| 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 |
| 12.2.564668382613504.1 |
$x^{12} + 4 x^{10} - 2 x^{8} - 22 x^{6} - 24 x^{4} - 9 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 13^{10}$ |
$2$ |
$16.9557155647$ |
$33.18477908865881$ |
|
|
✓ |
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$2$ |
$6$ |
$210.020992904$ |
| 12.2.2754990144000000.1 |
$x^{12} + 6 x^{10} + 6 x^{8} - 20 x^{6} - 42 x^{4} - 21 x^{2} - 1$ |
$12$ |
[2,5] |
$-\,2^{12}\cdot 3^{16}\cdot 5^{6}$ |
$3$ |
$19.349808478363364$ |
$37.870363967348204$ |
|
|
? |
$C_2\wr C_6$ (as 12T134) |
trivial |
trivial |
$2$ |
$6$ |
$531.8214388817978$ |
| 12.0.10070955730726912.1 |
$x^{12} + 13 x^{10} + 60 x^{8} + 121 x^{6} + 111 x^{4} + 46 x^{2} + 7$ |
$12$ |
[0,6] |
$2^{12}\cdot 7\cdot 592661^{2}$ |
$3$ |
$21.5570447818$ |
$7972.692218411225$ |
✓ |
|
✓ |
$C_2^6.S_6$ (as 12T293) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$167.472794978$ |
| 16.4.101...000.4 |
$x^{16} + 8 x^{14} + 22 x^{12} + 17 x^{10} - 27 x^{8} - 58 x^{6} - 33 x^{4} - 2 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{16}\cdot 5^{8}\cdot 251^{4}$ |
$3$ |
$17.8005502824$ |
|
|
|
? |
$C_2^7.(C_2\times S_4)$ (as 16T1665) |
trivial |
trivial |
$2$ |
$9$ |
$4719.24941014$ |
| 16.0.157...000.1 |
$x^{16} + 4 x^{14} + 5 x^{12} + 6 x^{10} + 19 x^{8} + 41 x^{6} + 40 x^{4} + 14 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{16}\cdot 5^{12}\cdot 9929^{2}$ |
$3$ |
$21.1285983697$ |
|
|
|
? |
$C_2^6.S_4\wr C_2$ (as 16T1868) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$5197.82838653$ |
| 16.4.692...728.3 |
$x^{16} + 14 x^{14} + 63 x^{12} + 85 x^{10} - 404 x^{8} - 1479 x^{6} - 1923 x^{4} + 2777$ |
$16$ |
[4,6] |
$2^{22}\cdot 2777^{5}$ |
$2$ |
$30.9053528581$ |
|
|
|
? |
$C_2\wr Q_8.S_4$ (as 16T1847) |
trivial |
trivial |
$2$ |
$9$ |
$601871.2421$ |
| 16.8.161...000.1 |
$x^{16} + x^{14} - 94 x^{12} + 46 x^{10} + 346 x^{8} - 190 x^{6} - 160 x^{4} + 50 x^{2} + 25$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4}$ |
$4$ |
$37.6267504013$ |
|
|
|
? |
$C_2^6:(C_2\times S_4)$ (as 16T1521) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$3993464.92878$ |
| 16.12.161...000.1 |
$x^{16} - 20 x^{14} + 134 x^{12} - 335 x^{10} + 109 x^{8} + 650 x^{6} - 505 x^{4} - 250 x^{2} + 25$ |
$16$ |
[12,2] |
$2^{16}\cdot 3^{12}\cdot 5^{10}\cdot 83^{4}$ |
$4$ |
$37.6267504013$ |
|
|
|
? |
$C_2^7.(C_2\times S_4)$ (as 16T1665) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$10051446.4363$ |
| 16.12.347...248.1 |
$x^{16} - 12 x^{14} + 37 x^{12} + 50 x^{10} - 404 x^{8} + 535 x^{6} - 74 x^{4} - 117 x^{2} + 13$ |
$16$ |
[12,2] |
$2^{16}\cdot 11^{4}\cdot 13^{9}\cdot 43^{4}$ |
$4$ |
$39.4764795947$ |
|
|
|
? |
$C_2^6.(C_4\times S_4)$ (as 16T1667) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$16613259.0114$ |
| 16.8.125...000.1 |
$x^{16} - 2 x^{14} - 75 x^{12} - 148 x^{10} + 150 x^{8} + 355 x^{6} - 17 x^{4} - 29 x^{2} + 1$ |
$16$ |
[8,4] |
$2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 2791^{4}$ |
$4$ |
$42.7794572824$ |
|
|
|
? |
$C_2^6.\POPlus(4,3)$ (as 16T1836) |
trivial |
$[2]$ |
$2$ |
$11$ |
$13710304.2776$ |
| 16.12.367...000.1 |
$x^{16} - 85 x^{14} + 2739 x^{12} - 40352 x^{10} + 240461 x^{8} - 36335 x^{6} - 2915250 x^{4} + 1098500 x^{2} + 1373125$ |
$16$ |
[12,2] |
$2^{16}\cdot 5^{4}\cdot 11^{4}\cdot 13^{11}\cdot 43^{4}$ |
$5$ |
$81.3436838555$ |
|
|
|
? |
$C_2^6.(C_4\times S_4)$ (as 16T1667) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$13$ |
$7280662137.23$ |
| 18.2.422...592.1 |
$x^{18} - 3 x^{12} + 9 x^{10} + 6 x^{8} - 23 x^{6} - 36 x^{4} - 15 x^{2} - 3$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{19}\cdot 31^{6}$ |
$3$ |
$15.901394767$ |
|
|
|
? |
$C_2^3\wr C_3.S_3^2$ (as 18T734) |
trivial |
trivial |
$2$ |
$9$ |
$4119.5902444$ |
| 18.4.219...744.2 |
$x^{18} + 9 x^{14} - x^{12} + 27 x^{10} - 6 x^{8} + 25 x^{6} - 9 x^{4} - 6 x^{2} + 1$ |
$18$ |
[4,7] |
$-\,2^{12}\cdot 3^{18}\cdot 7^{12}$ |
$3$ |
$17.42635720069111$ |
|
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T657) |
trivial |
trivial |
$2$ |
$10$ |
$12040.425107941623$ |
| 18.2.593...088.1 |
$x^{18} + 6 x^{16} + 6 x^{14} - 69 x^{12} - 441 x^{10} - 1341 x^{8} - 2241 x^{6} - 1998 x^{4} - 783 x^{2} - 27$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{21}\cdot 7^{12}$ |
$3$ |
$20.9279563564$ |
|
|
|
? |
$C_2^4:A_4^2.D_6$ (as 18T657) |
trivial |
$[2]$ |
$2$ |
$9$ |
$33272.9745321$ |
| 18.12.110...176.1 |
$x^{18} - 10 x^{16} + 26 x^{14} + 29 x^{12} - 188 x^{10} + 125 x^{8} + 158 x^{6} - 81 x^{4} + 3 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 37^{4}\cdot 229^{6}$ |
$3$ |
$21.6664502136$ |
$657.7159307568076$ |
|
|
? |
$C_2\times A_4^3.S_4$ (as 18T764) |
trivial |
$[2]$ |
$2$ |
$14$ |
$382025.335018$ |
| 18.8.125...184.2 |
$x^{18} + 5 x^{16} + x^{14} - 20 x^{12} - 13 x^{10} + 22 x^{8} + 13 x^{6} - 8 x^{4} - 3 x^{2} + 1$ |
$18$ |
[8,5] |
$-\,2^{12}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$21.8194591003$ |
$104.27721702727186$ |
|
|
? |
$C_2^5.(A_4\times S_4)$ (as 18T544) |
trivial |
$[2]$ |
$2$ |
$12$ |
$189234.717146$ |
| 18.6.548...888.2 |
$x^{18} - 15 x^{16} + 87 x^{14} - 277 x^{12} + 576 x^{10} - 831 x^{8} + 851 x^{6} - 633 x^{4} + 321 x^{2} - 107$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{6}\cdot 107^{9}$ |
$3$ |
$23.6820323951$ |
$225.5543797844839$ |
|
|
? |
$C_2^5.S_4^2$ (as 18T623) |
trivial |
trivial |
$2$ |
$11$ |
$234279.764604$ |
| 18.2.161...304.1 |
$x^{18} - 18 x^{14} - 39 x^{12} - 9 x^{10} + 21 x^{6} + 9 x^{4} - 9 x^{2} - 4$ |
$18$ |
[2,8] |
$2^{14}\cdot 3^{44}$ |
$2$ |
$25.1437958292$ |
$68.9397038608126$ |
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T593) |
trivial |
trivial |
$2$ |
$9$ |
$1206135.67404$ |
| 18.0.484...912.2 |
$x^{18} + 18 x^{14} + 27 x^{12} + 72 x^{10} - 99 x^{6} - 27 x^{4} + 27 x^{2} + 48$ |
$18$ |
[0,9] |
$-\,2^{14}\cdot 3^{45}$ |
$2$ |
$26.7262223901$ |
|
|
|
? |
$C_2^2:A_4^2.S_4$ (as 18T590) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$292191.584311$ |
| 18.12.804...776.6 |
$x^{18} - 28 x^{14} + 54 x^{12} + 49 x^{10} - 189 x^{8} + 132 x^{6} - 7 x^{4} - 14 x^{2} + 1$ |
$18$ |
[12,3] |
$-\,2^{18}\cdot 7^{12}\cdot 53^{6}$ |
$3$ |
$27.4907958178$ |
|
|
|
? |
$C_2^4:(C_6\times S_4)$ (as 18T367) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$3018182.39969$ |
| 18.0.886...752.4 |
$x^{18} + 2 x^{16} - 5 x^{14} + 13 x^{12} + 64 x^{10} + 45 x^{8} + 97 x^{6} + 153 x^{4} + 27$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 3^{9}\cdot 107^{8}$ |
$3$ |
$27.6400591859$ |
|
|
|
? |
$C_2^6:S_3^2$ (as 18T371) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$126720.97831$ |
| 18.0.220...376.1 |
$x^{18} + 20 x^{16} + 153 x^{14} + 573 x^{12} + 1136 x^{10} + 1219 x^{8} + 707 x^{6} + 211 x^{4} + 28 x^{2} + 1$ |
$18$ |
[0,9] |
$-\,2^{12}\cdot 257^{6}\cdot 43237^{2}$ |
$3$ |
$33.0440116274$ |
$13048.095961157862$ |
✓ |
|
? |
$C_2\times S_4^3.S_4$ (as 18T912) |
$[2, 8]$ |
$[2, 8]$ |
$2$ |
$8$ |
$95074.4744327$ |
| 18.10.119...552.4 |
$x^{18} - 25 x^{16} - 245 x^{14} + 5904 x^{12} - 6438 x^{10} - 120153 x^{8} + 120584 x^{6} + 400574 x^{4} - 331462 x^{2} - 148877$ |
$18$ |
[10,4] |
$2^{18}\cdot 7^{12}\cdot 53^{9}$ |
$3$ |
$53.28029537487781$ |
$104.27721702727186$ |
|
|
? |
$C_2^4:(A_4\times S_4)$ (as 18T462) |
$[2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$372788420.8495806$ |
| 18.0.161...464.1 |
$x^{18} + 30 x^{16} + 298 x^{14} + 1453 x^{12} + 3945 x^{10} + 6162 x^{8} + 5379 x^{6} + 2364 x^{4} + 397 x^{2} + 4$ |
$18$ |
[0,9] |
$-\,2^{18}\cdot 13^{8}\cdot 229^{8}$ |
$3$ |
$69.9731942834$ |
|
✓ |
|
? |
$C_2\wr C_9.C_6$ (as 18T656) |
$[2, 2, 320]$ |
$[2, 2, 320]$ |
$2$ |
$8$ |
$2578541.04453$ |
| 18.16.180...000.1 |
$x^{18} - x^{17} - 128 x^{16} + 3 x^{15} + 6745 x^{14} + 7297 x^{13} - 182721 x^{12} - 427804 x^{11} + 2428094 x^{10} + 10108718 x^{9} - 6884230 x^{8} - 101964173 x^{7} - 171939012 x^{6} + 187792795 x^{5} + 1219578806 x^{4} + 2274145760 x^{3} + 2281855540 x^{2} + 1249636670 x + 295064741$ |
$18$ |
[16,1] |
$-\,2^{12}\cdot 5^{9}\cdot 7^{12}\cdot 379^{2}\cdot 106405699^{2}$ |
$5$ |
$195.87130405$ |
$376651093.0820548$ |
|
|
? |
$C_3^6.C_2\wr C_6$ (as 18T857) |
$[3]$ |
$[6]$ |
$2$ |
$16$ |
$127101380105000$ |
| 20.0.199...000.2 |
$x^{20} + 4 x^{18} + 7 x^{16} + 17 x^{14} + 52 x^{12} + 97 x^{10} + 115 x^{8} + 107 x^{6} + 84 x^{4} + 35 x^{2} + 5$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{11}\cdot 53^{8}$ |
$3$ |
$20.652272498538895$ |
|
|
|
? |
$C_2^8.(C_4\times A_5)$ (as 20T672) |
trivial |
trivial |
$2$ |
$9$ |
$86312.90409176698$ |
| 20.6.626...696.2 |
$x^{20} - 3 x^{18} - 4 x^{16} + 28 x^{14} - 67 x^{12} + 83 x^{10} - 40 x^{8} - 17 x^{6} + 21 x^{4} - 2 x^{2} - 1$ |
$20$ |
[6,7] |
$-\,2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4}$ |
$4$ |
$21.869116491920124$ |
|
|
|
? |
$C_2^{10}.C_2^4:S_5$ (as 20T992) |
trivial |
$[2]$ |
$2$ |
$12$ |
$306007.97270574694$ |
| 20.8.700...000.1 |
$x^{20} + 30 x^{18} + 107 x^{16} - 3047 x^{14} - 19063 x^{12} + 85855 x^{10} + 623392 x^{8} - 697444 x^{6} - 5534298 x^{4} - 2254714 x^{2} + 1771561$ |
$20$ |
[8,6] |
$2^{16}\cdot 5^{10}\cdot 11^{10}\cdot 149^{4}\cdot 541^{4}$ |
$5$ |
$123.67503672$ |
|
|
|
|
$C_2^9.\SOPlus(4,4)$ (as 20T1008) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$13$ |
$60546016367200$ |
| 21.1.363...000.1 |
$x^{21} + 63 x^{17} - 84 x^{16} + 28 x^{15} + 1134 x^{13} - 3024 x^{12} + 3024 x^{11} - 1344 x^{10} + 5327 x^{9} - 20412 x^{8} + 31833 x^{7} - 20034 x^{6} - 5292 x^{5} + 18648 x^{4} - 14672 x^{3} + 6048 x^{2} - 1344 x + 128$ |
$21$ |
[1,10] |
$2^{12}\cdot 3^{19}\cdot 5^{9}\cdot 7^{22}$ |
$4$ |
$61.4607212865$ |
|
|
|
? |
$C_3^7:C_2\wr C_7.C_6$ (as 21T142) |
trivial |
trivial |
$2$ |
$10$ |
$115877205330$ |
| 22.0.261...704.1 |
$x^{22} + 6 x^{20} + 16 x^{18} + 18 x^{16} + 4 x^{14} + 6 x^{12} + 25 x^{10} + 3 x^{8} - 19 x^{6} - 4 x^{4} + 4 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$17.6294938054$ |
|
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
trivial |
$2$ |
$10$ |
$24986.318925$ |
