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 |
6.2.287296.1 |
$x^{6} - 2 x^{4} + x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 67^{2}$ |
$2$ |
$8.12309620089$ |
$46.65822308917137$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$2.66813409643$ |
6.2.613089.1 |
$x^{6} - 3 x^{3} - 3 x + 4$ |
$6$ |
[2,2] |
$3^{6}\cdot 29^{2}$ |
$2$ |
$9.21695047706$ |
$43.411061746661886$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$5.16689103695$ |
6.2.678976.2 |
$x^{6} - 2 x^{5} + x^{4} + 4 x^{3} - 8 x^{2} + 6 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 103^{2}$ |
$2$ |
$9.37509629531$ |
$62.14933365424415$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$4.78847334648$ |
6.2.700569.1 |
$x^{6} - x^{3} - 3 x^{2} - 1$ |
$6$ |
[2,2] |
$3^{6}\cdot 31^{2}$ |
$2$ |
$9.42414195717$ |
$45.38470726494543$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$5.79814154368$ |
6.2.817216.1 |
$x^{6} - x^{5} + 2 x^{4} - 5 x^{3} + 4 x^{2} - 7 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 113^{2}$ |
$2$ |
$9.66917625422$ |
$66.10951268092151$ |
|
|
|
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$5.01110117014$ |
6.2.1002001.1 |
$x^{6} - x^{5} + 3 x^{3} - 5 x^{2} + 3 x - 2$ |
$6$ |
[2,2] |
$7^{2}\cdot 11^{2}\cdot 13^{2}$ |
$3$ |
$10.0033322228$ |
$72.35019594505421$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$7.4773629989$ |
6.2.1083681.1 |
$x^{6} - x^{5} + x^{4} + x^{3} - 4 x^{2} + 2 x - 1$ |
$6$ |
[2,2] |
$3^{2}\cdot 347^{2}$ |
$2$ |
$10.1348403037$ |
$85.52904258589746$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$5.55519154978$ |
6.2.1087849.1 |
$x^{6} - x^{5} + 2 x^{4} - 3 x^{2} + 2 x - 4$ |
$6$ |
[2,2] |
$7^{2}\cdot 149^{2}$ |
$2$ |
$10.1413266033$ |
$44.66751866436731$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$7.27153589404$ |
6.2.1108809.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - 3 x^{2} + 3 x + 2$ |
$6$ |
[2,2] |
$3^{8}\cdot 13^{2}$ |
$2$ |
$10.173634329$ |
$52.890557812781545$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$11.3653259027$ |
6.2.1597696.2 |
$x^{6} - 3 x^{5} - x^{4} + 4 x^{3} + 2 x^{2} - 2 x - 2$ |
$6$ |
[2,2] |
$2^{8}\cdot 79^{2}$ |
$2$ |
$10.8122403515$ |
$82.66399398860597$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$10.9265768621$ |
6.2.1658944.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - 8 x^{2} + 4 x + 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{2}\cdot 23^{2}$ |
$3$ |
$10.8802436508$ |
$49.63723766902059$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$13.7028740673$ |
6.2.1679616.2 |
$x^{6} - 3 x^{5} + 3 x^{4} - 6 x^{2} + 6 x - 2$ |
$6$ |
[2,2] |
$2^{8}\cdot 3^{8}$ |
$2$ |
$10.902723557$ |
$31.655357399783927$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$12.2562739075$ |
6.2.1871424.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 10 x^{3} - 6 x^{2} - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$11.1009982058$ |
$87.1382968205312$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$10.9132906552$ |
6.2.1871424.2 |
$x^{6} - 3 x^{5} + 5 x^{4} - 4 x^{3} - 4 x + 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{4}\cdot 19^{2}$ |
$3$ |
$11.1009982058$ |
$53.34374068187387$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$14.6721654669$ |
6.2.1971216.1 |
$x^{6} - 3 x^{5} + 3 x^{4} - 2$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{6}\cdot 13^{2}$ |
$3$ |
$11.1975334705$ |
$37.22560348698383$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$13.6737422635$ |
6.2.2286144.1 |
$x^{6} + 3 x^{4} - 4 x^{3} - 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{6}\cdot 7^{2}$ |
$3$ |
$11.4775870966$ |
$47.60056374127741$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$14.9234969276$ |
6.2.2471184.1 |
$x^{6} - x^{5} + 5 x^{4} - 6 x^{3} + 7 x^{2} - x - 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{2}\cdot 131^{2}$ |
$3$ |
$11.6274419659$ |
$100.29435415357345$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$15.4726734134$ |
6.2.2845969.1 |
$x^{6} - x^{5} + x^{4} - 5 x^{3} - 2 x^{2} + x - 4$ |
$6$ |
[2,2] |
$7^{2}\cdot 241^{2}$ |
$2$ |
$11.904331921$ |
$56.80770110941843$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$15.9544033446$ |
6.2.3013696.1 |
$x^{6} - 2 x^{5} + x^{4} - 2 x^{3} - x^{2} + 6 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{2}\cdot 31^{2}$ |
$3$ |
$12.0184900138$ |
$45.73842460452808$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$14.0084437346$ |
6.2.3083536.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 6 x^{3} - 3 x^{2} - 8 x - 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 439^{2}$ |
$2$ |
$12.0644678526$ |
$115.52421048794992$ |
|
|
|
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$14.9184503823$ |
6.2.3272481.1 |
$x^{6} - 3 x^{4} - 5 x^{3} + 9 x^{2} + 3 x - 4$ |
$6$ |
[2,2] |
$3^{6}\cdot 67^{2}$ |
$2$ |
$12.1846443013$ |
$75.86677290064749$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$15.1606381841$ |
6.2.3370896.1 |
$x^{6} - 6 x^{4} - 2 x^{3} + 9 x^{2} - 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{6}\cdot 17^{2}$ |
$3$ |
$12.2449653058$ |
$68.26048219990749$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$16.9372811434$ |
6.2.3381921.1 |
$x^{6} - x^{5} - x^{4} + 3 x^{3} + 4 x^{2} - x - 1$ |
$6$ |
[2,2] |
$3^{2}\cdot 613^{2}$ |
$2$ |
$12.2516310476$ |
$124.98779613609612$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$14.2162130692$ |
6.2.3674889.1 |
$x^{6} + 3 x^{4} - 2 x^{3} - 6 x^{2} + 3 x + 2$ |
$6$ |
[2,2] |
$3^{6}\cdot 71^{2}$ |
$2$ |
$12.4224532483$ |
$78.85707097103246$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$20.5775327677$ |
6.2.3936256.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 8 x^{3} - 2 x^{2} - 4 x + 4$ |
$6$ |
[2,2] |
$2^{12}\cdot 31^{2}$ |
$2$ |
$12.5655226096$ |
$66.38555910891195$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$34.1913245317$ |
6.2.4322241.1 |
$x^{6} - 3 x^{4} - 7 x^{3} + 12 x + 8$ |
$6$ |
[2,2] |
$3^{6}\cdot 7^{2}\cdot 11^{2}$ |
$3$ |
$12.7629625953$ |
$83.2393907385606$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$10.9710331682$ |
6.2.4380649.1 |
$x^{6} - x^{3} + x^{2} + 8 x + 4$ |
$6$ |
[2,2] |
$7^{2}\cdot 13^{2}\cdot 23^{2}$ |
$3$ |
$12.7915471535$ |
$118.30319640710158$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$11.2562630426$ |
6.2.4468996.1 |
$x^{6} - 2 x^{5} + x^{4} - 7 x^{3} + 8 x^{2} + 15 x - 18$ |
$6$ |
[2,2] |
$2^{2}\cdot 7^{2}\cdot 151^{2}$ |
$3$ |
$12.8341859594$ |
$71.37955412067545$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$32.9468803358$ |
6.2.4665600.1 |
$x^{6} - 3 x^{5} + 3 x^{4} + 4 x^{3} - 6 x^{2} - 6 x + 2$ |
$6$ |
[2,2] |
$2^{8}\cdot 3^{6}\cdot 5^{2}$ |
$3$ |
$12.9266081402$ |
$60.378187187262796$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$24.5839184171$ |
6.2.4700224.1 |
$x^{6} - x^{5} - 7 x^{4} + 8 x^{3} + 7 x^{2} - 7 x + 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 271^{2}$ |
$2$ |
$12.9425472539$ |
$118.447124166229$ |
|
|
|
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$19.8570491795$ |
6.2.4717584.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + 4 x^{2} + 4 x - 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{2}\cdot 181^{2}$ |
$3$ |
$12.9505021098$ |
$87.97643127781974$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$32.1657293542$ |
6.2.4721929.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 7 x^{3} + 4 x^{2} - 8 x - 3$ |
$6$ |
[2,2] |
$41^{2}\cdot 53^{2}$ |
$2$ |
$12.9524892975$ |
$90.34605106988568$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$24.5998915912$ |
6.2.4765489.2 |
$x^{6} - x^{5} - 2 x^{4} + 4 x^{3} + x^{2} - 6 x - 4$ |
$6$ |
[2,2] |
$37^{2}\cdot 59^{2}$ |
$2$ |
$12.9723277254$ |
$92.18682756148694$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$13.2755245472$ |
6.2.5125696.3 |
$x^{6} - 2 x^{5} - x^{4} + 4 x^{2} - 8 x + 5$ |
$6$ |
[2,2] |
$2^{6}\cdot 283^{2}$ |
$2$ |
$13.1308288547$ |
$121.91840822251436$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$11.4131054516$ |
6.2.5391684.1 |
$x^{6} - 8 x^{3} + 9 x^{2} + 6 x - 4$ |
$6$ |
[2,2] |
$2^{2}\cdot 3^{6}\cdot 43^{2}$ |
$3$ |
$13.2420148873$ |
$89.60537124338641$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$35.2432776775$ |
6.2.5645376.3 |
$x^{6} - 2 x^{3} - 6 x^{2} + 6 x + 2$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{6}\cdot 11^{2}$ |
$3$ |
$13.3438805434$ |
$51.06600236898078$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$19.9514043069$ |
6.2.5953600.1 |
$x^{6} - x^{5} - 5 x^{4} + 2 x^{3} + 2 x^{2} - 4 x + 4$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{2}\cdot 61^{2}$ |
$3$ |
$13.4626309945$ |
$128.15775362157103$ |
|
|
|
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$18.9697847185$ |
6.2.6235009.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 7 x^{3} - 9 x + 4$ |
$6$ |
[2,2] |
$11^{2}\cdot 227^{2}$ |
$2$ |
$13.5666570748$ |
$123.41849533348507$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$22.9657561253$ |
6.2.6305121.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 6 x^{2} + 3 x - 6$ |
$6$ |
[2,2] |
$3^{8}\cdot 31^{2}$ |
$2$ |
$13.5919646883$ |
$53.263548045331994$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$31.6168938284$ |
6.2.6416089.1 |
$x^{6} - x^{5} - 3 x^{3} - x^{2} + x + 2$ |
$6$ |
[2,2] |
$17^{2}\cdot 149^{2}$ |
$2$ |
$13.631544425$ |
$80.70350840661953$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$22.3429302563$ |
6.2.6477025.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 5 x^{3} + 2 x^{2} - 5$ |
$6$ |
[2,2] |
$5^{2}\cdot 509^{2}$ |
$2$ |
$13.6530368444$ |
$142.54878622404607$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$24.2267105193$ |
6.2.6477025.2 |
$x^{6} - x^{5} + 2 x^{4} - 3 x^{2} + 6 x - 4$ |
$6$ |
[2,2] |
$5^{2}\cdot 509^{2}$ |
$2$ |
$13.6530368444$ |
$65.968847074147$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$21.951896796$ |
6.2.6579225.1 |
$x^{6} - 3 x^{5} - 3 x^{4} + 8 x^{3} + 9 x^{2} - 3 x - 4$ |
$6$ |
[2,2] |
$3^{6}\cdot 5^{2}\cdot 19^{2}$ |
$3$ |
$13.6887079062$ |
$58.617219339366585$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$25.6527960065$ |
6.2.6718464.1 |
$x^{6} - 3 x^{4} - 12 x^{3} - 9 x^{2} + 1$ |
$6$ |
[2,2] |
$2^{10}\cdot 3^{8}$ |
$2$ |
$13.7365709106$ |
$31.655357399783927$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$24.4670136709$ |
6.2.6754801.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 9 x^{3} - 4 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$23^{2}\cdot 113^{2}$ |
$2$ |
$13.7489255359$ |
$85.97214828439625$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$28.1695815998$ |
6.2.6801664.2 |
$x^{6} - x^{5} - 5 x^{4} - 2 x^{3} + 12 x^{2} + 10 x + 2$ |
$6$ |
[2,2] |
$2^{8}\cdot 163^{2}$ |
$2$ |
$13.764777501$ |
$119.35805347734977$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$29.5760987849$ |
6.2.6827769.1 |
$x^{6} - x^{5} + 3 x^{4} - 4 x^{3} - 4 x - 1$ |
$6$ |
[2,2] |
$3^{2}\cdot 13^{2}\cdot 67^{2}$ |
$3$ |
$13.7735683946$ |
$78.3839112255464$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$33.5256140266$ |
6.2.6843456.2 |
$x^{6} - 2 x^{5} + 5 x^{4} - 6 x^{3} + 7 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{2}\cdot 109^{2}$ |
$3$ |
$13.778837549$ |
$88.72512521539116$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$26.3086623007$ |
6.2.6885376.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} - 4 x - 2$ |
$6$ |
[2,2] |
$2^{12}\cdot 41^{2}$ |
$2$ |
$13.7928689615$ |
$79.98742682830643$ |
|
|
? |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$45.3416317221$ |
6.2.6953769.1 |
$x^{6} - 2 x^{5} + x^{4} + 3 x^{3} - 9 x^{2} + 9 x - 6$ |
$6$ |
[2,2] |
$3^{4}\cdot 293^{2}$ |
$2$ |
$13.8156093066$ |
$100.5586315449672$ |
|
|
✓ |
$A_6$ (as 6T15) |
trivial |
$2$ |
$3$ |
$36.1907614823$ |