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 |
6.2.242000.2 |
$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 2 x^{2} - 4 x + 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{3}\cdot 11^{2}$ |
$3$ |
$7.89409886204$ |
$22.119575491524458$ |
|
|
|
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$2.36794627144$ |
6.0.309123.2 |
$x^{6} - 3 x^{5} + x^{4} - 2 x^{3} + 7 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 107^{2}$ |
$2$ |
$8.22284088511$ |
$17.916472867168917$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$4.78251036365$ |
6.2.406125.1 |
$x^{6} - x^{5} + 3 x^{4} + 3 x^{2} + 4 x + 1$ |
$6$ |
[2,2] |
$3^{2}\cdot 5^{3}\cdot 19^{2}$ |
$3$ |
$8.60551014102$ |
$27.57706419990631$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$2.77416683434$ |
6.2.739328.4 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$2^{11}\cdot 19^{2}$ |
$2$ |
$9.50910243332$ |
$15.533349925214662$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$6.38670865949$ |
6.2.836352.2 |
$x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + 2 x^{2} - 2$ |
$6$ |
[2,2] |
$2^{8}\cdot 3^{3}\cdot 11^{2}$ |
$3$ |
$9.706548971$ |
$21.58717165964639$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$7.93898266213$ |
6.0.861184.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 9 x^{2} + 6 x + 5$ |
$6$ |
[0,3] |
$-\,2^{10}\cdot 29^{2}$ |
$2$ |
$9.75399792215$ |
$37.756522709569445$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$4$ |
$2$ |
$18.5668112868$ |
6.2.903168.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 3 x^{2} + 2 x + 1$ |
$6$ |
[2,2] |
$2^{11}\cdot 3^{2}\cdot 7^{2}$ |
$3$ |
$9.83168804874$ |
$22.58643281430495$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$6.82051877032$ |
6.0.906304.1 |
$x^{6} - 2 x^{5} + 6 x^{4} - 10 x^{3} + 15 x^{2} - 6 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7^{2}\cdot 17^{2}$ |
$3$ |
$9.83736946892$ |
$34.984711477348505$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$4$ |
$2$ |
$6.66923517878$ |
6.0.1000188.1 |
$x^{6} - x^{3} + 2$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 3^{6}\cdot 7^{3}$ |
$3$ |
$10.0003133088$ |
$19.31541720291671$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$10.0689969862$ |
6.2.1058000.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 6 x^{3} + x^{2} - 4 x + 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{3}\cdot 23^{2}$ |
$3$ |
$10.0944101005$ |
$17.0229798060099$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$5.22809710773$ |
6.0.1081600.1 |
$x^{6} - 2 x^{5} + 6 x^{4} - 2 x^{3} + 4 x^{2} + 4 x + 2$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 5^{2}\cdot 13^{2}$ |
$3$ |
$10.1315940382$ |
$26.565928937544715$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$4$ |
$2$ |
$12.6715941121$ |
6.2.1083392.1 |
$x^{6} - 2 x^{5} - x^{4} + 4 x^{3} - 8 x + 2$ |
$6$ |
[2,2] |
$2^{11}\cdot 23^{2}$ |
$2$ |
$10.1343897876$ |
$32.350317596360256$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$12.3920171623$ |
6.0.1156923.2 |
$x^{6} - 3 x^{5} + 2 x^{3} + 6 x + 7$ |
$6$ |
[0,3] |
$-\,3^{7}\cdot 23^{2}$ |
$2$ |
$10.2459148551$ |
$17.278473921432806$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$13.0555448826$ |
6.0.1166400.3 |
$x^{6} - 4 x^{3} + 5$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{6}\cdot 5^{2}$ |
$3$ |
$10.2598556801$ |
$26.895424784384943$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$4$ |
$2$ |
$15.6256684781$ |
6.2.1168128.1 |
$x^{6} - x^{4} - 2 x^{3} + x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$2^{8}\cdot 3^{3}\cdot 13^{2}$ |
$3$ |
$10.2623874154$ |
$24.13030750868067$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$9.78267231766$ |
6.2.1331712.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 6 x^{3} + 7 x^{2} - 8 x + 2$ |
$6$ |
[2,2] |
$2^{9}\cdot 3^{2}\cdot 17^{2}$ |
$3$ |
$10.4890233496$ |
$32.38954907047272$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$9.45534943522$ |
6.2.1382400.1 |
$x^{6} - 2 x^{4} - 4 x^{3} - 8 x^{2} - 8 x - 2$ |
$6$ |
[2,2] |
$2^{11}\cdot 3^{3}\cdot 5^{2}$ |
$3$ |
$10.5545313495$ |
$18.047994736019533$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$9.55707700765$ |
6.0.1415907.2 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} - 2 x^{2} + 9 x + 7$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 229^{2}$ |
$2$ |
$10.5967442974$ |
$26.210684844162312$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$9.8085042287$ |
6.2.1453248.5 |
$x^{6} - 2 x^{5} + 2 x^{4} + 3 x^{2} - 4 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{3}\cdot 29^{2}$ |
$3$ |
$10.6428176781$ |
$18.65475810617763$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$5.16041924809$ |
6.2.1458000.1 |
$x^{6} - 2 x^{3} - 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{6}\cdot 5^{3}$ |
$3$ |
$10.6486099793$ |
$16.324507030901437$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$6.56419033192$ |
6.0.1492992.5 |
$x^{6} - 2 x^{5} + x^{4} + 4 x^{3} + x^{2} - 2 x + 3$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 3^{6}$ |
$2$ |
$10.6907846177$ |
$26.706109521254483$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$13.6352060827$ |
6.2.1492992.5 |
$x^{6} - 4 x^{3} + 2$ |
$6$ |
[2,2] |
$2^{11}\cdot 3^{6}$ |
$2$ |
$10.6907846177$ |
$16.3891614959171$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$9.91964275176$ |
6.0.1494108.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 9 x^{3} + 16 x^{2} - 17 x + 8$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 3^{2}\cdot 7^{3}\cdot 11^{2}$ |
$4$ |
$10.6921160829$ |
$35.97974667452217$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$13.1800395213$ |
6.2.1601613.1 |
$x^{6} - x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} + 3 x - 3$ |
$6$ |
[2,2] |
$3^{6}\cdot 13^{3}$ |
$2$ |
$10.8166538264$ |
$27.020537039282146$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$10.9073168925$ |
6.0.1617984.1 |
$x^{6} - 3 x^{4} - 6 x^{3} + 9 x^{2} + 12 x + 4$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 53^{2}$ |
$3$ |
$10.83500303$ |
$48.877374517097394$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$4$ |
$2$ |
$19.731342365$ |
6.2.1778112.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} - x^{2} - 2 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{4}\cdot 7^{3}$ |
$3$ |
$11.0067690039$ |
$22.89500214913901$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$10.1073260945$ |
6.2.1782272.2 |
$x^{6} - 2 x^{5} - x^{4} + 2 x^{3} - x^{2} - 4 x - 2$ |
$6$ |
[2,2] |
$2^{9}\cdot 59^{2}$ |
$2$ |
$11.0110566592$ |
$21.72556098240043$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$12.2796346377$ |
6.0.1783323.1 |
$x^{6} - 2 x^{5} + 2 x^{3} + 6 x^{2} + 13 x + 7$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 257^{2}$ |
$2$ |
$11.0121385908$ |
$27.76688675382964$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$17.5674074053$ |
6.0.1849600.1 |
$x^{6} - 2 x^{5} + 6 x^{4} - 18 x^{3} + 28 x^{2} - 20 x + 10$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 5^{2}\cdot 17^{2}$ |
$3$ |
$11.0793165135$ |
$37.25268761649149$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$4$ |
$2$ |
$21.5483081193$ |
6.0.1878268.1 |
$x^{6} - x^{5} + 4 x^{4} - 6 x^{3} + 14 x^{2} - 12 x + 8$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 7^{3}\cdot 37^{2}$ |
$3$ |
$11.107754177$ |
$25.546802223478856$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$14.1709428264$ |
6.2.1922000.2 |
$x^{6} - x^{5} + 6 x^{4} - 5 x^{3} + 8 x^{2} - 9 x - 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{3}\cdot 31^{2}$ |
$3$ |
$11.1504457879$ |
$19.762983718745776$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$6.17514424795$ |
6.0.2101707.1 |
$x^{6} - 3 x^{4} - 10 x^{3} + 6 x^{2} + 18 x + 7$ |
$6$ |
[0,3] |
$-\,3^{7}\cdot 31^{2}$ |
$2$ |
$11.3178003472$ |
$20.05960194310363$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$19.4679096417$ |
6.2.2178000.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} - 9 x + 9$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{2}\cdot 5^{3}\cdot 11^{2}$ |
$4$ |
$11.3852606917$ |
$30.408435986026603$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$8.40337650445$ |
6.2.2278125.2 |
$x^{6} - 5 x^{3} + 5$ |
$6$ |
[2,2] |
$3^{6}\cdot 5^{5}$ |
$2$ |
$11.47086737$ |
$17.585042122521724$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$6.76080862331$ |
6.2.2365632.1 |
$x^{6} - x^{4} - 2 x^{3} - 5 x^{2} - 2 x - 2$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{3}\cdot 37^{2}$ |
$3$ |
$11.5431550983$ |
$38.464353655440554$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$17.0642072304$ |
6.2.2377892.1 |
$x^{6} - x^{5} + 2 x^{4} - 4 x^{3} + x^{2} - 3 x - 4$ |
$6$ |
[2,2] |
$2^{2}\cdot 11^{2}\cdot 17^{3}$ |
$3$ |
$11.5531041274$ |
$21.707382906759687$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$21.3322576377$ |
6.2.2415125.3 |
$x^{6} - x^{5} - x^{4} + 2 x^{3} - 6 x^{2} + 5 x + 11$ |
$6$ |
[2,2] |
$5^{3}\cdot 139^{2}$ |
$2$ |
$11.5830590114$ |
$26.362852652928137$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$5.53714332355$ |
6.0.2433600.1 |
$x^{6} - 2 x^{5} + 4 x^{4} + 4 x^{3} + 8 x^{2} - 6 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 5^{2}\cdot 13^{2}$ |
$4$ |
$11.5977799953$ |
$56.001482941967396$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$4$ |
$2$ |
$8.43434802479$ |
6.2.2450000.1 |
$x^{6} - x^{5} + 5 x^{3} - 10 x^{2} - x + 11$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{5}\cdot 7^{2}$ |
$3$ |
$11.6107697845$ |
$16.05871118442657$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$8.47995581686$ |
6.2.2508800.2 |
$x^{6} - 2 x^{4} - 4 x^{3} + 6 x^{2} + 8 x - 8$ |
$6$ |
[2,2] |
$2^{11}\cdot 5^{2}\cdot 7^{2}$ |
$3$ |
$11.6567551308$ |
$32.72982527225799$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$19.3889971903$ |
6.0.2592000.1 |
$x^{6} - 2 x^{5} + 6 x^{4} - 4 x^{3} + 4 x^{2} + 4$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 3^{4}\cdot 5^{3}$ |
$3$ |
$11.7203118178$ |
$24.37923101332429$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[2]$ |
$2$ |
$2$ |
$7.94454036335$ |
6.2.2676429.1 |
$x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{3} - 2 x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$3^{3}\cdot 7^{3}\cdot 17^{2}$ |
$3$ |
$11.7830925222$ |
$30.297648883452823$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$10.8799017096$ |
6.0.2695275.1 |
$x^{6} - 3 x^{3} + 5$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 5^{2}\cdot 11^{3}$ |
$3$ |
$11.7968805103$ |
$34.93959039247001$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$13.6927005705$ |
6.0.2696112.2 |
$x^{6} - 3 x^{5} - 5 x^{4} + 10 x^{3} + 13 x^{2} + 5 x + 7$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 79^{2}$ |
$3$ |
$11.7974910053$ |
$30.789608636681304$ |
|
|
|
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$25.0550376032$ |
6.2.2847312.1 |
$x^{6} - x^{5} + 2 x^{4} - 7 x^{3} + 2 x^{2} + 5 x + 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$11.9052680037$ |
$20.620529060204074$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$17.7972677375$ |
6.2.2847312.2 |
$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} - 2 x^{2} + 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{4}\cdot 13^{3}$ |
$3$ |
$11.9052680037$ |
$31.200628666555602$ |
|
|
|
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$16.4690464425$ |
6.2.2888000.2 |
$x^{6} - x^{5} - 3 x^{4} + 8 x^{3} - 5 x^{2} - 7 x + 11$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{3}\cdot 19^{2}$ |
$3$ |
$11.9334549556$ |
$45.0331572624958$ |
|
|
|
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$11.2508342366$ |
6.0.2958147.3 |
$x^{6} - x^{5} + 11 x^{4} - 8 x^{3} + 34 x^{2} - 15 x + 21$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 331^{2}$ |
$2$ |
$11.9812820497$ |
$31.51190251317746$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$6$ |
$2$ |
$22.0136207743$ |
6.0.3359232.3 |
$x^{6} - 2 x^{3} + 3$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 3^{8}$ |
$2$ |
$12.2378934159$ |
$27.05790946495165$ |
|
|
✓ |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$2$ |
$20.0773038392$ |
6.2.3403125.1 |
$x^{6} - x^{5} + 5 x^{4} + 9 x - 9$ |
$6$ |
[2,2] |
$3^{2}\cdot 5^{5}\cdot 11^{2}$ |
$3$ |
$12.2644002947$ |
$32.7564946789548$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$2$ |
$3$ |
$8.45816079277$ |