| 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 |
| 6.2.287296.2 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{3} + 2 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 67^{2}$ |
$2$ |
$8.12309620089$ |
$23.15167380558045$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$2.67502842472$ |
| 6.2.341056.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 3 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 73^{2}$ |
$2$ |
$8.35867839276$ |
$24.166091947189145$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$3.12548344321$ |
| 6.2.426409.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - x^{3} - 2 x^{2} + x - 2$ |
$6$ |
[2,2] |
$653^{2}$ |
$1$ |
$8.67569735858$ |
$25.553864678361276$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$5.12057992032$ |
| 6.2.678976.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} + x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 103^{2}$ |
$2$ |
$9.37509629531$ |
$28.705400188814647$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$3.5916864468$ |
| 6.2.732736.3 |
$x^{6} - 2 x^{5} - 2 x^{4} + 6 x^{3} + x^{2} - 6 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 107^{2}$ |
$2$ |
$9.49491879705$ |
$29.257477676655586$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$4.90420269496$ |
| 6.2.1000000.1 |
$x^{6} - 2 x^{5} - 5 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{6}$ |
$2$ |
$10.0$ |
$22.91954538992328$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$6.41869647304$ |
| 6.2.1125721.1 |
$x^{6} - x^{5} + x^{4} + 3 x^{3} - 5 x^{2} + 5 x - 3$ |
$6$ |
[2,2] |
$1061^{2}$ |
$1$ |
$10.1993335461$ |
$32.57299494980466$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$6.58504721467$ |
| 6.2.1132096.1 |
$x^{6} - 2 x^{5} + x^{4} - 4 x^{3} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{2}\cdot 19^{2}$ |
$3$ |
$10.208937444$ |
$32.61901286060018$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$6.31800868473$ |
| 6.2.1784896.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 6 x^{3} + 2 x^{2} - 6 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 167^{2}$ |
$2$ |
$11.0137568928$ |
$36.55133376499413$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$8.03425745514$ |
| 6.2.1907161.1 |
$x^{6} - x^{5} + x^{4} - 7 x^{3} - 7 x^{2} - x + 1$ |
$6$ |
[2,2] |
$1381^{2}$ |
$1$ |
$11.136051384$ |
$37.16180835212409$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$7.31625255109$ |
| 6.2.1993744.1 |
$x^{6} - x^{5} - 3 x^{4} + x^{3} + 4 x + 4$ |
$6$ |
[2,2] |
$2^{4}\cdot 353^{2}$ |
$2$ |
$11.2187610729$ |
$29.824558022304043$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$21.1057316431$ |
| 6.2.2005056.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} - 5 x^{2} - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{2}\cdot 59^{2}$ |
$3$ |
$11.229344816$ |
$37.62977544445356$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$10.8918966152$ |
| 6.2.2271049.1 |
$x^{6} - x^{5} - 3 x^{4} - x^{3} - x^{2} - 3 x - 1$ |
$6$ |
[2,2] |
$11^{2}\cdot 137^{2}$ |
$2$ |
$11.4649214639$ |
$38.82009788756334$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
$[2]$ |
$2$ |
$3$ |
$5.32310274652$ |
| 6.2.2334784.1 |
$x^{6} + 2 x^{4} - 2 x^{3} + 5 x^{2} + 6 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 191^{2}$ |
$2$ |
$11.517930441$ |
$39.08964057138413$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$7.55859600808$ |
| 6.2.2383936.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 4 x^{3} + 4 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 193^{2}$ |
$2$ |
$11.5579931303$ |
$39.293765408777$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$6.26546656622$ |
| 6.2.2411809.1 |
$x^{6} - x^{5} - 3 x^{4} + 4 x^{2} + 1$ |
$6$ |
[2,2] |
$1553^{2}$ |
$1$ |
$11.5804068771$ |
$39.408120990476064$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$12.4081255624$ |
| 6.2.2572816.1 |
$x^{6} - x^{5} - x^{4} + 3 x^{3} - 4 x^{2} + 2 x - 2$ |
$6$ |
[2,2] |
$2^{4}\cdot 401^{2}$ |
$2$ |
$11.7058095676$ |
$31.787681293477327$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$21.3302940596$ |
| 6.2.2640625.1 |
$x^{6} - x^{5} - 5 x^{4} - 5 x^{3} + 3 x + 2$ |
$6$ |
[2,2] |
$5^{6}\cdot 13^{2}$ |
$2$ |
$11.7566734386$ |
$29.21680229647359$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.2880210209$ |
| 6.2.2676496.1 |
$x^{6} - x^{5} + x^{4} + x^{3} - 4 x^{2} + 2 x - 2$ |
$6$ |
[2,2] |
$2^{4}\cdot 409^{2}$ |
$2$ |
$11.7831416835$ |
$32.10319951054733$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$26.0842699598$ |
| 6.2.2689600.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + 4 x^{3} - 11 x^{2} + 10 x - 5$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{2}\cdot 41^{2}$ |
$3$ |
$11.7927370799$ |
$40.496913462633174$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$8.94388407599$ |
| 6.2.2849344.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 3 x^{2} - 2 x - 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 211^{2}$ |
$2$ |
$11.9066836263$ |
$41.08527716834828$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$12.2769288583$ |
| 6.2.2903616.1 |
$x^{6} + 2 x^{4} - 2 x^{3} - 7 x^{2} - 6 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{2}\cdot 71^{2}$ |
$3$ |
$11.9441852397$ |
$41.27953488110059$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.2105809829$ |
| 6.2.3003289.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + x^{3} - 5 x^{2} + 4 x - 3$ |
$6$ |
[2,2] |
$1733^{2}$ |
$1$ |
$12.0115629287$ |
$41.6293165929973$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$18.0151298435$ |
| 6.2.3125824.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} - 3 x^{2} + 2 x - 7$ |
$6$ |
[2,2] |
$2^{6}\cdot 13^{2}\cdot 17^{2}$ |
$3$ |
$12.091887192$ |
$42.04759208325728$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$10.9160096532$ |
| 6.2.3272481.2 |
$x^{6} - 3 x^{5} + 3 x^{4} + 4 x^{3} - 12 x^{2} + 12 x - 3$ |
$6$ |
[2,2] |
$3^{6}\cdot 67^{2}$ |
$2$ |
$12.1846443013$ |
$29.49027790468186$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$23.0995851531$ |
| 6.2.3794704.1 |
$x^{6} - x^{5} - x^{4} - x^{3} - 2 x^{2} + 2 x + 6$ |
$6$ |
[2,2] |
$2^{4}\cdot 487^{2}$ |
$2$ |
$12.4890570897$ |
$35.030887836273955$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
$[2]$ |
$2$ |
$3$ |
$16.7370942797$ |
| 6.2.4116841.1 |
$x^{6} - x^{5} - x^{4} + 5 x^{3} - 5 x^{2} + 3 x + 1$ |
$6$ |
[2,2] |
$2029^{2}$ |
$1$ |
$12.6598146998$ |
$45.044422518220834$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.0027241748$ |
| 6.2.4214809.1 |
$x^{6} - 2 x^{4} - 3 x^{3} - 7 x + 4$ |
$6$ |
[2,2] |
$2053^{2}$ |
$1$ |
$12.709534659$ |
$45.31004303683677$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$15.7136307326$ |
| 6.2.4338889.1 |
$x^{6} - 2 x^{5} + x^{4} - x^{3} + 2 x^{2} + 4 x + 1$ |
$6$ |
[2,2] |
$2083^{2}$ |
$1$ |
$12.771142673$ |
$45.639894828976104$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
$[2]$ |
$2$ |
$3$ |
$11.3327900133$ |
| 6.2.4494400.1 |
$x^{6} - 2 x^{5} - 2 x^{3} + 5 x^{2} + 2 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{2}\cdot 53^{2}$ |
$3$ |
$12.8463165771$ |
$46.04345773288535$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.4613040851$ |
| 6.2.4840000.1 |
$x^{6} - 2 x^{5} - 3 x^{4} + 4 x^{3} + 6 x^{2} - 8 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 5^{4}\cdot 11^{2}$ |
$3$ |
$13.0059144685$ |
$27.42971776263377$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$17.4143397661$ |
| 6.2.4950625.2 |
$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} + x^{2} - 9 x + 8$ |
$6$ |
[2,2] |
$5^{4}\cdot 89^{2}$ |
$2$ |
$13.0549938561$ |
$27.585128172099004$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$27.2511423383$ |
| 6.2.5058001.1 |
$x^{6} - 2 x^{5} - 3 x^{3} + 4 x^{2} + 7 x + 2$ |
$6$ |
[2,2] |
$13^{2}\cdot 173^{2}$ |
$2$ |
$13.1017653935$ |
$47.4236228055175$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$24.4337513794$ |
| 6.2.5094049.1 |
$x^{6} - 2 x^{5} + x^{4} - 5 x^{3} + 2 x^{2} + 4 x + 1$ |
$6$ |
[2,2] |
$37^{2}\cdot 61^{2}$ |
$2$ |
$13.1172819325$ |
$47.50789408087881$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$18.5736774623$ |
| 6.2.5257849.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - x^{3} - 5 x^{2} + 3 x + 1$ |
$6$ |
[2,2] |
$2293^{2}$ |
$1$ |
$13.186656243$ |
$47.885279575251516$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.7779214614$ |
| 6.2.5271616.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 8 x^{3} + 7 x^{2} - 4 x - 5$ |
$6$ |
[2,2] |
$2^{6}\cdot 7^{2}\cdot 41^{2}$ |
$3$ |
$13.1924045682$ |
$47.916594202843754$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$16.021877389$ |
| 6.2.5326864.1 |
$x^{6} - x^{5} - x^{4} - x^{3} - 2 x^{2} - 2$ |
$6$ |
[2,2] |
$2^{4}\cdot 577^{2}$ |
$2$ |
$13.2153479267$ |
$38.13068176126259$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$36.9207009926$ |
| 6.2.5345344.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 4 x^{2} + 4 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 17^{4}$ |
$2$ |
$13.2229780369$ |
$18.700114874768015$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$15.6591494173$ |
| 6.2.5419584.1 |
$x^{6} - 2 x^{5} - 4 x^{4} + 6 x^{3} + 9 x^{2} - 18 x + 9$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{2}\cdot 97^{2}$ |
$3$ |
$13.253410775$ |
$48.249352327259274$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$19.7437923939$ |
| 6.2.5721664.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 8 x^{3} - 6 x - 17$ |
$6$ |
[2,2] |
$2^{6}\cdot 13^{2}\cdot 23^{2}$ |
$3$ |
$13.373766154$ |
$48.908077042549934$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$16.8272084374$ |
| 6.2.6031936.3 |
$x^{6} - 4 x^{4} - 2 x^{3} + 5 x^{2} + 8 x + 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 307^{2}$ |
$2$ |
$13.4919934234$ |
$49.558046773455466$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.9345426299$ |
| 6.2.6270016.1 |
$x^{6} - 2 x^{5} - 8 x^{3} + 19 x^{2} - 8 x - 3$ |
$6$ |
[2,2] |
$2^{6}\cdot 313^{2}$ |
$2$ |
$13.5793226729$ |
$50.039984012787215$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$18.4361063166$ |
| 6.2.6270016.2 |
$x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + 5 x^{2} + 4 x - 2$ |
$6$ |
[2,2] |
$2^{6}\cdot 313^{2}$ |
$2$ |
$13.5793226729$ |
$50.039984012787215$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$39.4151141486$ |
| 6.2.6661561.1 |
$x^{6} - 2 x^{5} + 5 x^{4} - 3 x^{3} + x^{2} + x - 2$ |
$6$ |
[2,2] |
$29^{2}\cdot 89^{2}$ |
$2$ |
$13.7171114796$ |
$50.80354318352215$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$27.1010615486$ |
| 6.2.6806881.1 |
$x^{6} - 3 x^{5} + x^{4} + 3 x^{3} + x^{2} + 3 x - 13$ |
$6$ |
[2,2] |
$2609^{2}$ |
$1$ |
$13.766536578$ |
$51.07837115648854$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$14.5369021532$ |
| 6.2.6974881.1 |
$x^{6} - x^{5} - 2 x^{4} - 13 x^{3} - 7 x^{2} - x + 1$ |
$6$ |
[2,2] |
$19^{2}\cdot 139^{2}$ |
$2$ |
$13.8225912961$ |
$51.39066063011839$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$21.1073942656$ |
| 6.2.7011904.3 |
$x^{6} - 2 x^{5} + x^{4} + 2 x^{2} + 4 x + 1$ |
$6$ |
[2,2] |
$2^{6}\cdot 331^{2}$ |
$2$ |
$13.8347928332$ |
$51.45872132107443$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$18.5141277548$ |
| 6.2.7123561.1 |
$x^{6} - x^{5} + 3 x^{4} + 3 x^{3} + 8 x^{2} + 7 x - 2$ |
$6$ |
[2,2] |
$17^{2}\cdot 157^{2}$ |
$2$ |
$13.8712689153$ |
$51.66236541235796$ |
|
|
? |
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$19.8951698865$ |
| 6.2.7139584.1 |
$x^{6} - 2 x^{4} - 4 x^{3} - 3 x^{2} - 4 x + 8$ |
$6$ |
[2,2] |
$2^{8}\cdot 167^{2}$ |
$2$ |
$13.8764641476$ |
$51.69139193328034$ |
|
|
|
$\PSL(2,5)$ (as 6T12) |
trivial |
$2$ |
$3$ |
$73.5673001093$ |
| 6.2.7327849.1 |
$x^{6} - x^{5} + x^{4} - 5 x^{3} + 3 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$2707^{2}$ |
$1$ |
$13.9367898651$ |
$52.028838157314254$ |
|
|
✓ |
$\PSL(2,5)$ (as 6T12) |
$[2]$ |
$2$ |
$3$ |
$7.39120528062$ |
