Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
6.0.121328851.1 |
x6 - 3x5 - x4 - 12x3 + 71x2 + 96x + 163 |
$6$ |
[0,3] |
$-\,7^{2}\cdot 19^{5}$ |
$2$ |
$22.2498633197$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$25.678740087$ |
6.0.158470336.1 |
x6 - 3x5 - x4 - 12x3 + 52x2 + 20x + 68 |
$6$ |
[0,3] |
$-\,2^{6}\cdot 19^{5}$ |
$2$ |
$23.2625862551$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$33.1099798427$ |
6.2.255038197.2 |
x6 - 3x5 - x4 + 7x3 - 5x2 - 18x - 8 |
$6$ |
[2,2] |
$19^{5}\cdot 103$ |
$2$ |
$25.1826176489$ |
|
|
? |
$S_6$ (as 6T16) |
$[3]$ |
$2$ |
$3$ |
$109.257774467$ |
6.0.398651939.1 |
x6 - x5 + 2x4 + 8x3 + 18x2 + 14x + 7 |
$6$ |
[0,3] |
$-\,7\cdot 19^{5}\cdot 23$ |
$3$ |
$27.1289080431$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[6]$ |
$2$ |
$2$ |
$17.441380723$ |
6.0.633881344.1 |
x6 - 2x5 + 8x4 - 12x3 + 41x2 - 46x + 68 |
$6$ |
[0,3] |
$-\,2^{8}\cdot 19^{5}$ |
$2$ |
$29.3090220978$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$2$ |
$17.7437539865$ |
6.0.775018987.1 |
x6 - 2x5 + 8x4 - 12x3 + 22x2 - 27x + 11 |
$6$ |
[0,3] |
$-\,19^{5}\cdot 313$ |
$2$ |
$30.3076356089$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$27.0762162451$ |
6.0.814636571.1 |
x6 - x5 + 2x4 - 11x3 - x2 + 14x + 7 |
$6$ |
[0,3] |
$-\,7\cdot 19^{5}\cdot 47$ |
$3$ |
$30.560513722$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$33.1239091084$ |
6.0.990439600.1 |
x6 - x5 + 2x4 - 49x3 + 132x2 - 195x + 425 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{2}\cdot 19^{5}$ |
$3$ |
$31.5721869692$ |
✓ |
|
? |
$D_{6}$ (as 6T3) |
$[3, 3]$ |
$2$ |
$2$ |
$33.5100484823$ |
6.0.1198431916.1 |
x6 - 2x5 + 8x4 + 7x3 + 22x2 + 11x + 11 |
$6$ |
[0,3] |
$-\,2^{2}\cdot 11^{2}\cdot 19^{5}$ |
$3$ |
$32.5913408098$ |
|
|
✓ |
$S_6$ (as 6T16) |
$[12]$ |
$2$ |
$2$ |
$18.1491876721$ |
6.0.1238049500.1 |
x6 - 3x5 + 18x4 - 12x3 + 52x2 + 96x + 144 |
$6$ |
[0,3] |
$-\,2^{2}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$32.7684828824$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[24]$ |
$2$ |
$2$ |
$43.5806451898$ |
6.2.1267762688.2 |
x6 - 38x3 - 38x2 - 76x + 323 |
$6$ |
[2,2] |
$2^{9}\cdot 19^{5}$ |
$2$ |
$32.8982649779$ |
|
|
? |
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$3$ |
$142.50146044$ |
6.2.1604512152.2 |
x6 - 3x5 + 18x4 + 7x3 - 24x2 - 18x - 8 |
$6$ |
[2,2] |
$2^{3}\cdot 3^{4}\cdot 19^{5}$ |
$3$ |
$34.2155743935$ |
|
|
? |
$S_6$ (as 6T16) |
$[3]$ |
$2$ |
$3$ |
$563.484847448$ |
6.0.1941261616.2 |
x6 - 2x5 - 11x4 + 26x3 + 41x2 - 8x + 125 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 19^{5}$ |
$3$ |
$35.3194564398$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3, 3]$ |
$2$ |
$2$ |
$47.6633763961$ |
6.0.1941261616.4 |
x6 - 3x5 - 20x4 + 45x3 + 280x2 + 381x + 163 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 7^{2}\cdot 19^{5}$ |
$3$ |
$35.3194564398$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3, 3]$ |
$2$ |
$2$ |
$14.3254424945$ |
6.0.2693995712.1 |
x6 - x5 + 2x4 - 11x3 + 37x2 + 14x + 26 |
$6$ |
[0,3] |
$-\,2^{6}\cdot 17\cdot 19^{5}$ |
$3$ |
$37.3020600324$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$2$ |
$120.778731975$ |
6.0.2785611375.2 |
x6 - 2x5 + 8x4 + 7x3 + 41x2 + 49x + 49 |
$6$ |
[0,3] |
$-\,3^{2}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$37.5105490623$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$201.155012087$ |
6.2.2971318800.1 |
x6 - x5 - 17x4 - 11x3 + 56x2 - 24x - 12 |
$6$ |
[2,2] |
$2^{4}\cdot 3\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$37.9162060871$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$3$ |
$347.761220736$ |
6.4.3961758400.1 |
x6 - 2x5 - 11x4 - 12x3 + 79x2 - 8x - 65 |
$6$ |
[4,1] |
$-\,2^{6}\cdot 5^{2}\cdot 19^{5}$ |
$3$ |
$39.7784629537$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$4$ |
$491.373929148$ |
6.2.4278699072.6 |
x6 - 3x5 - 20x4 + 26x3 + 109x2 + 229x + 106 |
$6$ |
[2,2] |
$2^{6}\cdot 3^{3}\cdot 19^{5}$ |
$3$ |
$40.2919813093$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$3$ |
$1264.61896163$ |
6.0.4578307051.1 |
x6 - x5 + 21x4 + 8x3 + 37x2 + 128x + 83 |
$6$ |
[0,3] |
$-\,19^{5}\cdot 43^{2}$ |
$2$ |
$40.7490497829$ |
|
|
? |
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$50.3262544452$ |
6.4.4952198000.1 |
x6 - 3x5 - x4 + 7x3 - 24x2 + 20x + 68 |
$6$ |
[4,1] |
$-\,2^{4}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$41.2857013566$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$4$ |
$802.340667575$ |
6.0.4952198000.1 |
x6 - 3x5 + 37x4 - 69x3 + 394x2 - 360x + 1170 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5^{3}\cdot 19^{5}$ |
$3$ |
$41.2857013566$ |
✓ |
|
? |
$D_{6}$ (as 6T3) |
$[3, 24]$ |
$2$ |
$2$ |
$33.5100484823$ |
6.2.5071050752.1 |
x6 - 38x2 - 76x - 38 |
$6$ |
[2,2] |
$2^{11}\cdot 19^{5}$ |
$2$ |
$41.4492165506$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$3$ |
$172.468305585$ |
6.2.5071050752.2 |
x6 - 19x2 - 38 |
$6$ |
[2,2] |
$2^{11}\cdot 19^{5}$ |
$2$ |
$41.4492165506$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$302.368128692$ |
6.0.5945113699.1 |
x6 - x5 + 2x4 + 122x3 + 474x2 + 888x + 881 |
$6$ |
[0,3] |
$-\,7^{4}\cdot 19^{5}$ |
$2$ |
$42.5624573566$ |
✓ |
✓ |
? |
$C_6$ (as 6T1) |
$[3, 3]$ |
$2$ |
$2$ |
$43.4693954291$ |
6.0.6440333499.1 |
x6 - x5 - 17x4 + 8x3 + 113x2 + 33x + 7 |
$6$ |
[0,3] |
$-\,3^{2}\cdot 17^{2}\cdot 19^{5}$ |
$3$ |
$43.1338336893$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$179.112758889$ |
6.0.7220304684.1 |
x6 - 3x5 + 18x4 - 31x3 + 90x2 - 18x + 11 |
$6$ |
[0,3] |
$-\,2^{2}\cdot 3^{6}\cdot 19^{5}$ |
$3$ |
$43.9635331467$ |
|
|
? |
$S_6$ (as 6T16) |
$[6]$ |
$2$ |
$2$ |
$115.586430031$ |
6.2.7487723376.1 |
x6 - x5 + 2x4 + 8x3 - 172x2 + 128x - 848 |
$6$ |
[2,2] |
$2^{4}\cdot 3^{3}\cdot 7\cdot 19^{5}$ |
$4$ |
$44.2308173916$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$3$ |
$2562.62144217$ |
6.0.7765046464.3 |
x6 - 2x5 + 27x4 - 12x3 + 117x2 + 106x + 334 |
$6$ |
[0,3] |
$-\,2^{6}\cdot 7^{2}\cdot 19^{5}$ |
$3$ |
$44.4997266393$ |
|
|
? |
$\PGL(2,5)$ (as 6T14) |
$[6]$ |
$2$ |
$2$ |
$251.742416555$ |
6.2.8240457472.1 |
x6 - 19x4 - 76x3 - 133x2 - 114x - 38 |
$6$ |
[2,2] |
$2^{8}\cdot 13\cdot 19^{5}$ |
$3$ |
$44.9426372856$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$113.649646409$ |
6.4.8913956400.1 |
x6 - 3x5 - 20x4 + 45x3 - 100x2 - 75x + 125 |
$6$ |
[4,1] |
$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$45.53497309$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$4$ |
$972.144542593$ |
6.0.8913956400.2 |
x6 - x5 + 2x4 - 11x3 + 208x2 - 81x + 729 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$45.53497309$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3, 3]$ |
$2$ |
$2$ |
$89.364999505$ |
6.0.9025380855.1 |
x6 - 19x3 + 171x2 + 57x + 95 |
$6$ |
[0,3] |
$-\,3^{6}\cdot 5\cdot 19^{5}$ |
$3$ |
$45.6293472724$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$145.956738157$ |
6.0.9213564379.1 |
x6 - 2x5 + 8x4 + 26x3 + 98x2 + 68x + 277 |
$6$ |
[0,3] |
$-\,19^{5}\cdot 61^{2}$ |
$2$ |
$45.7865526325$ |
|
|
|
$S_3\times C_3$ (as 6T5) |
$[3]$ |
$2$ |
$2$ |
$190.951190149$ |
6.2.9594883625.1 |
x6 - 2x5 + 8x4 + 26x3 - 35x2 + 125x + 125 |
$6$ |
[2,2] |
$5^{3}\cdot 19^{5}\cdot 31$ |
$3$ |
$46.0970661173$ |
|
|
? |
$S_6$ (as 6T16) |
$[3]$ |
$2$ |
$3$ |
$445.812444761$ |
6.0.9706308080.1 |
x6 - 2x5 + 8x4 + 26x3 - 16x2 + 106x + 277 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 5\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$46.1858575737$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$2$ |
$344.947400183$ |
6.0.11115208411.1 |
x6 - x5 + 40x4 - 11x3 + 607x2 - 100x + 3028 |
$6$ |
[0,3] |
$-\,19^{5}\cdot 67^{2}$ |
$2$ |
$47.241056508$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$436.357425607$ |
6.2.11885275200.1 |
x6 - 2x5 - 11x4 - 12x3 + 60x2 - 160x + 220 |
$6$ |
[2,2] |
$2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$47.7714261812$ |
|
|
? |
$S_6$ (as 6T16) |
$[6]$ |
$2$ |
$3$ |
$832.113910247$ |
6.6.11885275200.1 |
x6 - 19x4 + 95x2 - 57 |
$6$ |
[6,0] |
$2^{6}\cdot 3\cdot 5^{2}\cdot 19^{5}$ |
$4$ |
$47.7714261812$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[3]$ |
$2$ |
$5$ |
$974.213798824$ |
6.0.12234405159.1 |
x6 - 19x3 - 114x2 + 285x + 1900 |
$6$ |
[0,3] |
$-\,3^{4}\cdot 19^{5}\cdot 61$ |
$3$ |
$48.0024948587$ |
|
|
? |
$S_6$ (as 6T16) |
$[2, 6]$ |
$2$ |
$2$ |
$145.36042744$ |
6.2.13103515908.2 |
x6 - 3x5 - x4 - 50x3 - 119x2 - 113x + 49 |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$48.5547035305$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$3$ |
$1511.47519463$ |
6.2.13103515908.4 |
x6 - 3x5 - x4 - 12x3 - 5x2 - 75x + 87 |
$6$ |
[2,2] |
$2^{2}\cdot 3^{3}\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$48.5547035305$ |
|
|
? |
$S_3^2$ (as 6T9) |
$[3]$ |
$2$ |
$3$ |
$926.560177511$ |
6.2.14440609368.2 |
x6 - 19x3 - 57x2 + 285x - 266 |
$6$ |
[2,2] |
$2^{3}\cdot 3^{6}\cdot 19^{5}$ |
$3$ |
$49.3473974668$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
$[3]$ |
$2$ |
$3$ |
$1232.72007801$ |
6.2.14856594000.2 |
x6 - 3x5 + 18x4 - 31x3 + 52x2 - 37x - 103 |
$6$ |
[2,2] |
$2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$ |
$4$ |
$49.5815244795$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$257.844555041$ |
6.2.14856594000.3 |
x6 - 2x5 + 8x4 + 64x3 + 60x2 + 296x + 524 |
$6$ |
[2,2] |
$2^{4}\cdot 3\cdot 5^{3}\cdot 19^{5}$ |
$4$ |
$49.5815244795$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$3$ |
$142.277248721$ |
6.0.16480914944.1 |
x6 - 38x3 + 152x2 - 304x + 665 |
$6$ |
[0,3] |
$-\,2^{9}\cdot 13\cdot 19^{5}$ |
$3$ |
$50.4464047041$ |
|
|
? |
$S_4\times C_2$ (as 6T11) |
$[2, 6]$ |
$2$ |
$2$ |
$122.946853133$ |
6.2.17114796288.3 |
x6 - 2x5 + 8x4 - 12x3 - 111x2 - 46x - 8 |
$6$ |
[2,2] |
$2^{8}\cdot 3^{3}\cdot 19^{5}$ |
$3$ |
$50.7647153936$ |
|
|
|
$S_4\times C_2$ (as 6T11) |
$[12]$ |
$2$ |
$3$ |
$430.403173701$ |
6.2.17114796288.4 |
x6 - 2x5 + 8x4 - 12x3 + 60x2 - 768x + 1056 |
$6$ |
[2,2] |
$2^{8}\cdot 3^{3}\cdot 19^{5}$ |
$3$ |
$50.7647153936$ |
|
|
|
$\PGL(2,5)$ (as 6T14) |
$[3]$ |
$2$ |
$3$ |
$2184.02214118$ |
6.0.17471354544.1 |
x6 - x5 - 36x4 + 141x3 + 588x2 - 2513x + 2401 |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{2}\cdot 7^{2}\cdot 19^{5}$ |
$4$ |
$50.9394708738$ |
|
|
|
$D_{6}$ (as 6T3) |
$[3]$ |
$2$ |
$2$ |
$296.818695167$ |
6.0.17748677632.1 |
x6 - 3x5 - 20x4 + 26x3 + 223x2 + 343x + 182 |
$6$ |
[0,3] |
$-\,2^{10}\cdot 7\cdot 19^{5}$ |
$3$ |
$51.073348655$ |
|
|
|
$S_4\times C_2$ (as 6T11) |
$[6]$ |
$2$ |
$2$ |
$569.259414457$ |