| 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 |
| 6.0.16807.1 |
$x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,7^{5}$ |
$1$ |
$5.0611401848$ |
$5.061140184796386$ |
✓ |
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$14$ |
$2$ |
$2.10181872849$ |
| 6.6.453789.1 |
$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} + 8 x^{2} - 8 x + 1$ |
$6$ |
[6,0] |
$3^{3}\cdot 7^{5}$ |
$2$ |
$8.7661519443$ |
$8.766151944295878$ |
|
✓ |
✓ |
$C_6$ (as 6T1) |
trivial |
$2$ |
$5$ |
$4.39996237517$ |
| 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 |
$2$ |
$4$ |
$3.69839946438$ |
| 6.4.1075648.1 |
$x^{6} - 7 x^{2} + 7$ |
$6$ |
[4,1] |
$-\,2^{6}\cdot 7^{5}$ |
$2$ |
$10.1222803696$ |
$14.315066180821045$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$6.08029800965$ |
| 6.2.1394981.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - x^{3} + 2 x^{2} - 4 x - 13$ |
$6$ |
[2,2] |
$7^{5}\cdot 83$ |
$2$ |
$10.5704801598$ |
$46.10918148832558$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$4.89094715278$ |
| 6.4.1899191.1 |
$x^{6} - x^{5} - 6 x^{4} - x^{3} - 6 x^{2} - 8 x + 8$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 113$ |
$2$ |
$11.1282816092$ |
$53.800658143076376$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$8.8734657542$ |
| 6.2.2336173.1 |
$x^{6} - x^{5} + x^{4} - 8 x^{3} - 6 x^{2} - 15 x - 13$ |
$6$ |
[2,2] |
$7^{5}\cdot 139$ |
$2$ |
$11.5190721912$ |
$59.66996276060805$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$5.9718100677$ |
| 6.6.2806769.1 |
$x^{6} - 3 x^{5} - 5 x^{4} + 15 x^{3} + 11 x^{2} - 19 x - 13$ |
$6$ |
[6,0] |
$7^{5}\cdot 167$ |
$2$ |
$11.8768456335$ |
$65.40434523039623$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$14.4402840644$ |
| 6.4.2840383.1 |
$x^{6} - 2 x^{5} - 3 x^{4} - x^{3} + 2 x^{2} + 24 x + 8$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 13^{2}$ |
$2$ |
$11.9004344759$ |
$18.248200448594663$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$11.120808723$ |
| 6.4.3310979.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 13 x^{3} - 12 x^{2} - 25 x + 29$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 197$ |
$2$ |
$12.2084183891$ |
$71.03648762517525$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$10.0802875363$ |
| 6.2.3747961.1 |
$x^{6} - x^{5} + x^{4} + 13 x^{3} - 27 x^{2} + 27 x - 27$ |
$6$ |
[2,2] |
$7^{5}\cdot 223$ |
$2$ |
$12.4632845495$ |
$75.57894027667932$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$9.93140583337$ |
| 6.6.4218557.1 |
$x^{6} - 2 x^{5} - 10 x^{4} + 20 x^{3} + 16 x^{2} - 25 x - 13$ |
$6$ |
[6,0] |
$7^{5}\cdot 251$ |
$2$ |
$12.7114176109$ |
$80.1835402842152$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$17.0690643057$ |
| 6.4.4722767.1 |
$x^{6} - x^{5} + x^{4} + 13 x^{3} - 27 x^{2} - 15 x + 29$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 281$ |
$2$ |
$12.9528723819$ |
$84.84016932806762$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$13.9792891022$ |
| 6.0.4974872.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 6 x^{3} + 2 x^{2} - 4 x + 8$ |
$6$ |
[0,3] |
$-\,2^{3}\cdot 7^{5}\cdot 37$ |
$3$ |
$13.0656288897$ |
$87.07514818343749$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$14.7877340934$ |
| 6.2.5159749.1 |
$x^{6} - 3 x^{5} + 2 x^{4} + x^{3} - 31 x^{2} + 30 x - 41$ |
$6$ |
[2,2] |
$7^{5}\cdot 307$ |
$2$ |
$13.1453280677$ |
$88.67833991927998$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$7.64870171495$ |
| 6.4.5663959.1 |
$x^{6} - x^{5} - 6 x^{4} + 13 x^{3} - 6 x^{2} - 36 x + 43$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 337$ |
$2$ |
$13.3511912437$ |
$92.91018334899674$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$16.4100485417$ |
| 6.0.5916064.1 |
$x^{6} - x^{5} + 8 x^{4} - 8 x^{3} + 15 x^{2} - 15 x + 8$ |
$6$ |
[0,3] |
$-\,2^{5}\cdot 7^{5}\cdot 11$ |
$3$ |
$13.4484472526$ |
$59.81815787764817$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$14.1364887199$ |
| 6.2.7042133.1 |
$x^{6} - x^{5} + 8 x^{4} + 6 x^{3} + x^{2} + 55 x - 41$ |
$6$ |
[2,2] |
$7^{5}\cdot 419$ |
$2$ |
$13.8447155469$ |
$103.59895582242794$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$10.5130910686$ |
| 6.4.7075747.1 |
$x^{6} - x^{5} - 6 x^{4} - 8 x^{3} + x^{2} + 41 x + 43$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 421$ |
$2$ |
$13.8557077986$ |
$103.84591435120448$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$14.452517522$ |
| 6.4.7546343.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 6 x^{3} - 26 x^{2} + 24 x + 29$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 449$ |
$2$ |
$14.0052034959$ |
$107.24363779079017$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$18.0033884387$ |
| 6.2.8453921.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 15 x^{3} - 12 x^{2} - 39 x - 41$ |
$6$ |
[2,2] |
$7^{5}\cdot 503$ |
$2$ |
$14.2728170011$ |
$113.50953882820106$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$13.296230431$ |
| 6.0.8605184.1 |
$x^{6} + 14 x^{4} + 56 x^{2} + 56$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 7^{5}$ |
$2$ |
$14.3150661808$ |
$14.315066180821045$ |
✓ |
✓ |
? |
$C_6$ (as 6T1) |
$[4]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.8605184.1 |
$x^{6} - 28 x^{2} + 56$ |
$6$ |
[4,1] |
$-\,2^{9}\cdot 7^{5}$ |
$2$ |
$14.3150661808$ |
$24.0749756711442$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$17.8264963005$ |
| 6.0.8958131.1 |
$x^{6} - 3 x^{5} + 16 x^{4} - 27 x^{3} + 67 x^{2} - 54 x + 71$ |
$6$ |
[0,3] |
$-\,7^{5}\cdot 13\cdot 41$ |
$3$ |
$14.4112914565$ |
$116.84549458192946$ |
✓ |
|
✓ |
$A_4\times C_2$ (as 6T6) |
$[2, 2]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.4.8958131.1 |
$x^{6} - x^{5} - 6 x^{4} + 6 x^{3} - 20 x^{2} + 6 x + 43$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 13\cdot 41$ |
$3$ |
$14.4112914565$ |
$116.84549458192946$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$17.2454688494$ |
| 6.4.8958131.2 |
$x^{6} - 2 x^{5} - 3 x^{4} + 20 x^{3} - 33 x^{2} - 25 x + 71$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 13\cdot 41$ |
$3$ |
$14.4112914565$ |
$116.84549458192946$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$15.5201248496$ |
| 6.2.9395113.1 |
$x^{6} - x^{5} + x^{4} - x^{3} - 13 x^{2} - x - 83$ |
$6$ |
[2,2] |
$7^{5}\cdot 13\cdot 43$ |
$3$ |
$14.5261436515$ |
$119.66145262079968$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$7.82089044605$ |
| 6.6.9395113.1 |
$x^{6} - x^{5} - 13 x^{4} + 13 x^{3} + 43 x^{2} - 29 x - 41$ |
$6$ |
[6,0] |
$7^{5}\cdot 13\cdot 43$ |
$3$ |
$14.5261436515$ |
$119.66145262079968$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$28.1640469152$ |
| 6.2.9395113.2 |
$x^{6} - x^{5} + 8 x^{4} - 15 x^{3} + 8 x^{2} - 64 x - 41$ |
$6$ |
[2,2] |
$7^{5}\cdot 13\cdot 43$ |
$3$ |
$14.5261436515$ |
$119.66145262079968$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$6.88429385434$ |
| 6.2.9865709.1 |
$x^{6} - 2 x^{5} + 4 x^{4} + 6 x^{3} - 40 x^{2} + 87 x - 97$ |
$6$ |
[2,2] |
$7^{5}\cdot 587$ |
$2$ |
$14.6449552924$ |
$122.62172386035188$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$10.2004192986$ |
| 6.4.10369919.1 |
$x^{6} - 3 x^{5} - 5 x^{4} + 15 x^{3} - 24 x^{2} + 16 x + 64$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 617$ |
$2$ |
$14.7671230594$ |
$125.71611416834841$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$21.390499488$ |
| 6.0.10504375.1 |
$x^{6} - x^{5} + x^{4} + 6 x^{3} + 8 x^{2} - 29 x + 22$ |
$6$ |
[0,3] |
$-\,5^{4}\cdot 7^{5}$ |
$2$ |
$14.7988636759$ |
$14.798863675926578$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$20.6759380692$ |
| 6.2.10806901.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - 29 x^{3} + 30 x^{2} - 81 x - 27$ |
$6$ |
[2,2] |
$7^{5}\cdot 643$ |
$2$ |
$14.8690605101$ |
$128.337582183916$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$10.8726120528$ |
| 6.4.11311111.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 22 x^{3} - 19 x^{2} + 66 x + 43$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 673$ |
$2$ |
$14.9824973901$ |
$131.29733127492813$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$23.3847926975$ |
| 6.0.11781707.1 |
$x^{6} - x^{5} + 15 x^{4} - 22 x^{3} + 78 x^{2} - 71 x + 113$ |
$6$ |
[0,3] |
$-\,7^{5}\cdot 701$ |
$2$ |
$15.0846314192$ |
$134.00079521809832$ |
✓ |
|
? |
$A_4\times C_2$ (as 6T6) |
$[4]$ |
$2$ |
$2$ |
$2.10181872849$ |
| 6.2.12218689.1 |
$x^{6} - x^{5} + 8 x^{4} - 15 x^{3} + 8 x^{2} + 20 x - 104$ |
$6$ |
[2,2] |
$7^{5}\cdot 727$ |
$2$ |
$15.1764700257$ |
$136.46320661008556$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$17.603214332$ |
| 6.0.12252303.1 |
$x^{6} + 7$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 7^{5}$ |
$2$ |
$15.1834205544$ |
$18.234330849744854$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$18.0843079982$ |
| 6.4.12722899.1 |
$x^{6} - x^{5} - 13 x^{4} + 20 x^{3} + 22 x^{2} - 99 x + 113$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 757$ |
$2$ |
$15.2790967146$ |
$139.25035352706192$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$21.0641861355$ |
| 6.0.12975004.2 |
$x^{6} - x^{5} + x^{4} - 8 x^{3} + 8 x^{2} + 20 x + 8$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 7^{5}\cdot 193$ |
$3$ |
$15.3291444515$ |
$111.61271818722955$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$16.3102873176$ |
| 6.2.13159881.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - 15 x^{3} + 30 x^{2} - 4 x - 104$ |
$6$ |
[2,2] |
$3^{3}\cdot 7^{5}\cdot 29$ |
$3$ |
$15.3653335977$ |
$47.207172944415866$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$8.61644913542$ |
| 6.2.13630477.1 |
$x^{6} - 3 x^{5} + 16 x^{4} - 27 x^{3} + 39 x^{2} - 26 x - 83$ |
$6$ |
[2,2] |
$7^{5}\cdot 811$ |
$2$ |
$15.4555753125$ |
$144.13146261590634$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$11.6847357827$ |
| 6.2.13983424.1 |
$x^{6} - 49 x^{2} - 91$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$61.3793853682179$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$6.55758997185$ |
| 6.6.13983424.1 |
$x^{6} - 14 x^{4} + 63 x^{2} - 91$ |
$6$ |
[6,0] |
$2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$61.3793853682179$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$34.3142136752$ |
| 6.2.13983424.2 |
$x^{6} + 7 x^{4} - 21 x^{2} - 91$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$36.496400897189325$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$7.55304290767$ |
| 6.2.13983424.3 |
$x^{6} + 7 x^{4} - 14 x^{2} - 91$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{5}\cdot 13$ |
$3$ |
$15.5215678516$ |
$61.3793853682179$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$9.16115584606$ |
| 6.2.14101073.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - x^{3} + 2 x^{2} + 80 x - 104$ |
$6$ |
[2,2] |
$7^{5}\cdot 839$ |
$2$ |
$15.5432569609$ |
$146.5984394015329$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$3$ |
$19.7634353993$ |
| 6.4.14134687.1 |
$x^{6} - x^{5} - 6 x^{4} - x^{3} - 34 x^{2} - 22 x + 71$ |
$6$ |
[4,1] |
$-\,7^{5}\cdot 29^{2}$ |
$2$ |
$15.5494261469$ |
$27.255074007139722$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$4$ |
$26.6850123674$ |
| 6.0.14605283.1 |
$x^{6} + 7 x^{4} + 14 x^{2} - 7 x + 7$ |
$6$ |
[0,3] |
$-\,7^{5}\cdot 11\cdot 79$ |
$3$ |
$15.6345359733$ |
$149.19636937295002$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$10.4789807858$ |
| 6.2.15512861.1 |
$x^{6} - 2 x^{5} + 4 x^{4} + 6 x^{3} - 40 x^{2} - 25 x - 125$ |
$6$ |
[2,2] |
$7^{5}\cdot 13\cdot 71$ |
$3$ |
$15.7924187137$ |
$153.76207007080262$ |
|
|
? |
$A_4\times C_2$ (as 6T6) |
$[2]$ |
$2$ |
$3$ |
$6.33744967676$ |
| 6.6.15512861.1 |
$x^{6} - 3 x^{5} - 12 x^{4} + 29 x^{3} + 53 x^{2} - 68 x - 83$ |
$6$ |
[6,0] |
$7^{5}\cdot 13\cdot 71$ |
$3$ |
$15.7924187137$ |
$153.76207007080262$ |
|
|
✓ |
$A_4\times C_2$ (as 6T6) |
trivial |
$2$ |
$5$ |
$33.827924796$ |
