| 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 |
| 12.0.36083978714052.2 |
$x^{12} - 2 x^{9} + 3 x^{6} - 3 x^{3} + 2$ |
$12$ |
[0,6] |
$2^{2}\cdot 3^{12}\cdot 257^{3}$ |
$3$ |
$13.482679207291174$ |
$126.95913357461518$ |
|
|
✓ |
$C_3^3:(S_3\times S_4)$ (as 12T258) |
trivial |
$2$ |
$5$ |
$99.90263410903717$ |
| 12.0.69657034752000.1 |
$x^{12} - 2 x^{9} + 2$ |
$12$ |
[0,6] |
$2^{20}\cdot 3^{12}\cdot 5^{3}$ |
$3$ |
$14.2423093702$ |
$35.41705012468423$ |
|
|
✓ |
$S_3^3:C_2$ (as 12T156) |
trivial |
$4$ |
$5$ |
$329.074204255$ |
| 12.0.15196929064453125.1 |
$x^{12} - 11 x^{9} + 51 x^{6} - 121 x^{3} + 121$ |
$12$ |
[0,6] |
$3^{12}\cdot 5^{9}\cdot 11^{4}$ |
$3$ |
$22.3089768604$ |
$82.50875193999316$ |
|
|
? |
$C_3^2:C_4\times S_3$ (as 12T119) |
trivial |
$10$ |
$5$ |
$8255.75011032$ |
| 12.0.247...000.1 |
$x^{12} - 45 x^{10} - 30 x^{9} + 855 x^{8} + 1050 x^{7} - 6605 x^{6} - 8910 x^{5} + 24885 x^{4} + 34860 x^{3} - 10980 x^{2} - 14640 x + 4880$ |
$12$ |
[0,6] |
$2^{8}\cdot 3^{12}\cdot 5^{11}\cdot 61^{2}$ |
$4$ |
$41.3128727171$ |
$676.0566890381432$ |
|
|
? |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
trivial |
$10$ |
$5$ |
$279058.582648$ |
| 15.1.580...024.1 |
$x^{15} + 6 x - 2$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 3^{13}\cdot 53\cdot 5156339\cdot 81321571$ |
$5$ |
$60.8491649708$ |
$1420311487.1845126$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$73354383.3614$ |
| 15.1.329...207.1 |
$x^{15} - 3 x - 7$ |
$15$ |
[1,7] |
$-\,3^{13}\cdot 7^{14}\cdot 13679\cdot 2230979$ |
$4$ |
$79.6587059221$ |
$8326919.909664639$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$409037440.16$ |
| 16.0.373...000.1 |
$x^{16} - 8 x^{13} + 12 x^{12} - 48 x^{9} + 72 x^{8} + 128 x^{7} - 384 x^{6} + 472 x^{4} - 864 x + 648$ |
$16$ |
[0,8] |
$2^{50}\cdot 3^{12}\cdot 5^{4}$ |
$3$ |
$29.7373441233$ |
|
|
|
? |
$(C_2^2:S_4)^2.D_6$ (as 16T1880) |
trivial |
$4$ |
$7$ |
$710010.087501$ |
| 16.2.739...407.1 |
$x^{16} - 5 x + 3$ |
$16$ |
[2,7] |
$-\,3^{13}\cdot 11\cdot 19\cdot 97579\cdot 139871\cdot 1625982889$ |
$6$ |
$55.1832993875$ |
$339769095874.5369$ |
|
|
? |
$S_{16}$ (as 16T1954) |
trivial |
$2$ |
$8$ |
$86413756.9305$ |
| 16.2.963...424.1 |
$x^{16} - 4 x - 6$ |
$16$ |
[2,7] |
$-\,2^{32}\cdot 3^{13}\cdot 127\cdot 1108409495539$ |
$4$ |
$74.817382146$ |
|
|
|
? |
$S_{16}$ (as 16T1954) |
trivial |
$2$ |
$8$ |
$2021007462.93$ |
| 16.0.103...000.1 |
$x^{16} - 24 x^{14} + 252 x^{12} - 1460 x^{10} - 156 x^{9} + 5163 x^{8} + 1872 x^{7} - 12204 x^{6} - 8424 x^{5} + 21770 x^{4} + 12912 x^{3} - 17064 x^{2} - 21492 x + 19359$ |
$16$ |
[0,8] |
$2^{12}\cdot 3^{12}\cdot 5^{10}\cdot 41^{6}\cdot 101^{2}$ |
$5$ |
$75.1283426828$ |
$16410.366517078503$ |
|
|
|
$A_4^2\wr C_2.D_4$ (as 16T1910) |
trivial |
$2$ |
$7$ |
$692580963.544$ |
| 16.12.790...000.1 |
$x^{16} - 42 x^{14} - 64 x^{13} + 461 x^{12} + 1248 x^{11} + 432 x^{10} + 1164 x^{9} + 2031 x^{8} - 21254 x^{7} - 46809 x^{6} + 4722 x^{5} + 72517 x^{4} + 39926 x^{3} - 3741 x^{2} - 4082 x + 31$ |
$16$ |
[12,2] |
$2^{16}\cdot 3^{12}\cdot 5^{8}\cdot 29^{4}\cdot 28669^{2}$ |
$5$ |
$85.3359458353$ |
|
|
|
? |
$C_2^8.S_3\wr C_2^2$ (as 16T1931) |
$[2]$ |
$2$ |
$13$ |
$3194825276.96$ |
| 16.0.132...000.1 |
$x^{16} + 24 x^{14} - 64 x^{13} + 204 x^{12} - 1152 x^{11} + 2824 x^{10} - 8256 x^{9} + 27246 x^{8} - 66816 x^{7} + 153096 x^{6} - 340416 x^{5} + 701116 x^{4} - 1174656 x^{3} + 1362456 x^{2} - 948672 x + 301401$ |
$16$ |
[0,8] |
$2^{40}\cdot 3^{12}\cdot 5^{14}\cdot 61^{2}$ |
$4$ |
$88.1415966607$ |
|
|
|
? |
$C_2^8.C_3^3:(C_4\times S_3)$ (as 16T1893) |
$[2]$ |
$10$ |
$7$ |
$2877703003.79$ |
| 18.2.714...104.2 |
$x^{18} - 2 x^{15} - 3 x^{12} + 11 x^{9} - 6 x^{6} - 8 x^{3} + 8$ |
$18$ |
[2,8] |
$2^{6}\cdot 3^{18}\cdot 257^{6}$ |
$3$ |
$24.031209398$ |
|
|
|
? |
$C_3^3:(S_3\times S_4)$ (as 18T448) |
trivial |
$2$ |
$9$ |
$136953.918289$ |
| 18.2.173...625.1 |
$x^{18} - 4 x^{15} + 6 x^{12} + x^{9} - 29 x^{6} + 45 x^{3} + 5$ |
$18$ |
[2,8] |
$3^{14}\cdot 5^{14}\cdot 29^{6}$ |
$3$ |
$25.2466433652$ |
$205.90421028609154$ |
|
|
? |
$\He_3^2:(C_4\times S_3)$ (as 18T604) |
trivial |
$2$ |
$9$ |
$251706.315064$ |
| 18.2.839...625.1 |
$x^{18} - x^{15} + 4 x^{12} - 2 x^{9} + 6 x^{6} - 5 x^{3} + 1$ |
$18$ |
[2,8] |
$3^{18}\cdot 5^{12}\cdot 31^{6}$ |
$3$ |
$27.5563582502$ |
|
|
|
|
$\He_3^2:(C_2\times C_4)$ (as 18T496) |
trivial |
$2$ |
$9$ |
$1728743.0126$ |
| 18.6.320...704.1 |
$x^{18} - 18 x^{16} - 8 x^{15} + 135 x^{14} + 120 x^{13} - 544 x^{12} - 720 x^{11} + 1263 x^{10} + 2256 x^{9} - 1674 x^{8} - 4104 x^{7} + 1227 x^{6} + 4536 x^{5} - 720 x^{4} - 2848 x^{3} + 594 x^{2} + 768 x - 256$ |
$18$ |
[6,6] |
$2^{46}\cdot 3^{18}\cdot 7^{6}$ |
$3$ |
$33.738011288$ |
|
|
|
|
$\He_3^2:(C_2\times C_4)$ (as 18T496) |
trivial |
$2$ |
$11$ |
$95402934.4538$ |
| 18.6.703...125.1 |
$x^{18} - 21 x^{16} - 11 x^{15} + 189 x^{14} + 123 x^{13} - 916 x^{12} - 585 x^{11} + 2565 x^{10} + 1710 x^{9} - 3465 x^{8} - 525 x^{7} + 5420 x^{6} - 495 x^{5} - 4455 x^{4} + 1485 x^{3} + 1305 x^{2} - 870 x + 145$ |
$18$ |
[6,6] |
$3^{18}\cdot 5^{15}\cdot 29^{6}$ |
$3$ |
$35.242138826$ |
|
|
|
|
$C_3^4:(C_4\times S_3)$ (as 18T345) |
trivial |
$2$ |
$11$ |
$26802581.5981$ |
| 18.12.390...000.1 |
$x^{18} - 15 x^{16} + 54 x^{14} - 54 x^{13} - 152 x^{12} - 198 x^{11} + 963 x^{10} + 4868 x^{9} - 1305 x^{8} - 16842 x^{7} - 2915 x^{6} + 20682 x^{5} + 3600 x^{4} - 11352 x^{3} + 2592 x - 576$ |
$18$ |
[12,3] |
$-\,2^{12}\cdot 3^{22}\cdot 5^{9}\cdot 19^{3}\cdot 61^{3}$ |
$5$ |
$44.055530865$ |
$1623.413108833333$ |
|
|
? |
$\He_3^2:(S_3\times D_4)$ (as 18T674) |
trivial |
$2$ |
$14$ |
$341941627.153$ |
| 18.18.986...816.1 |
$x^{18} - 117 x^{16} - 24 x^{15} + 5409 x^{14} + 1602 x^{13} - 130691 x^{12} - 36036 x^{11} + 1820784 x^{10} + 252602 x^{9} - 15152256 x^{8} + 1649760 x^{7} + 74699590 x^{6} - 32228280 x^{5} - 199571904 x^{4} + 159400920 x^{3} + 206197488 x^{2} - 265997088 x + 65225664$ |
$18$ |
[18,0] |
$2^{20}\cdot 3^{22}\cdot 7^{10}\cdot 101^{6}$ |
$4$ |
$113.561732337$ |
$1366.6418438452893$ |
|
|
|
$C_3^5:(C_2\times S_4)$ (as 18T580) |
trivial |
$2$ |
$17$ |
$63714888623800$ |
| 18.6.818...000.1 |
$x^{18} - 12 x^{15} + 11 x^{12} + 152 x^{9} + 131 x^{6} + 28 x^{3} + 1$ |
$18$ |
[6,6] |
$2^{18}\cdot 3^{18}\cdot 5^{12}\cdot 53^{9}$ |
$4$ |
$127.723022714$ |
|
|
|
? |
$C_3^3:(S_3\times S_4)$ (as 18T445) |
$[2]$ |
$2$ |
$11$ |
$3041083520770$ |
| 18.18.244...016.1 |
$x^{18} - 441 x^{16} - 644 x^{15} + 64890 x^{14} + 163380 x^{13} - 3763557 x^{12} - 12444138 x^{11} + 79411752 x^{10} + 287570318 x^{9} - 744150015 x^{8} - 2921529450 x^{7} + 3000978589 x^{6} + 14338287684 x^{5} - 2706224724 x^{4} - 32395159104 x^{3} - 9829847664 x^{2} + 26464974480 x + 15953665392$ |
$18$ |
[18,0] |
$2^{20}\cdot 3^{22}\cdot 7^{14}\cdot 101^{9}$ |
$4$ |
$377.646214425$ |
|
|
|
|
$C_3^3:(S_3\times S_4)$ (as 18T445) |
$[6]$ |
$2$ |
$17$ |
$243520234387000000$ |
| 21.9.210...648.1 |
$x^{21} - 27 x^{17} - 36 x^{16} - 39 x^{15} - 54 x^{14} + 45 x^{13} + 208 x^{12} + 945 x^{11} + 2526 x^{10} + 3985 x^{9} + 5076 x^{8} + 3393 x^{7} - 5790 x^{6} - 18252 x^{5} - 22104 x^{4} - 15056 x^{3} - 6048 x^{2} - 1344 x - 128$ |
$21$ |
[9,6] |
$2^{14}\cdot 3^{21}\cdot 107^{3}\cdot 21557^{3}$ |
$4$ |
$38.619258655$ |
|
|
|
? |
$C_3^7.(C_2^7.S_7)$ (as 21T152) |
trivial |
$2$ |
$14$ |
$572421980.598$ |
| 30.0.426...291.1 |
$x^{30} - 3 x + 5$ |
$30$ |
[0,15] |
$-\,3^{29}\cdot 71\cdot 467\cdot 51628578737\cdot 9899468832468151\cdot 3663798440144491003$ |
$6$ |
$132.124748935$ |
|
|
|
? |
$S_{30}$ (as 30T5712) |
not computed |
$2$ |
$14$ |
|
