| 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 |
| 6.0.9747.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + 4 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 19^{2}$ |
$2$ |
$4.62180723059$ |
$12.332838034173273$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$0.601543105945$ |
| 6.0.10816.1 |
$x^{6} - x^{4} - 2 x^{3} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 13^{2}$ |
$2$ |
$4.70266937544$ |
$11.057549627357744$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$0.434147804699$ |
| 6.0.21168.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - x^{3} - 2 x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$5.25952638099$ |
$10.061112020813587$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$1.11901604193$ |
| 6.0.36963.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 2 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 37^{2}$ |
$2$ |
$5.77157754914$ |
$19.232176827720277$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$1.53091151046$ |
| 6.0.41472.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 3^{4}$ |
$2$ |
$5.88336550687$ |
$12.237893415933033$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$0.632381281465$ |
| 6.0.73008.1 |
$x^{6} - x^{5} - 4 x^{4} + 3 x^{3} + 6 x^{2} - 5 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 13^{2}$ |
$3$ |
$6.46489896343$ |
$15.201141185311545$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$2.60467330873$ |
| 6.0.87616.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 4 x^{3} + 3 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 37^{2}$ |
$2$ |
$6.66444370329$ |
$22.20740493717357$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$1.99857728103$ |
| 6.0.107163.1 |
$x^{6} - x^{3} + 7$ |
$6$ |
[0,3] |
$-\,3^{7}\cdot 7^{2}$ |
$2$ |
$6.8919292503$ |
$13.183786372359444$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$3.73241572462$ |
| 6.0.107811.1 |
$x^{6} - x^{4} - 2 x^{3} + 3 x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 11^{3}$ |
$2$ |
$6.89885757355$ |
$14.350202036282921$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$1.3637383458$ |
| 6.0.143883.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{2} + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 73^{2}$ |
$2$ |
$7.2388278302$ |
$30.253516886595015$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$5.95218303116$ |
| 6.0.177147.1 |
$x^{6} - 3 x^{3} + 3$ |
$6$ |
[0,3] |
$-\,3^{11}$ |
$1$ |
$7.4941485989$ |
$10.808432596584025$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$4.94709921977$ |
| 6.0.184832.1 |
$x^{6} - 2 x^{5} + x^{4} + 2 x^{3} - 4 x + 3$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 19^{2}$ |
$2$ |
$7.54737960296$ |
$20.13944017607579$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$2.37416675486$ |
| 6.0.223587.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 5 x^{2} + 3 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$7.79066311269$ |
$35.04194650073235$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$8.14200974075$ |
| 6.0.223587.2 |
$x^{6} + x^{4} - 2 x^{3} - 5 x^{2} + 2 x + 4$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7^{2}\cdot 13^{2}$ |
$3$ |
$7.79066311269$ |
$35.04194650073235$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$6.17969009809$ |
| 6.0.238144.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 8 x^{3} + 12 x^{2} - 12 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 61^{2}$ |
$2$ |
$7.8729943662$ |
$30.99202014514269$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$3.91336396199$ |
| 6.0.314928.1 |
$x^{6} - 2 x^{3} + 4$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{9}$ |
$2$ |
$8.24837782199$ |
$10.529202818387967$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$8.09420874351$ |
| 6.0.320787.3 |
$x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 5 x^{2} + 2 x + 4$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 109^{2}$ |
$2$ |
$8.273757606$ |
$39.52255016061654$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$8.30552733847$ |
| 6.0.336091.1 |
$x^{6} - x^{5} + x^{4} + 5 x^{2} + 4 x + 1$ |
$6$ |
[0,3] |
$-\,7^{2}\cdot 19^{3}$ |
$2$ |
$8.33827371165$ |
$15.950543793511486$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$2.3409784627$ |
| 6.0.341056.1 |
$x^{6} - 5 x^{4} + 10 x^{2} - 6 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 73^{2}$ |
$2$ |
$8.35867839276$ |
$34.93375223681704$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$3.47739996254$ |
| 6.0.369603.2 |
$x^{6} - 5 x^{3} + 13$ |
$6$ |
[0,3] |
$-\,3^{7}\cdot 13^{2}$ |
$2$ |
$8.47141416141$ |
$19.919129971779828$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$6.28997810614$ |
| 6.0.392000.1 |
$x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{3}\cdot 7^{2}$ |
$3$ |
$8.55488832192$ |
$16.364912636128995$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[2]$ |
$2$ |
$2$ |
$1.96225500494$ |
| 6.0.415152.1 |
$x^{6} - x^{5} + 8 x^{4} - 3 x^{3} + 18 x^{2} + x + 13$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 31^{2}$ |
$3$ |
$8.63709816787$ |
$27.132413077361097$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$5.77967825133$ |
| 6.0.419904.3 |
$x^{6} - 2 x^{3} + 9 x^{2} - 12 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{8}$ |
$2$ |
$8.65349742184$ |
$14.100858664870902$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$5.28645643215$ |
| 6.0.435483.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - x^{3} - 5 x^{2} + 4 x + 4$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 127^{2}$ |
$2$ |
$8.70619788983$ |
$43.7619274017317$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$8.72305712935$ |
| 6.0.469567.1 |
$x^{6} - x^{5} + 3 x^{4} + 2 x^{3} + 6 x^{2} + 3 x + 2$ |
$6$ |
[0,3] |
$-\,7^{3}\cdot 37^{2}$ |
$2$ |
$8.81623033275$ |
$29.37763536393462$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$8.84422065671$ |
| 6.0.602176.1 |
$x^{6} - 2 x^{5} - 4 x^{4} + 11 x^{2} + 14 x + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 97^{2}$ |
$2$ |
$9.18940178441$ |
$42.222552577696334$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$6.37089333685$ |
| 6.0.634207.1 |
$x^{6} - x^{5} - 3 x^{4} + x^{3} + 7 x^{2} - 5 x + 1$ |
$6$ |
[0,3] |
$-\,7^{3}\cdot 43^{2}$ |
$2$ |
$9.26912001145$ |
$32.473417069603315$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$2.61100445619$ |
| 6.0.648000.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 7 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{4}\cdot 5^{3}$ |
$3$ |
$9.30241765448$ |
$19.349808478363364$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
$[2]$ |
$2$ |
$2$ |
$1.72572602223$ |
| 6.0.677376.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 6 x^{3} + 8 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 3^{3}\cdot 7^{2}$ |
$3$ |
$9.3714106217$ |
$17.926863604818365$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
$[2]$ |
$2$ |
$2$ |
$1.82916788897$ |
| 6.0.717363.1 |
$x^{6} + x^{4} - x^{3} - 8 x^{2} + x + 7$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 163^{2}$ |
$2$ |
$9.46142378863$ |
$51.68355322882323$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$7.19643004224$ |
| 6.6.722000.1 |
$x^{6} - x^{5} - 6 x^{4} + 7 x^{3} + 4 x^{2} - 5 x + 1$ |
$6$ |
[6,0] |
$2^{4}\cdot 5^{3}\cdot 19^{2}$ |
$3$ |
$9.47158947509$ |
$25.274004971349576$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$5$ |
$6.412993699$ |
| 6.0.760384.2 |
$x^{6} - 2 x^{5} - 5 x^{4} + 14 x^{3} + 2 x^{2} - 24 x + 16$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 109^{2}$ |
$2$ |
$9.55371236207$ |
$45.636709948584894$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$23.6107741773$ |
| 6.0.798768.2 |
$x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 2 x^{2} - x + 7$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 43^{2}$ |
$3$ |
$9.63245028763$ |
$33.74630765446885$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$10.3432301122$ |
| 6.0.826875.2 |
$x^{6} - x^{5} + 9 x^{4} - 6 x^{3} + 26 x^{2} - 11 x + 19$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 5^{4}\cdot 7^{2}$ |
$3$ |
$9.68813042775$ |
$18.532726798013343$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$6.05528089807$ |
| 6.0.884547.1 |
$x^{6} - 3 x^{5} + 4 x^{4} + 2 x^{3} - 5 x^{2} + x + 7$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 181^{2}$ |
$2$ |
$9.7976100951$ |
$55.4216788307774$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$10.6673193119$ |
| 6.0.946688.1 |
$x^{6} + 4 x^{4} + 3 x^{2} - 4 x + 4$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 43^{2}$ |
$2$ |
$9.90910610278$ |
$34.715543100649214$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$13.3161738607$ |
| 6.0.964467.2 |
$x^{6} - 5 x^{3} + 7$ |
$6$ |
[0,3] |
$-\,3^{9}\cdot 7^{2}$ |
$2$ |
$9.93988199983$ |
$24.27210940016998$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$10.6568548914$ |
| 6.0.964467.3 |
$x^{6} - 4 x^{3} + 7$ |
$6$ |
[0,3] |
$-\,3^{9}\cdot 7^{2}$ |
$2$ |
$9.93988199983$ |
$24.27210940016998$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$19.0550135313$ |
| 6.0.1069227.2 |
$x^{6} - 3 x^{5} + 4 x^{4} + 2 x^{3} - 8 x^{2} + 4 x + 7$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 199^{2}$ |
$2$ |
$10.1121845306$ |
$59.037688463437995$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$10.3447446286$ |
| 6.0.1218375.1 |
$x^{6} - x^{5} + 3 x^{4} - 6 x^{3} + 11 x^{2} - 8 x + 4$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 5^{3}\cdot 19^{2}$ |
$3$ |
$10.3346751465$ |
$27.57706419990631$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
$[2]$ |
$2$ |
$2$ |
$7.96571554767$ |
| 6.0.1271403.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 2 x^{3} - 5 x^{2} + 5 x + 7$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7^{2}\cdot 31^{2}$ |
$3$ |
$10.4083176671$ |
$62.5461309714934$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$12.9872656093$ |
| 6.0.1271403.2 |
$x^{6} + x^{4} - 3 x^{3} - 8 x^{2} + 3 x + 9$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7^{2}\cdot 31^{2}$ |
$3$ |
$10.4083176671$ |
$62.5461309714934$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$23.1964095513$ |
| 6.0.1279091.2 |
$x^{6} - 2 x^{5} - 2 x^{3} + 6 x^{2} - 4 x + 5$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 31^{2}$ |
$2$ |
$10.4187809477$ |
$32.729356890496106$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$7.19083504469$ |
| 6.0.1539727.1 |
$x^{6} - 3 x^{5} + 3 x^{4} + x^{3} + x^{2} - 5 x + 11$ |
$6$ |
[0,3] |
$-\,7^{3}\cdot 67^{2}$ |
$2$ |
$10.7458462117$ |
$43.64477126883613$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$4.66274205903$ |
| 6.0.1577536.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 6 x^{3} + 17 x^{2} + 8 x + 4$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 157^{2}$ |
$2$ |
$10.7893814242$ |
$58.20537575864297$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
trivial |
$4$ |
$2$ |
$36.7571962807$ |
| 6.0.1607472.1 |
$x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{3} - 8 x^{2} + 3 x + 9$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 61^{2}$ |
$3$ |
$10.8232386871$ |
$42.60564860398539$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$6$ |
$2$ |
$29.8334308694$ |
| 6.0.1714608.2 |
$x^{6} - 3 x^{5} - 6 x^{4} + 13 x^{3} + 24 x^{2} + 9 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{7}\cdot 7^{2}$ |
$3$ |
$10.940255742$ |
$20.927956356407396$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$6$ |
$2$ |
$6.76797174418$ |
| 6.0.1724976.1 |
$x^{6} - x^{5} - 2 x^{4} - x^{3} + 8 x^{2} - 5 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{4}\cdot 11^{3}$ |
$3$ |
$10.9512537696$ |
$22.779525808351707$ |
|
|
✓ |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$2.65030466524$ |
| 6.0.1724976.2 |
$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} + 6 x^{2} - 15 x + 9$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{4}\cdot 11^{3}$ |
$3$ |
$10.9512537696$ |
$22.779525808351707$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$4.2524698409$ |
| 6.0.1822139.1 |
$x^{6} - 3 x^{5} + 7 x^{4} - 4 x^{3} + 8 x^{2} - x + 3$ |
$6$ |
[0,3] |
$-\,11^{3}\cdot 37^{2}$ |
$2$ |
$11.0517296001$ |
$36.82681487204538$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$2$ |
$2$ |
$8.96357349109$ |
