\,7^{4}\cdot 419$ |
$2$ |
$10.0100066002$ |
$74.9041197736908$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$5.78403530293$ |
