| 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 |
| 6.0.85184.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 2$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 11^{3}$ |
$2$ |
$6.63324958071$ |
$13.559578056516557$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$1.3029280043$ |
| 6.0.109744.1 |
$x^{6} - x^{5} + 2 x^{4} + x^{3} + 2 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 19^{3}$ |
$2$ |
$6.9193207684$ |
$14.446141500988903$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$1.52875462561$ |
| 6.0.205379.2 |
$x^{6} - 2 x^{5} + 2 x^{4} + 2 x^{3} - 2 x^{2} + x + 2$ |
$6$ |
[0,3] |
$-\,59^{3}$ |
$1$ |
$7.68114574787$ |
$21.288203285487665$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$3.35280923175$ |
| 6.0.268119.1 |
$x^{6} + 4 x^{4} - 3 x^{3} + 8 x^{2} - 5 x + 3$ |
$6$ |
[0,3] |
$-\,3^{2}\cdot 31^{3}$ |
$2$ |
$8.03010575986$ |
$22.755265011491122$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$2.50844731734$ |
| 6.0.304175.1 |
$x^{6} - 3 x^{5} + 7 x^{4} - 9 x^{3} + 13 x^{2} - 9 x + 11$ |
$6$ |
[0,3] |
$-\,5^{2}\cdot 23^{3}$ |
$2$ |
$8.20075654918$ |
$23.48447625945622$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$1.53372978314$ |
| 6.0.596183.1 |
$x^{6} - 2 x^{5} + 3 x^{4} + 4 x^{3} + 2 x^{2} - 6 x + 25$ |
$6$ |
[0,3] |
$-\,7^{2}\cdot 23^{3}$ |
$2$ |
$9.17409566827$ |
$27.787207043050365$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$3.19318980921$ |
| 6.0.658503.2 |
$x^{6} - 3 x^{5} + 5 x^{4} - 5 x^{3} + x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 29^{3}$ |
$2$ |
$9.32737905309$ |
$21.645076535339435$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$1.99694638495$ |
| 6.0.686000.2 |
$x^{6} - x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{3}\cdot 7^{3}$ |
$3$ |
$9.39119127122$ |
$22.84218775885815$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$3.89654357502$ |
| 6.0.778688.1 |
$x^{6} + 3 x^{4} + 8 x^{2} + 23$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{3}$ |
$2$ |
$9.59166304663$ |
$13.564659966250536$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$1.869536401$ |
| 6.0.778688.2 |
$x^{6} + x^{4} + 23$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{3}$ |
$2$ |
$9.59166304663$ |
$29.705773854413227$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$2.62714841936$ |
| 6.0.778688.3 |
$x^{6} + 8 x^{4} + 23 x^{2} + 23$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 23^{3}$ |
$2$ |
$9.59166304663$ |
$29.705773854413227$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$3.11321197886$ |
| 6.2.810448.1 |
$x^{6} - 3 x^{5} + 6 x^{4} - 7 x^{3} + 2 x^{2} + x - 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 37^{3}$ |
$2$ |
$9.65578363947$ |
$23.81430748424474$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$3$ |
$3.83081054963$ |
| 6.0.1043504.1 |
$x^{6} - x^{5} + 2 x^{4} - 7 x^{3} + 4 x^{2} - 7 x + 19$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 11^{3}$ |
$3$ |
$10.0712262622$ |
$25.367647698351508$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$2.90302198149$ |
| 6.0.1080000.1 |
$x^{6} - 2 x^{5} + x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 5^{4}$ |
$3$ |
$10.1290945696$ |
$14.963135389464592$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$6.88127956141$ |
| 6.0.1225043.2 |
$x^{6} - 2 x^{5} + x^{4} - 2 x^{3} + 5 x^{2} - 2 x + 4$ |
$6$ |
[0,3] |
$-\,107^{3}$ |
$1$ |
$10.3440804328$ |
$33.26885339635829$ |
|
|
|
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$6.34536325041$ |
| 6.0.1272112.2 |
$x^{6} - x^{5} + 2 x^{4} - 3 x^{3} + 10 x^{2} - 13 x + 5$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 43^{3}$ |
$2$ |
$10.4092848117$ |
$26.65557193897237$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$5.89926571325$ |
| 6.0.1280000.1 |
$x^{6} - x^{4} + 2 x^{2} + 2$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 5^{4}$ |
$2$ |
$10.4200146192$ |
$19.670368273611786$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$6.10314271143$ |
| 6.0.1362944.1 |
$x^{6} + 3 x^{4} + 11 x^{2} + 11$ |
$6$ |
[0,3] |
$-\,2^{10}\cdot 11^{3}$ |
$2$ |
$10.5296273624$ |
$27.119156113033114$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$5.16663240464$ |
| 6.0.1362944.2 |
$x^{6} + 7 x^{4} + 15 x^{2} + 11$ |
$6$ |
[0,3] |
$-\,2^{10}\cdot 11^{3}$ |
$2$ |
$10.5296273624$ |
$14.891141822623867$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$3.28744265772$ |
| 6.0.1472207.1 |
$x^{6} - x^{5} + 10 x^{4} - 13 x^{3} + 38 x^{2} - 32 x + 40$ |
$6$ |
[0,3] |
$-\,11^{2}\cdot 23^{3}$ |
$2$ |
$10.6658338256$ |
$34.833107461122644$ |
|
|
? |
$S_4$ (as 6T8) |
$[3]$ |
$2$ |
$2$ |
$1.88006056175$ |
| 6.0.1906624.1 |
$x^{6} + 9 x^{4} + 28 x^{2} + 31$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 31^{3}$ |
$2$ |
$11.1355287257$ |
$15.748015748023622$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$3.48399256122$ |
| 6.0.1906624.2 |
$x^{6} - 3 x^{4} + 31$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 31^{3}$ |
$2$ |
$11.1355287257$ |
$37.15919215997363$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$4.14615966242$ |
| 6.0.1906624.3 |
$x^{6} + x^{4} + 31$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 31^{3}$ |
$2$ |
$11.1355287257$ |
$37.15919215997363$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$7.58972973504$ |
| 6.0.1929375.1 |
$x^{6} - 3 x^{5} + 4 x^{4} - 3 x^{3} + 8 x^{2} - 2 x + 3$ |
$6$ |
[0,3] |
$-\,3^{2}\cdot 5^{4}\cdot 7^{3}$ |
$3$ |
$11.1575654001$ |
$21.795365695370254$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$8.58786924773$ |
| 6.0.2122416.2 |
$x^{6} - x^{5} + 4 x^{4} - 5 x^{3} + 4 x^{2} - x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 17^{3}$ |
$3$ |
$11.336311$ |
$30.2945353545942$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$5.99070132357$ |
| 6.0.2239488.1 |
$x^{6} + 3 x^{4} + 3 x^{2} + 3$ |
$6$ |
[0,3] |
$-\,2^{10}\cdot 3^{7}$ |
$2$ |
$11.438211516$ |
$16.17607385516733$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$6.37541787273$ |
| 6.0.2255067.1 |
$x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 12 x^{2} - 5 x + 2$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 17^{4}$ |
$2$ |
$11.4514348937$ |
$15.070935874553902$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$21.3442129741$ |
| 6.0.2685619.2 |
$x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} + x^{2} - 6 x + 4$ |
$6$ |
[0,3] |
$-\,139^{3}$ |
$1$ |
$11.7898261226$ |
$40.48191980421225$ |
|
|
|
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$8.96268009572$ |
| 6.0.2744000.1 |
$x^{6} + 5 x^{4} - 2 x^{3} + 5 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{3}\cdot 7^{3}$ |
$3$ |
$11.8321595662$ |
$21.602807404215152$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$4.27747389474$ |
| 6.0.2744000.2 |
$x^{6} + 2 x^{4} - 6 x^{3} + 8 x^{2} - 6 x + 2$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{3}\cdot 7^{3}$ |
$3$ |
$11.8321595662$ |
$19.85995155932405$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$6.01144043422$ |
| 6.2.3241792.1 |
$x^{6} + x^{4} - 4 x^{3} + 7 x^{2} - 2 x - 5$ |
$6$ |
[2,2] |
$2^{6}\cdot 37^{3}$ |
$2$ |
$12.1655250606$ |
$33.678516622742016$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$3$ |
$15.6308880782$ |
| 6.2.3241792.2 |
$x^{6} + x^{4} - 12 x^{3} - 9 x^{2} - 6 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 37^{3}$ |
$2$ |
$12.1655250606$ |
$13.655340178276088$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$3$ |
$8.04483567198$ |
| 6.0.3499200.4 |
$x^{6} - 6 x^{4} - 4 x^{3} + 12 x^{2} + 18 x + 10$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{7}\cdot 5^{2}$ |
$3$ |
$12.321439841$ |
$18.08540037460562$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$8.01244437977$ |
| 6.0.3516263.1 |
$x^{6} - 3 x^{5} + 13 x^{4} - 15 x^{3} + 51 x^{2} - 43 x + 133$ |
$6$ |
[0,3] |
$-\,17^{2}\cdot 23^{3}$ |
$2$ |
$12.3314333078$ |
$43.3032345860592$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$6.87299149023$ |
| 6.0.3599024.1 |
$x^{6} - x^{5} + 2 x^{4} + 7 x^{3} + 4 x^{2} - 7 x + 41$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 11^{3}\cdot 13^{2}$ |
$3$ |
$12.379339033$ |
$34.57027655313122$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$7.2499916206$ |
| 6.0.3604711.1 |
$x^{6} - x^{5} + x^{4} + x^{3} + 29 x^{2} - 61 x + 81$ |
$6$ |
[0,3] |
$-\,11^{2}\cdot 31^{3}$ |
$2$ |
$12.3825970919$ |
$18.466185312619388$ |
|
|
? |
$S_4$ (as 6T8) |
$[4]$ |
$2$ |
$2$ |
$2.66678957171$ |
| 6.0.3950784.1 |
$x^{6} + x^{4} - 6 x^{3} + 5 x^{2} + 16 x + 9$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 19^{3}$ |
$3$ |
$12.5732402567$ |
$16.948805249221287$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$9.02344376484$ |
| 6.0.3950784.2 |
$x^{6} + 3 x^{4} - 2 x^{3} + 9 x^{2} + 12 x + 23$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{2}\cdot 19^{3}$ |
$3$ |
$12.5732402567$ |
$35.3856754294667$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$5.18901599535$ |
| 6.0.4148928.2 |
$x^{6} - 2 x^{5} + 8 x^{4} - 18 x^{3} + 24 x^{2} - 18 x + 6$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 7^{4}$ |
$3$ |
$12.6762068204$ |
$18.725839469079336$ |
|
|
? |
$S_4$ (as 6T8) |
$[3]$ |
$2$ |
$2$ |
$7.01009779079$ |
| 6.0.4174016.1 |
$x^{6} - 2 x^{5} + 12 x^{4} - 14 x^{3} + 36 x^{2} - 22 x + 38$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7^{2}\cdot 11^{3}$ |
$3$ |
$12.6889499661$ |
$19.699129000227927$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$5.25117013555$ |
| 6.0.4392287.1 |
$x^{6} - x^{5} - x^{4} - 7 x^{3} - 17 x^{2} + 77 x + 121$ |
$6$ |
[0,3] |
$-\,19^{2}\cdot 23^{3}$ |
$2$ |
$12.7972047438$ |
$20.904544960366874$ |
|
|
? |
$S_4$ (as 6T8) |
$[4]$ |
$2$ |
$2$ |
$2.31676098288$ |
| 6.0.4478976.1 |
$x^{6} + 3 x^{4} + 6 x^{2} + 6$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 3^{7}$ |
$2$ |
$12.8389583272$ |
$24.23672593327708$ |
|
|
|
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$21.3626103869$ |
| 6.0.4499456.1 |
$x^{6} - x^{5} + 5 x^{4} - 6 x^{3} + 17 x^{2} + 5 x + 1$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 13^{3}$ |
$2$ |
$12.848724038$ |
$24.255161140409015$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$6.7725321598$ |
| 6.0.4499456.2 |
$x^{6} - x^{5} - 7 x^{4} + 2 x^{3} + 25 x^{2} + 29 x + 13$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 13^{3}$ |
$2$ |
$12.848724038$ |
$46.05640148399133$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$12.2059111798$ |
| 6.0.4499456.3 |
$x^{6} + 4 x^{4} + 13 x^{2} + 26$ |
$6$ |
[0,3] |
$-\,2^{11}\cdot 13^{3}$ |
$2$ |
$12.848724038$ |
$27.385300168092183$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$9.79762364234$ |
| 6.0.5034679.1 |
$x^{6} - x^{5} + 12 x^{4} - 3 x^{3} + 48 x^{2} + 4 x + 88$ |
$6$ |
[0,3] |
$-\,13^{2}\cdot 31^{3}$ |
$2$ |
$13.0916774794$ |
$47.368861483262386$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$7.90739633571$ |
| 6.0.5088448.1 |
$x^{6} - 2 x^{5} + 4 x^{4} + 10 x^{3} - 2 x + 10$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 43^{3}$ |
$2$ |
$13.1148770486$ |
$14.720951755301632$ |
|
|
? |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$14.1028494106$ |
| 6.0.5088448.2 |
$x^{6} - 2 x^{5} + 2 x^{4} + 4 x^{3} - 4 x^{2} + 2 x + 6$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 43^{3}$ |
$2$ |
$13.1148770486$ |
$37.69667134890642$ |
|
|
✓ |
$S_4$ (as 6T8) |
$[2]$ |
$2$ |
$2$ |
$9.17258214096$ |
| 6.0.5120000.1 |
$x^{6} + 4 x^{4} + 7 x^{2} + 2$ |
$6$ |
[0,3] |
$-\,2^{13}\cdot 5^{4}$ |
$2$ |
$13.1283957589$ |
$19.670368273611786$ |
|
|
✓ |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$22.0757111746$ |
| 6.0.5120000.2 |
$x^{6} - 4 x^{4} + 2 x^{2} + 8$ |
$6$ |
[0,3] |
$-\,2^{13}\cdot 5^{4}$ |
$2$ |
$13.1283957589$ |
$23.39214190570293$ |
|
|
? |
$S_4$ (as 6T8) |
trivial |
$2$ |
$2$ |
$20.913364343$ |
