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 |
6.0.121328851.1 |
$x^{6} - 3 x^{5} - x^{4} - 12 x^{3} + 71 x^{2} + 96 x + 163$ |
$6$ |
[0,3] |
$-\,7^{2}\cdot 19^{5}$ |
$2$ |
$22.2498633197$ |
$42.56245735661763$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$25.678740087$ |
6.0.158470336.1 |
$x^{6} - 3 x^{5} - x^{4} - 12 x^{3} + 52 x^{2} + 20 x + 68$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 19^{5}$ |
$2$ |
$23.2625862551$ |
$32.89826497785412$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$33.1099798427$ |
6.2.255038197.2 |
$x^{6} - 3 x^{5} - x^{4} + 7 x^{3} - 5 x^{2} - 18 x - 8$ |
$6$ |
[2,2] |
$19^{5}\cdot 103$ |
$2$ |
$25.1826176489$ |
$118.044732713371$ |
|
|
? |
$S_6$ (as 6T16) |
$[3]$ |
$2$ |
$3$ |
$109.257774467$ |
6.0.398651939.1 |
$x^{6} - x^{5} + 2 x^{4} + 8 x^{3} + 18 x^{2} + 14 x + 7$ |
$6$ |
[0,3] |
$-\,7\cdot 19^{5}\cdot 23$ |
$3$ |
$27.1289080431$ |
$147.58456474469543$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[6]$ |
$2$ |
$2$ |
$17.441380723$ |
6.0.633881344.1 |
$x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 41 x^{2} - 46 x + 68$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 19^{5}$ |
$2$ |
$29.3090220978$ |
$46.52517251022511$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$2$ |
$17.7437539865$ |
6.0.775018987.1 |
$x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 22 x^{2} - 27 x + 11$ |
$6$ |
[0,3] |
$-\,19^{5}\cdot 313$ |
$2$ |
$30.3076356089$ |
$205.7785816925322$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$27.0762162451$ |
6.0.814636571.1 |
$x^{6} - x^{5} + 2 x^{4} - 11 x^{3} - x^{2} + 14 x + 7$ |
$6$ |
[0,3] |
$-\,7\cdot 19^{5}\cdot 47$ |
$3$ |
$30.560513722$ |
$210.972548831587$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$33.1239091084$ |
6.0.990439600.1 |
$x^{6} - x^{5} + 2 x^{4} - 49 x^{3} + 132 x^{2} - 195 x + 425$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{2}\cdot 19^{5}$ |
$3$ |
$31.5721869692$ |
$41.28570135662403$ |
✓ |
|
? |
$D_{6}$ (as 6T3) |
$[3, 3]$ |
$2$ |
$2$ |
$33.5100484823$ |
6.0.1198431916.1 |
$x^{6} - 2 x^{5} + 8 x^{4} + 7 x^{3} + 22 x^{2} + 11 x + 11$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 11^{2}\cdot 19^{5}$ |
$3$ |
$32.5913408098$ |
$91.32221878783788$ |
|
|
✓ |
$S_6$ (as 6T16) |
$[12]$ |
$2$ |
$2$ |
$18.1491876721$ |
6.0.1238049500.1 |
$x^{6} - 3 x^{5} + 18 x^{4} - 12 x^{3} + 52 x^{2} + 96 x + 144$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$32.7684828824$ |
$41.28570135662403$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[24]$ |
$2$ |
$2$ |
$43.5806451898$ |
6.2.1267762688.2 |
$x^{6} - 38 x^{3} - 38 x^{2} - 76 x + 323$ |
$6$ |
[2,2] |
$2^{9}\cdot 19^{5}$ |
$2$ |
$32.8982649779$ |
$32.89826497785412$ |
|
|
? |
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$3$ |
$142.50146044$ |
6.2.1604512152.2 |
$x^{6} - 3 x^{5} + 18 x^{4} + 7 x^{3} - 24 x^{2} - 18 x - 8$ |
$6$ |
[2,2] |
$2^{3}\cdot 3^{4}\cdot 19^{5}$ |
$3$ |
$34.2155743935$ |
$118.52622651923237$ |
|
|
? |
$S_6$ (as 6T16) |
$[3]$ |
$2$ |
$3$ |
$563.484847448$ |
6.0.1941261616.2 |
$x^{6} - 2 x^{5} - 11 x^{4} + 26 x^{3} + 41 x^{2} - 8 x + 125$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 19^{5}$ |
$3$ |
$35.3194564398$ |
$67.56368958224645$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3, 3]$ |
$2$ |
$2$ |
$47.6633763961$ |
6.0.1941261616.4 |
$x^{6} - 3 x^{5} - 20 x^{4} + 45 x^{3} + 280 x^{2} + 381 x + 163$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 19^{5}$ |
$3$ |
$35.3194564398$ |
$67.56368958224645$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3, 3]$ |
$2$ |
$2$ |
$14.3254424945$ |
6.0.2693995712.1 |
$x^{6} - x^{5} + 2 x^{4} - 11 x^{3} + 37 x^{2} + 14 x + 26$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 17\cdot 19^{5}$ |
$3$ |
$37.3020600324$ |
$135.6430214032508$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$2$ |
$120.778731975$ |
6.0.2785611375.2 |
$x^{6} - 2 x^{5} + 8 x^{4} + 7 x^{3} + 41 x^{2} + 49 x + 49$ |
$6$ |
[0,3] |
$-\,3^{2}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$37.5105490623$ |
$77.03066227877103$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$201.155012087$ |
6.2.2971318800.1 |
$x^{6} - x^{5} - 17 x^{4} - 11 x^{3} + 56 x^{2} - 24 x - 12$ |
$6$ |
[2,2] |
$2^{4}\cdot 3\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$37.9162060871$ |
$71.50893237578813$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$3$ |
$347.761220736$ |
6.4.3961758400.1 |
$x^{6} - 2 x^{5} - 11 x^{4} - 12 x^{3} + 79 x^{2} - 8 x - 65$ |
$6$ |
[4,1] |
$-\,2^{6}\cdot 5^{2}\cdot 19^{5}$ |
$3$ |
$39.7784629537$ |
$58.38679879062299$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$4$ |
$491.373929148$ |
6.2.4278699072.6 |
$x^{6} - 3 x^{5} - 20 x^{4} + 26 x^{3} + 109 x^{2} + 229 x + 106$ |
$6$ |
[2,2] |
$2^{6}\cdot 3^{3}\cdot 19^{5}$ |
$3$ |
$40.2919813093$ |
$56.98146642250715$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$3$ |
$1264.61896163$ |
6.0.4578307051.1 |
$x^{6} - x^{5} + 21 x^{4} + 8 x^{3} + 37 x^{2} + 128 x + 83$ |
$6$ |
[0,3] |
$-\,19^{5}\cdot 43^{2}$ |
$2$ |
$40.7490497829$ |
$142.76014197190915$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$50.3262544452$ |
6.0.4952198000.1 |
$x^{6} - 3 x^{5} + 37 x^{4} - 69 x^{3} + 394 x^{2} - 360 x + 1170$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$41.2857013566$ |
$41.28570135662403$ |
✓ |
|
? |
$D_{6}$ (as 6T3) |
$[3, 24]$ |
$2$ |
$2$ |
$33.5100484823$ |
6.4.4952198000.1 |
$x^{6} - 3 x^{5} - x^{4} + 7 x^{3} - 24 x^{2} + 20 x + 68$ |
$6$ |
[4,1] |
$-\,2^{4}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$41.2857013566$ |
$61.73652320549103$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$4$ |
$802.340667575$ |
6.2.5071050752.1 |
$x^{6} - 38 x^{2} - 76 x - 38$ |
$6$ |
[2,2] |
$2^{11}\cdot 19^{5}$ |
$2$ |
$41.4492165506$ |
$41.4492165506177$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$3$ |
$172.468305585$ |
6.2.5071050752.2 |
$x^{6} - 19 x^{2} - 38$ |
$6$ |
[2,2] |
$2^{11}\cdot 19^{5}$ |
$2$ |
$41.4492165506$ |
$46.52517251022511$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$302.368128692$ |
6.0.5945113699.1 |
$x^{6} - x^{5} + 2 x^{4} + 122 x^{3} + 474 x^{2} + 888 x + 881$ |
$6$ |
[0,3] |
$-\,7^{4}\cdot 19^{5}$ |
$2$ |
$42.5624573566$ |
$42.56245735661763$ |
✓ |
✓ |
? |
$C_6$ (as 6T1) |
$[3, 3]$ |
$2$ |
$2$ |
$43.4693954291$ |
6.0.6440333499.1 |
$x^{6} - x^{5} - 17 x^{4} + 8 x^{3} + 113 x^{2} + 33 x + 7$ |
$6$ |
[0,3] |
$-\,3^{2}\cdot 17^{2}\cdot 19^{5}$ |
$3$ |
$43.1338336893$ |
$83.06404740184547$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$179.112758889$ |
6.0.7220304684.1 |
$x^{6} - 3 x^{5} + 18 x^{4} - 31 x^{3} + 90 x^{2} - 18 x + 11$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 3^{6}\cdot 19^{5}$ |
$3$ |
$43.9635331467$ |
$84.91473799091418$ |
|
|
? |
$S_6$ (as 6T16) |
$[6]$ |
$2$ |
$2$ |
$115.586430031$ |
6.2.7487723376.1 |
$x^{6} - x^{5} + 2 x^{4} + 8 x^{3} - 172 x^{2} + 128 x - 848$ |
$6$ |
[2,2] |
$2^{4}\cdot 3^{3}\cdot 7\cdot 19^{5}$ |
$4$ |
$44.2308173916$ |
$134.3108123083544$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$3$ |
$2562.62144217$ |
6.0.7765046464.3 |
$x^{6} - 2 x^{5} + 27 x^{4} - 12 x^{3} + 117 x^{2} + 106 x + 334$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7^{2}\cdot 19^{5}$ |
$3$ |
$44.4997266393$ |
$87.04062769690785$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[6]$ |
$2$ |
$2$ |
$251.742416555$ |
6.2.8240457472.1 |
$x^{6} - 19 x^{4} - 76 x^{3} - 133 x^{2} - 114 x - 38$ |
$6$ |
[2,2] |
$2^{8}\cdot 13\cdot 19^{5}$ |
$3$ |
$44.9426372856$ |
$167.74889508542427$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$113.649646409$ |
6.4.8913956400.1 |
$x^{6} - 3 x^{5} - 20 x^{4} + 45 x^{3} - 100 x^{2} - 75 x + 125$ |
$6$ |
[4,1] |
$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$45.53497309$ |
$71.50893237578813$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$4$ |
$972.144542593$ |
6.0.8913956400.2 |
$x^{6} - x^{5} + 2 x^{4} - 11 x^{3} + 208 x^{2} - 81 x + 729$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$45.53497309$ |
$93.50940526471025$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3, 3]$ |
$2$ |
$2$ |
$89.364999505$ |
6.0.9025380855.1 |
$x^{6} - 19 x^{3} + 171 x^{2} + 57 x + 95$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 5\cdot 19^{5}$ |
$3$ |
$45.6293472724$ |
$119.61383432614218$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$145.956738157$ |
6.0.9213564379.1 |
$x^{6} - 2 x^{5} + 8 x^{4} + 26 x^{3} + 98 x^{2} + 68 x + 277$ |
$6$ |
[0,3] |
$-\,19^{5}\cdot 61^{2}$ |
$2$ |
$45.7865526325$ |
$180.23863546164193$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$190.951190149$ |
6.2.9594883625.1 |
$x^{6} - 2 x^{5} + 8 x^{4} + 26 x^{3} - 35 x^{2} + 125 x + 125$ |
$6$ |
[2,2] |
$5^{3}\cdot 19^{5}\cdot 31$ |
$3$ |
$46.0970661173$ |
$247.61893496815384$ |
|
|
? |
$S_6$ (as 6T16) |
$[3]$ |
$2$ |
$3$ |
$445.812444761$ |
6.0.9706308080.1 |
$x^{6} - 2 x^{5} + 8 x^{4} + 26 x^{3} - 16 x^{2} + 106 x + 277$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$46.1858575737$ |
$137.62331624648237$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$344.947400183$ |
6.0.11115208411.1 |
$x^{6} - x^{5} + 40 x^{4} - 11 x^{3} + 607 x^{2} - 100 x + 3028$ |
$6$ |
[0,3] |
$-\,19^{5}\cdot 67^{2}$ |
$2$ |
$47.241056508$ |
$95.20623744210376$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$436.357425607$ |
6.2.11885275200.1 |
$x^{6} - 2 x^{5} - 11 x^{4} - 12 x^{3} + 60 x^{2} - 160 x + 220$ |
$6$ |
[2,2] |
$2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$47.7714261812$ |
$166.61481856879172$ |
|
|
? |
$S_6$ (as 6T16) |
$[6]$ |
$2$ |
$3$ |
$832.113910247$ |
6.6.11885275200.1 |
$x^{6} - 19 x^{4} + 95 x^{2} - 57$ |
$6$ |
[6,0] |
$2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$47.7714261812$ |
$101.1289019966601$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$5$ |
$974.213798824$ |
6.0.12234405159.1 |
$x^{6} - 19 x^{3} - 114 x^{2} + 285 x + 1900$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 19^{5}\cdot 61$ |
$3$ |
$48.0024948587$ |
$207.07795113150135$ |
|
|
? |
$S_6$ (as 6T16) |
$[2, 6]$ |
$2$ |
$2$ |
$145.36042744$ |
6.2.13103515908.2 |
$x^{6} - 3 x^{5} - x^{4} - 50 x^{3} - 119 x^{2} - 113 x + 49$ |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$48.5547035305$ |
$117.02374310326292$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$3$ |
$1511.47519463$ |
6.2.13103515908.4 |
$x^{6} - 3 x^{5} - x^{4} - 12 x^{3} - 5 x^{2} - 75 x + 87$ |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$48.5547035305$ |
$117.02374310326292$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$3$ |
$926.560177511$ |
6.2.14440609368.2 |
$x^{6} - 19 x^{3} - 57 x^{2} + 285 x - 266$ |
$6$ |
[2,2] |
$2^{3}\cdot 3^{6}\cdot 19^{5}$ |
$3$ |
$49.3473974668$ |
$122.19904906844997$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$3$ |
$1232.72007801$ |
6.2.14856594000.2 |
$x^{6} - 3 x^{5} + 18 x^{4} - 31 x^{3} + 52 x^{2} - 37 x - 103$ |
$6$ |
[2,2] |
$2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$ |
$4$ |
$49.5815244795$ |
$106.93079487456548$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$257.844555041$ |
6.2.14856594000.3 |
$x^{6} - 2 x^{5} + 8 x^{4} + 64 x^{3} + 60 x^{2} + 296 x + 524$ |
$6$ |
[2,2] |
$2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$ |
$4$ |
$49.5815244795$ |
$71.50893237578813$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$142.277248721$ |
6.0.16480914944.1 |
$x^{6} - 38 x^{3} + 152 x^{2} - 304 x + 665$ |
$6$ |
[0,3] |
$-\,2^{9}\cdot 13\cdot 19^{5}$ |
$3$ |
$50.4464047041$ |
$167.74889508542427$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[2, 6]$ |
$2$ |
$2$ |
$122.946853133$ |
6.2.17114796288.3 |
$x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} - 111 x^{2} - 46 x - 8$ |
$6$ |
[2,2] |
$2^{8}\cdot 3^{3}\cdot 19^{5}$ |
$3$ |
$50.7647153936$ |
$80.58396261861672$ |
|
|
|
$S_4\times C_2$ (as 6T11) |
$[12]$ |
$2$ |
$3$ |
$430.403173701$ |
6.2.17114796288.4 |
$x^{6} - 2 x^{5} + 8 x^{4} - 12 x^{3} + 60 x^{2} - 768 x + 1056$ |
$6$ |
[2,2] |
$2^{8}\cdot 3^{3}\cdot 19^{5}$ |
$3$ |
$50.7647153936$ |
$106.05445906309656$ |
|
|
|
$\PGL(2,5)$ (as 6T14) |
$[3]$ |
$2$ |
$3$ |
$2184.02214118$ |
6.0.17471354544.1 |
$x^{6} - x^{5} - 36 x^{4} + 141 x^{3} + 588 x^{2} - 2513 x + 2401$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{2}\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$50.9394708738$ |
$106.60256237449258$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$296.818695167$ |
6.0.17748677632.1 |
$x^{6} - 3 x^{5} - 20 x^{4} + 26 x^{3} + 223 x^{2} + 343 x + 182$ |
$6$ |
[0,3] |
$-\,2^{10}\cdot 7\cdot 19^{5}$ |
$3$ |
$51.073348655$ |
$207.01866750293144$ |
|
|
|
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$2$ |
$569.259414457$ |