| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 6.4.570152223.1 |
$x^{6} - 2 x^{5} - 8 x^{4} + 22 x^{3} - 46 x^{2} + 48 x - 11$ |
$6$ |
(4, 1) |
$-\,3^{3}\cdot 59\cdot 71^{3}$ |
$3$ |
$28.7959760484$ |
$112.10263154805956$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$4$ |
$310.970044396$ |
| 6.2.733001728.4 |
$x^{6} - 2 x^{5} - 3 x^{4} + 36 x^{3} - 28 x^{2} - 64 x - 28$ |
$6$ |
(2, 2) |
$2^{11}\cdot 71^{3}$ |
$2$ |
$30.0273841271$ |
$56.6841531092392$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$3$ |
$720.471457317$ |
| 6.4.1259846720.1 |
$x^{6} - 2 x^{5} + x^{4} + 34 x^{3} - 34 x^{2} + 5$ |
$6$ |
(4, 1) |
$-\,2^{6}\cdot 5\cdot 11\cdot 71^{3}$ |
$4$ |
$32.8639391865$ |
$124.97999839974395$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$4$ |
$414.252505185$ |
| 6.2.1959920636.1 |
$x^{6} - 6 x^{4} - 21 x^{3} + 9 x^{2} - 8 x - 14$ |
$6$ |
(2, 2) |
$2^{2}\cdot 37^{2}\cdot 71^{3}$ |
$3$ |
$35.375811758$ |
$102.50853622991599$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$612.722561078$ |
| 6.2.2174309325.1 |
$x^{6} - 3 x^{5} + 2 x^{4} - 14 x^{3} + 36 x^{2} - 57 x + 12$ |
$6$ |
(2, 2) |
$3^{5}\cdot 5^{2}\cdot 71^{3}$ |
$3$ |
$35.9931802576$ |
$184.64241745475834$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$950.153431202$ |
| 6.4.3556203696.1 |
$x^{6} - x^{5} - 26 x^{4} + 55 x^{3} + 148 x^{2} - 513 x + 361$ |
$6$ |
(4, 1) |
$-\,2^{4}\cdot 3^{3}\cdot 23\cdot 71^{3}$ |
$4$ |
$39.0688929079$ |
$111.10673448027337$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$4$ |
$485.586898203$ |
| 6.2.3865438800.2 |
$x^{6} - 2 x^{5} - 13 x^{4} + 36 x^{3} + 27 x^{2} - 12 x - 21$ |
$6$ |
(2, 2) |
$2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 71^{3}$ |
$4$ |
$39.615620889$ |
$74.77890718336825$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1809.79792022$ |
| 6.4.4008603200.1 |
$x^{6} - 22 x^{4} - 34 x^{3} + 50 x^{2} + 90 x + 5$ |
$6$ |
(4, 1) |
$-\,2^{6}\cdot 5^{2}\cdot 7\cdot 71^{3}$ |
$4$ |
$39.8564712155$ |
$130.37316023617117$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$4$ |
$2234.07755067$ |
| 6.2.4261646277.2 |
$x^{6} - x^{5} - 10 x^{4} + x^{3} + 25 x^{2} + 40 x - 11$ |
$6$ |
(2, 2) |
$3^{5}\cdot 7^{2}\cdot 71^{3}$ |
$3$ |
$40.2651727445$ |
$167.07077788031484$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$844.641314492$ |
| 6.4.4435591023.2 |
$x^{6} - 15 x^{4} - 17 x^{3} + 3 x^{2} + 21 x + 19$ |
$6$ |
(4, 1) |
$-\,3^{6}\cdot 17\cdot 71^{3}$ |
$3$ |
$40.5345400422$ |
$129.0471646971052$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$4$ |
$865.4820841$ |
| 6.2.5112042813.1 |
$x^{6} - x^{5} - 160 x^{4} + 105 x^{3} + 8481 x^{2} - 3128 x - 148823$ |
$6$ |
(2, 2) |
$3^{3}\cdot 23^{2}\cdot 71^{3}$ |
$3$ |
$41.5048721478$ |
$69.99285677838846$ |
|
|
? |
$D_{6}$ (as 6T3) |
$[7]$ |
$[14]$ |
$2$ |
$3$ |
$47.777738655$ |
| 6.2.5566231872.2 |
$x^{6} + 9 x^{4} - 16 x^{3} - 33 x^{2} - 72 x + 135$ |
$6$ |
(2, 2) |
$2^{6}\cdot 3^{5}\cdot 71^{3}$ |
$3$ |
$42.0978790112$ |
$123.83860464330176$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1437.36383454$ |
| 6.2.6597015552.1 |
$x^{6} - 12 x^{4} - 56 x^{3} + 36 x^{2} + 336 x - 352$ |
$6$ |
(2, 2) |
$2^{11}\cdot 3^{2}\cdot 71^{3}$ |
$3$ |
$43.3069818548$ |
$98.17983316921564$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1890.63263646$ |
| 6.2.7576260048.4 |
$x^{6} - 2 x^{5} + 22 x^{4} - 100 x^{3} + 136 x^{2} - 84 x + 16$ |
$6$ |
(2, 2) |
$2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 71^{3}$ |
$4$ |
$44.3175570222$ |
$67.22995464325413$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$[2, 4]$ |
$2$ |
$3$ |
$375.431012388$ |
| 6.2.8796020736.1 |
$x^{6} - 6 x^{4} - 52 x^{3} + 9 x^{2} + 156 x + 108$ |
$6$ |
(2, 2) |
$2^{13}\cdot 3\cdot 71^{3}$ |
$3$ |
$45.4340070152$ |
$98.17983316921564$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$[6]$ |
$2$ |
$3$ |
$1081.05262325$ |
| 6.2.8813200464.1 |
$x^{6} - 2 x^{5} - x^{4} + 64 x^{3} - 61 x^{2} - 62 x + 109$ |
$6$ |
(2, 2) |
$2^{4}\cdot 3^{4}\cdot 19\cdot 71^{3}$ |
$4$ |
$45.4487847095$ |
$132.90263134757802$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$3$ |
$988.317073991$ |
| 6.2.9286716717.2 |
$x^{6} - x^{5} - 160 x^{4} + 109 x^{3} + 8479 x^{2} - 2490 x - 148929$ |
$6$ |
(2, 2) |
$3^{3}\cdot 31^{2}\cdot 71^{3}$ |
$3$ |
$45.846941249$ |
$81.25884567233281$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$[2]$ |
$2$ |
$3$ |
$529.908193056$ |
| 6.2.9286716717.3 |
$x^{6} - x^{5} - 8 x^{4} + 81 x^{3} + 135 x^{2} + 252 x - 477$ |
$6$ |
(2, 2) |
$3^{3}\cdot 31^{2}\cdot 71^{3}$ |
$3$ |
$45.846941249$ |
$81.25884567233281$ |
|
|
? |
$S_3^2$ (as 6T9) |
trivial |
$[2]$ |
$2$ |
$3$ |
$596.65472949$ |
| 6.2.11086651136.1 |
$x^{6} - 2 x^{5} + 74 x^{4} - 74 x^{3} - 140 x^{2} - 4900 x - 85750$ |
$6$ |
(2, 2) |
$2^{8}\cdot 11^{2}\cdot 71^{3}$ |
$3$ |
$47.2208061409$ |
$70.42045786807023$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$[2]$ |
$2$ |
$3$ |
$833.718609428$ |
| 6.2.12117434816.1 |
$x^{6} + 71 x^{4} - 357911$ |
$6$ |
(2, 2) |
$2^{6}\cdot 23^{2}\cdot 71^{3}$ |
$3$ |
$47.9256982144$ |
$135.92382417678704$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$[2]$ |
$2$ |
$3$ |
$288.82974823$ |
| 6.2.12117434816.2 |
$x^{6} - 2 x^{5} - 212 x^{4} + 286 x^{3} + 14979 x^{2} - 9656 x - 353011$ |
$6$ |
(2, 2) |
$2^{6}\cdot 23^{2}\cdot 71^{3}$ |
$3$ |
$47.9256982144$ |
$80.820789404707$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$[2]$ |
$2$ |
$3$ |
$820.808501584$ |
| 6.0.12862247607.1 |
$x^{6} - 3 x^{5} + 13 x^{4} + 3 x^{3} - 12 x^{2} + 115 x + 125$ |
$6$ |
(0, 3) |
$-\,3^{3}\cdot 11^{3}\cdot 71^{3}$ |
$3$ |
$48.4045452411$ |
$116.01512953420601$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[2]$ |
$[2]$ |
$2$ |
$2$ |
$575.135382738$ |
| 6.6.13229464293.2 |
$x^{6} - x^{5} - 30 x^{4} + 54 x^{3} + 206 x^{2} - 578 x + 367$ |
$6$ |
(6, 0) |
$3^{3}\cdot 37^{2}\cdot 71^{3}$ |
$3$ |
$48.6321768566$ |
$162.05320241458284$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$[2]$ |
$2$ |
$5$ |
$675.66728115$ |
| 6.2.16244506557.3 |
$x^{6} - 2 x^{5} + 30 x^{4} - 78 x^{3} + 206 x^{2} - 675 x + 263$ |
$6$ |
(2, 2) |
$3^{3}\cdot 41^{2}\cdot 71^{3}$ |
$3$ |
$50.3250738216$ |
$122.98780306395837$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1122.66831737$ |
| 6.2.16698695616.4 |
$x^{6} - 15 x^{4} - 70 x^{3} + 216 x^{2} - 114 x - 53$ |
$6$ |
(2, 2) |
$2^{6}\cdot 3^{6}\cdot 71^{3}$ |
$3$ |
$50.5568986391$ |
$130.346710665638$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1284.48250963$ |
| 6.4.16859039744.1 |
$x^{6} - 4 x^{4} - 24 x^{3} + 4 x^{2} + 48 x + 2$ |
$6$ |
(4, 1) |
$-\,2^{11}\cdot 23\cdot 71^{3}$ |
$3$ |
$50.6374863451$ |
$144.00627535948757$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$[6]$ |
$2$ |
$4$ |
$1398.23326014$ |
| 6.2.18708723792.1 |
$x^{6} - x^{5} - 158 x^{4} + 103 x^{3} + 8482 x^{2} - 3237 x - 154493$ |
$6$ |
(2, 2) |
$2^{4}\cdot 3^{3}\cdot 11^{2}\cdot 71^{3}$ |
$4$ |
$51.5237376899$ |
$76.83742603580221$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$[2]$ |
$2$ |
$3$ |
$847.281217164$ |
| 6.2.22012958144.1 |
$x^{6} - 211 x^{4} - 2 x^{3} + 15124 x^{2} - 428 x - 368063$ |
$6$ |
(2, 2) |
$2^{6}\cdot 31^{2}\cdot 71^{3}$ |
$3$ |
$52.9394877432$ |
$93.8296328459192$ |
|
|
? |
$D_{6}$ (as 6T3) |
trivial |
$[2]$ |
$2$ |
$3$ |
$798.109878497$ |
| 6.2.29686569984.5 |
$x^{6} - 49 x^{4} - 112 x^{3} + 192 x^{2} - 96 x + 12$ |
$6$ |
(2, 2) |
$2^{10}\cdot 3^{4}\cdot 71^{3}$ |
$3$ |
$55.6450670786$ |
$245.25808639511874$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2831.11084965$ |
| 6.2.30198740625.2 |
$x^{6} - x^{5} - 20 x^{4} + 25 x^{3} + 145 x^{2} - 43 x - 62$ |
$6$ |
(2, 2) |
$3^{3}\cdot 5^{5}\cdot 71^{3}$ |
$3$ |
$55.8039325782$ |
$122.26034596210266$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2866.40781879$ |
| 6.2.30305040192.7 |
$x^{6} - 2 x^{5} - 13 x^{4} - 30 x^{3} + 93 x^{2} + 24 x - 84$ |
$6$ |
(2, 2) |
$2^{6}\cdot 3^{3}\cdot 7^{2}\cdot 71^{3}$ |
$4$ |
$55.8366229722$ |
$143.73552808085262$ |
|
|
|
$\PGL(2,5)$ (as 6T14) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2970.19462486$ |
| 6.6.30969323008.1 |
$x^{6} - 2 x^{5} - 43 x^{4} - 14 x^{3} + 400 x^{2} + 424 x - 437$ |
$6$ |
(6, 0) |
$2^{9}\cdot 13^{2}\cdot 71^{3}$ |
$3$ |
$56.0387731323$ |
$131.7659111232115$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$[6]$ |
$2$ |
$5$ |
$1042.91029215$ |
| 6.2.30969323008.1 |
$x^{6} - 2 x^{5} + 37 x^{4} - 250 x^{3} + 3165 x^{2} - 6408 x - 39742$ |
$6$ |
(2, 2) |
$2^{9}\cdot 13^{2}\cdot 71^{3}$ |
$3$ |
$56.0387731323$ |
$85.93020423576334$ |
|
|
? |
$D_{6}$ (as 6T3) |
$[3]$ |
$[6]$ |
$2$ |
$3$ |
$608.935893862$ |
| 6.6.30969323008.2 |
$x^{6} - 26 x^{4} - 10 x^{3} + 169 x^{2} + 130 x - 117$ |
$6$ |
(6, 0) |
$2^{9}\cdot 13^{2}\cdot 71^{3}$ |
$3$ |
$56.0387731323$ |
$131.7659111232115$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$[2, 2, 6]$ |
$2$ |
$5$ |
$2274.97576604$ |
| 6.6.30969323008.3 |
$x^{6} - 2 x^{5} - 43 x^{4} + 114 x^{3} + 272 x^{2} - 972 x + 657$ |
$6$ |
(6, 0) |
$2^{9}\cdot 13^{2}\cdot 71^{3}$ |
$3$ |
$56.0387731323$ |
$131.7659111232115$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$[6]$ |
$2$ |
$5$ |
$1673.49060566$ |
| 6.4.31427449088.1 |
$x^{6} - 2 x^{5} - 13 x^{4} + 36 x^{3} - 257 x^{2} + 982 x - 1015$ |
$6$ |
(4, 1) |
$-\,2^{8}\cdot 7^{3}\cdot 71^{3}$ |
$3$ |
$56.1760918124$ |
$107.46099775418355$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$[2, 6]$ |
$2$ |
$4$ |
$2128.65188004$ |
| 6.2.33076702976.2 |
$x^{6} + 17 x^{4} - 2 x^{3} - 265 x^{2} + 338 x - 3407$ |
$6$ |
(2, 2) |
$2^{8}\cdot 19^{2}\cdot 71^{3}$ |
$3$ |
$56.6570166228$ |
$92.55061359288983$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$[2, 4]$ |
$2$ |
$3$ |
$1111.45260639$ |
| 6.2.35917084672.6 |
$x^{6} - 2 x^{5} + 11 x^{4} - 84 x^{3} + 99 x^{2} - 370 x + 233$ |
$6$ |
(2, 2) |
$2^{11}\cdot 7^{2}\cdot 71^{3}$ |
$3$ |
$57.4403194339$ |
$207.42464514045537$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$[6]$ |
$2$ |
$3$ |
$1735.74734243$ |
| 6.2.39278584784.3 |
$x^{6} - x^{5} - 20 x^{4} + 37 x^{3} + 68 x^{2} - 129 x + 81$ |
$6$ |
(2, 2) |
$2^{4}\cdot 19^{3}\cdot 71^{3}$ |
$3$ |
$58.3032331232$ |
$153.36433320477573$ |
|
|
|
$\PGL(2,5)$ (as 6T14) |
trivial |
$[2]$ |
$2$ |
$3$ |
$2718.15060228$ |
| 6.2.39278584784.4 |
$x^{6} - x^{5} + 13 x^{4} - 31 x^{3} + 23 x^{2} - 147 x + 214$ |
$6$ |
(2, 2) |
$2^{4}\cdot 19^{3}\cdot 71^{3}$ |
$3$ |
$58.3032331232$ |
$153.36433320477573$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
trivial |
$[2]$ |
$2$ |
$3$ |
$7464.22266721$ |
| 6.2.40828697325.2 |
$x^{6} - x^{5} + 3 x^{4} - 30 x^{3} - 67 x^{2} - 56 x + 1$ |
$6$ |
(2, 2) |
$3^{3}\cdot 5^{2}\cdot 13^{2}\cdot 71^{3}$ |
$4$ |
$58.6805605656$ |
$117.66477807738389$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[4]$ |
$[2, 4]$ |
$2$ |
$3$ |
$264.430649972$ |
| 6.4.42278236875.1 |
$x^{6} - 2 x^{5} - x^{4} - 31 x^{3} + 34 x^{2} + 33 x + 6$ |
$6$ |
(4, 1) |
$-\,3^{3}\cdot 5^{4}\cdot 7\cdot 71^{3}$ |
$4$ |
$59.0227551064$ |
$129.11191568658924$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$4$ |
$4590.78581543$ |
| 6.2.44346604544.1 |
$x^{6} + 71 x^{4} + 5041 x^{2} - 357911$ |
$6$ |
(2, 2) |
$2^{10}\cdot 11^{2}\cdot 71^{3}$ |
$3$ |
$59.4944876499$ |
$140.84091573614046$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1517.11203654$ |
| 6.2.44529854976.1 |
$x^{6} - 2 x^{5} - 5 x^{4} - 32 x^{3} - 24 x^{2} - 312 x - 420$ |
$6$ |
(2, 2) |
$2^{9}\cdot 3^{5}\cdot 71^{3}$ |
$3$ |
$59.5353914448$ |
$252.58727406709943$ |
|
|
|
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$18517.2231548$ |
| 6.2.45812608000.4 |
$x^{6} - 9 x^{4} - 132 x^{3} + 464 x^{2} - 116 x - 614$ |
$6$ |
(2, 2) |
$2^{10}\cdot 5^{3}\cdot 71^{3}$ |
$3$ |
$59.817855041$ |
$128.87366198354528$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$[2]$ |
$2$ |
$3$ |
$8349.61544307$ |
| 6.2.45812608000.5 |
$x^{6} - 14 x^{4} - 24 x^{3} - 164 x^{2} - 400 x - 424$ |
$6$ |
(2, 2) |
$2^{10}\cdot 5^{3}\cdot 71^{3}$ |
$3$ |
$59.817855041$ |
$141.9907328927196$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
$[2]$ |
$2$ |
$3$ |
$1772.50271398$ |
| 6.4.46179108864.2 |
$x^{6} - 2 x^{5} + 11 x^{4} - 16 x^{3} - 111 x^{2} - 30 x + 9$ |
$6$ |
(4, 1) |
$-\,2^{11}\cdot 3^{2}\cdot 7\cdot 71^{3}$ |
$4$ |
$59.8973476163$ |
$137.60276068406725$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[9]$ |
$[18]$ |
$2$ |
$4$ |
$1490.06942413$ |
| 6.0.50325149888.1 |
$x^{6} - 13 x^{4} - 4 x^{3} + 273 x^{2} + 26 x + 4$ |
$6$ |
(0, 3) |
$-\,2^{6}\cdot 13^{3}\cdot 71^{3}$ |
$3$ |
$60.7618301239$ |
$85.93020423576334$ |
|
|
|
$S_3^2$ (as 6T9) |
$[30]$ |
$[30]$ |
$2$ |
$2$ |
$130.180246022$ |
| 6.0.50325149888.5 |
$x^{6} - x^{5} + 56 x^{4} - 179 x^{3} - 56 x^{2} - 9217 x + 76193$ |
$6$ |
(0, 3) |
$-\,2^{6}\cdot 13^{3}\cdot 71^{3}$ |
$3$ |
$60.7618301239$ |
$85.93020423576334$ |
|
|
|
$D_{6}$ (as 6T3) |
$[30]$ |
$[30]$ |
$2$ |
$2$ |
$35.8874405812$ |
| 6.6.55816936272.1 |
$x^{6} - 2 x^{5} - 49 x^{4} + 72 x^{3} + 603 x^{2} - 550 x - 731$ |
$6$ |
(6, 0) |
$2^{4}\cdot 3^{3}\cdot 19^{2}\cdot 71^{3}$ |
$4$ |
$61.8198099808$ |
$164.96008287652745$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
trivial |
$[2]$ |
$2$ |
$5$ |
$3124.31041016$ |