| 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 |
| 6.2.525625.1 |
$x^{6} - x^{5} + x^{4} - x^{3} - 4 x^{2} + 5$ |
$6$ |
[2,2] |
$5^{4}\cdot 29^{2}$ |
$2$ |
$8.98350889572$ |
$31.561635639558343$ |
|
|
✓ |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$3.93902224288$ |
| 6.2.600625.1 |
$x^{6} - x^{5} + 4 x^{4} - 2 x^{3} + 6 x^{2} - 5 x + 1$ |
$6$ |
[2,2] |
$5^{4}\cdot 31^{2}$ |
$2$ |
$9.18545275007$ |
$32.99655748259533$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$4.26024588413$ |
| 6.2.802816.1 |
$x^{6} - 2 x^{5} - x^{4} + 6 x^{2} - 4 x + 2$ |
$6$ |
[2,2] |
$2^{14}\cdot 7^{2}$ |
$2$ |
$9.6405690567$ |
$24.616776431006123$ |
|
|
✓ |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$10.1197295749$ |
| 6.2.2175625.1 |
$x^{6} - x^{5} + x^{4} - 7 x^{3} - 6 x^{2} - 6 x - 1$ |
$6$ |
[2,2] |
$5^{4}\cdot 59^{2}$ |
$2$ |
$11.3831905748$ |
$50.67520462224516$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$8.77617960681$ |
| 6.2.2313441.1 |
$x^{6} - x^{5} - 3 x^{4} + x^{3} + 6 x^{2} - 3$ |
$6$ |
[2,2] |
$3^{4}\cdot 13^{4}$ |
$2$ |
$11.5003150512$ |
$29.622328050127763$ |
|
|
✓ |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$9.45129051038$ |
| 6.2.2325625.1 |
$x^{6} - x^{5} + 6 x^{4} - 2 x^{3} + 4 x^{2} + 9 x - 1$ |
$6$ |
[2,2] |
$5^{4}\cdot 61^{2}$ |
$2$ |
$11.5103875898$ |
$51.814032509245344$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$9.13573697255$ |
| 6.2.4100625.1 |
$x^{6} - 6 x^{4} - x^{3} + 9 x^{2} + 3 x - 11$ |
$6$ |
[2,2] |
$3^{8}\cdot 5^{4}$ |
$2$ |
$12.6514899795$ |
$23.574531309937974$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$13.878910599$ |
| 6.2.4100625.2 |
$x^{6} + 6 x^{4} - 3 x^{3} + 9 x^{2} - 9 x + 1$ |
$6$ |
[2,2] |
$3^{8}\cdot 5^{4}$ |
$2$ |
$12.6514899795$ |
$23.574531309937974$ |
|
|
✓ |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$12.3908061607$ |
| 6.2.4840000.2 |
$x^{6} - x^{5} + x^{4} - 12 x^{3} - 21 x^{2} - 11 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 11^{2}$ |
$3$ |
$13.0059144685$ |
$46.77720696848431$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$17.2190709914$ |
| 6.2.4950625.1 |
$x^{6} - x^{5} + 4 x^{4} - 10 x^{3} + 15 x - 5$ |
$6$ |
[2,2] |
$5^{4}\cdot 89^{2}$ |
$2$ |
$13.0549938561$ |
$66.65317489430973$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$13.5880018727$ |
| 6.2.7290000.1 |
$x^{6} - 6 x^{4} - 4 x^{3} + 9 x^{2} + 12 x - 16$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$13.9247665008$ |
$30.755720695068224$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$20.7156171475$ |
| 6.2.7290000.2 |
$x^{6} + 6 x^{4} - 2 x^{3} + 9 x^{2} - 6 x - 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$13.9247665008$ |
$30.755720695068224$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$22.118488972$ |
| 6.2.8254129.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 9 x^{3} + 5 x^{2} + 4 x - 4$ |
$6$ |
[2,2] |
$13^{4}\cdot 17^{2}$ |
$2$ |
$14.2160368973$ |
$45.264402832128994$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$13.5345224292$ |
| 6.2.11560000.1 |
$x^{6} - x^{5} - 4 x^{4} - 7 x^{3} - 16 x^{2} - 21 x - 11$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 17^{2}$ |
$3$ |
$15.036945962$ |
$38.99392548461692$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$9.6076343801$ |
| 6.2.11560000.3 |
$x^{6} - 2 x^{5} + 4 x^{4} + 4 x^{3} - 6 x^{2} + 18 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 17^{2}$ |
$3$ |
$15.036945962$ |
$38.99392548461692$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$8.78658345136$ |
| 6.2.11943936.1 |
$x^{6} + 6 x^{4} - 4 x^{3} + 9 x^{2} - 12 x - 4$ |
$6$ |
[2,2] |
$2^{14}\cdot 3^{6}$ |
$2$ |
$15.1190525987$ |
$30.93861708477606$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$51.2353137524$ |
| 6.2.11943936.2 |
$x^{6} + 6 x^{4} - 4 x^{3} - 9 x^{2} + 12 x - 4$ |
$6$ |
[2,2] |
$2^{14}\cdot 3^{6}$ |
$2$ |
$15.1190525987$ |
$30.93861708477606$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$51.6695566856$ |
| 6.2.12425625.1 |
$x^{6} - 3 x^{5} + 6 x^{4} - 15 x^{2} + 30 x - 20$ |
$6$ |
[2,2] |
$3^{2}\cdot 5^{4}\cdot 47^{2}$ |
$3$ |
$15.2190089969$ |
$39.7042557434005$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$8.76920848464$ |
| 6.2.12425625.2 |
$x^{6} - 3 x^{5} + 9 x^{4} - 9 x^{3} + 9 x^{2} + 12 x + 1$ |
$6$ |
[2,2] |
$3^{2}\cdot 5^{4}\cdot 47^{2}$ |
$3$ |
$15.2190089969$ |
$39.7042557434005$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$8.1176351334$ |
| 6.2.12780625.1 |
$x^{6} - 2 x^{5} - 6 x^{4} + 19 x^{3} - x^{2} - 37 x + 31$ |
$6$ |
[2,2] |
$5^{4}\cdot 11^{2}\cdot 13^{2}$ |
$3$ |
$15.2906289177$ |
$59.62947278091747$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$25.4001798079$ |
| 6.2.13875625.1 |
$x^{6} - x^{5} - x^{4} + 5 x^{3} - 10 x^{2} - 30 x - 5$ |
$6$ |
[2,2] |
$5^{4}\cdot 149^{2}$ |
$2$ |
$15.5015607169$ |
$93.97630145365427$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$27.1256017653$ |
| 6.2.14250625.1 |
$x^{6} - x^{5} + 9 x^{4} - 7 x^{3} + 16 x^{2} - 20 x + 1$ |
$6$ |
[2,2] |
$5^{4}\cdot 151^{2}$ |
$2$ |
$15.5706108965$ |
$94.81538251069664$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$9.26163116551$ |
| 6.2.14440000.2 |
$x^{6} - x^{5} - x^{4} - 12 x^{3} - 24 x^{2} - 20 x - 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 19^{2}$ |
$3$ |
$15.6049075071$ |
$67.34027682701665$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$32.9681500507$ |
| 6.2.15108769.1 |
$x^{6} - 3 x^{5} + x^{4} - x^{3} + 11 x^{2} - 24 x + 27$ |
$6$ |
[2,2] |
$13^{4}\cdot 23^{2}$ |
$2$ |
$15.7231001317$ |
$55.370197369340005$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$48.9485831157$ |
| 6.2.16370116.1 |
$x^{6} - 2 x^{5} + 7 x^{4} + 2 x^{3} + x^{2} + 24 x - 1$ |
$6$ |
[2,2] |
$2^{2}\cdot 7^{2}\cdot 17^{4}$ |
$3$ |
$15.9346291125$ |
$35.16190326674663$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$65.5654774057$ |
| 6.2.17682025.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 3 x^{3} + 3 x^{2} + 2 x - 7$ |
$6$ |
[2,2] |
$5^{2}\cdot 29^{4}$ |
$2$ |
$16.1406864159$ |
$36.540837865572115$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$36.7125862985$ |
| 6.2.18490000.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 6 x^{3} + 4 x^{2} - 12 x - 9$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{4}\cdot 43^{2}$ |
$3$ |
$16.2613333168$ |
$43.85223438605858$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$12.1323181179$ |
| 6.2.18490000.2 |
$x^{6} - 3 x^{5} + 11 x^{4} - 14 x^{3} + 21 x^{2} + 5 x - 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{4}\cdot 43^{2}$ |
$3$ |
$16.2613333168$ |
$43.85223438605858$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$12.2287639175$ |
| 6.2.20025625.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 19 x^{2} + 30 x + 20$ |
$6$ |
[2,2] |
$5^{4}\cdot 179^{2}$ |
$2$ |
$16.4790060512$ |
$106.20122443056758$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$33.524534177$ |
| 6.2.20475625.1 |
$x^{6} - x^{5} - 9 x^{4} - 7 x^{3} + 29 x^{2} + 44 x + 19$ |
$6$ |
[2,2] |
$5^{4}\cdot 181^{2}$ |
$2$ |
$16.5401532016$ |
$106.99082914207627$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$32.9717030762$ |
| 6.2.21160000.3 |
$x^{6} - 2 x^{5} + x^{4} - 20 x^{3} + 15 x^{2} + 30 x + 55$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 23^{2}$ |
$3$ |
$16.6310349884$ |
$45.35617421365923$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$12.6528260637$ |
| 6.2.21160000.4 |
$x^{6} - x^{5} + 5 x^{4} + 10 x^{3} - 10 x^{2} + 44 x + 76$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 23^{2}$ |
$3$ |
$16.6310349884$ |
$45.35617421365923$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$13.2486785184$ |
| 6.2.21855625.2 |
$x^{6} - x^{5} + 5 x^{4} + 15 x^{3} - 10 x^{2} + 54 x + 61$ |
$6$ |
[2,2] |
$5^{4}\cdot 11^{2}\cdot 17^{2}$ |
$3$ |
$16.7209342213$ |
$68.18891090211359$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$32.2834734795$ |
| 6.2.22325625.3 |
$x^{6} + 6 x^{4} - 7 x^{3} + 9 x^{2} - 21 x + 11$ |
$6$ |
[2,2] |
$3^{6}\cdot 5^{4}\cdot 7^{2}$ |
$3$ |
$16.7803341312$ |
$40.68599417585656$ |
|
|
✓ |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$32.4844814116$ |
| 6.2.22325625.4 |
$x^{6} - 9 x^{4} - 13 x^{3} + 9 x^{2} + 36 x + 31$ |
$6$ |
[2,2] |
$3^{6}\cdot 5^{4}\cdot 7^{2}$ |
$3$ |
$16.7803341312$ |
$40.68599417585656$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$33.2493908648$ |
| 6.2.24920064.1 |
$x^{6} - 2 x^{5} + 11 x^{4} - 12 x^{3} + 25 x^{2} - 14 x - 1$ |
$6$ |
[2,2] |
$2^{14}\cdot 3^{2}\cdot 13^{2}$ |
$3$ |
$17.0906347268$ |
$42.011171440958684$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$22.7867388452$ |
| 6.2.24920064.2 |
$x^{6} - 2 x^{5} + 9 x^{4} - 4 x^{3} + 21 x^{2} + 10 x + 1$ |
$6$ |
[2,2] |
$2^{14}\cdot 3^{2}\cdot 13^{2}$ |
$3$ |
$17.0906347268$ |
$42.011171440958684$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
$[3]$ |
$2$ |
$3$ |
$29.2334274192$ |
| 6.2.27541504.1 |
$x^{6} + 6 x^{4} - 8 x^{3} - 2 x^{2} - 32 x + 4$ |
$6$ |
[2,2] |
$2^{14}\cdot 41^{2}$ |
$2$ |
$17.3779259431$ |
$79.98742682830643$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$89.4602468688$ |
| 6.2.27825625.1 |
$x^{6} - x^{5} + 11 x^{4} - 11 x^{3} + 26 x^{2} - 10 x - 5$ |
$6$ |
[2,2] |
$5^{4}\cdot 211^{2}$ |
$2$ |
$17.4076770633$ |
$118.5084014818429$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$39.0118754543$ |
| 6.2.29160000.2 |
$x^{6} - 6 x^{4} - 4 x^{3} + 9 x^{2} + 12 x - 76$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$17.5441064293$ |
$43.49515732752436$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$47.0741915383$ |
| 6.2.29160000.5 |
$x^{6} + 6 x^{4} - 8 x^{3} + 9 x^{2} - 24 x - 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{6}\cdot 5^{4}$ |
$3$ |
$17.5441064293$ |
$43.49515732752436$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$46.7452120109$ |
| 6.2.32490000.1 |
$x^{6} - 2 x^{5} + 10 x^{3} - 20 x^{2} - 72 x - 81$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{2}\cdot 5^{4}\cdot 19^{2}$ |
$4$ |
$17.8631598771$ |
$82.47465868197851$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$45.8576518761$ |
| 6.2.33350625.1 |
$x^{6} - 3 x^{5} - 4 x^{4} + 10 x^{3} - 5 x^{2} + 10 x - 20$ |
$6$ |
[2,2] |
$3^{2}\cdot 5^{4}\cdot 7^{2}\cdot 11^{2}$ |
$4$ |
$17.9411659316$ |
$75.787737239626$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$42.6090332346$ |
| 6.2.34656769.1 |
$x^{6} + x^{4} - x^{3} - 7 x^{2} + 14 x - 7$ |
$6$ |
[2,2] |
$7^{2}\cdot 29^{4}$ |
$2$ |
$18.056407411$ |
$45.72957780079561$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$45.4047223855$ |
| 6.2.35700625.1 |
$x^{6} - 2 x^{5} + 6 x^{4} - 5 x^{3} - 25 x^{2} + 50 x - 20$ |
$6$ |
[2,2] |
$5^{4}\cdot 239^{2}$ |
$2$ |
$18.1459330085$ |
$128.77338261696713$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$44.7825543186$ |
| 6.2.36192256.1 |
$x^{6} - 2 x^{5} - 5 x^{4} - 16 x^{3} + 8 x + 28$ |
$6$ |
[2,2] |
$2^{14}\cdot 47^{2}$ |
$2$ |
$18.1873437751$ |
$87.61216116107356$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$103.424158967$ |
| 6.2.36300625.1 |
$x^{6} - x^{5} + 11 x^{4} - 21 x^{3} + 36 x^{2} - 110 x + 95$ |
$6$ |
[2,2] |
$5^{4}\cdot 241^{2}$ |
$2$ |
$18.1964087428$ |
$129.49078539012766$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$45.4628047085$ |
| 6.2.37015056.2 |
$x^{6} + 6 x^{4} - 6 x^{3} + 9 x^{2} - 18 x - 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{4}\cdot 13^{4}$ |
$3$ |
$18.2556122103$ |
$49.332028500674255$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$92.9323542043$ |
| 6.2.38130625.1 |
$x^{6} - x^{5} - 4 x^{4} - 2 x^{3} - 16 x^{2} - x + 59$ |
$6$ |
[2,2] |
$5^{4}\cdot 13^{2}\cdot 19^{2}$ |
$3$ |
$18.34618016$ |
$85.84234639792447$ |
|
|
? |
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$42.7931802738$ |
| 6.2.38440000.1 |
$x^{6} - 2 x^{5} - 6 x^{4} + 12 x^{3} - 4 x^{2} - 70 x - 55$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 31^{2}$ |
$3$ |
$18.3709055001$ |
$93.32835820701949$ |
|
|
|
$C_3^2:C_4$ (as 6T10) |
trivial |
$2$ |
$3$ |
$53.5458942072$ |
