| 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 |
Unit signature rank |
Max $p$ |
| 12.0.5015306502144.3 |
$x^{12} + 3 x^{10} - 5 x^{6} + 3 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{20}\cdot 3^{14}$ |
$2$ |
$11.438211516$ |
$16.17607385516733$ |
|
|
✓ |
$S_4$ (as 12T9) |
trivial |
trivial |
$6$ |
$5$ |
$112.73235666$ |
$0$ |
$3$ |
| 12.0.49331181715456.1 |
$x^{12} + x^{10} + 2 x^{8} - x^{6} + 2 x^{4} - 3 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{6}$ |
$2$ |
$13.8386415368$ |
$40.85985846931865$ |
|
|
✓ |
$C_2^5:S_4$ (as 12T191) |
trivial |
trivial |
$2$ |
$5$ |
$144.190113133$ |
$0$ |
$19$ |
| 12.4.49331181715456.2 |
$x^{12} - 6 x^{11} + 14 x^{10} - 14 x^{9} - 5 x^{8} + 32 x^{7} - 36 x^{6} + 20 x^{5} - 17 x^{4} + 14 x^{3} + 6 x^{2} - 6 x + 1$ |
$12$ |
(4, 4) |
$2^{20}\cdot 19^{6}$ |
$2$ |
$13.8386415368$ |
$40.85985846931865$ |
|
|
? |
$C_2^5:S_4$ (as 12T184) |
trivial |
trivial |
$2$ |
$7$ |
$151.914266561$ |
$4$ |
$19$ |
| 12.0.49331181715456.5 |
$x^{12} + x^{10} + 6 x^{8} + 3 x^{6} + 6 x^{4} + x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{6}$ |
$2$ |
$13.8386415368$ |
$40.85985846931865$ |
|
|
? |
$C_2^2:S_4$ (as 12T68) |
trivial |
trivial |
$2$ |
$5$ |
$68.7698359101$ |
$0$ |
$19$ |
| 12.0.49331181715456.7 |
$x^{12} + 3 x^{10} + 4 x^{8} + 3 x^{6} + 4 x^{4} + 3 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{6}$ |
$2$ |
$13.8386415368$ |
$19.570794546160904$ |
|
|
✓ |
$S_4$ (as 12T9) |
trivial |
trivial |
$2$ |
$5$ |
$84.7546117944$ |
$0$ |
$19$ |
| 12.0.174080000000000.1 |
$x^{12} - 9 x^{10} + 30 x^{8} - 4 x^{7} - 35 x^{6} - 4 x^{5} + 30 x^{4} - 9 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{20}\cdot 5^{10}\cdot 17$ |
$3$ |
$15.3719538932$ |
$117.83427198232499$ |
|
|
? |
$C_2\wr S_5$ (as 12T270) |
trivial |
trivial |
$2$ |
$5$ |
$196.031223012$ |
$0$ |
$17$ |
| 12.0.224771578003456.2 |
$x^{12} - x^{10} - 8 x^{8} + 11 x^{6} + 44 x^{4} - 121 x^{2} + 121$ |
$12$ |
(0, 6) |
$2^{20}\cdot 11^{8}$ |
$2$ |
$15.7028488211$ |
$27.119156113033114$ |
|
|
? |
$S_4$ (as 12T9) |
trivial |
trivial |
$2$ |
$5$ |
$168.671305297$ |
$0$ |
$11$ |
| 12.4.256000000000000.1 |
$x^{12} - 2 x^{11} - 4 x^{10} + 10 x^{9} - 5 x^{8} - 20 x^{7} + 40 x^{6} - 25 x^{4} + 30 x^{3} - 10 x + 5$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{12}$ |
$2$ |
$15.8740105197$ |
$28.57900880593445$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
trivial |
$2$ |
$7$ |
$506.047684117$ |
$4$ |
$5$ |
| 12.0.17808556599279616.4 |
$x^{12} - 6 x^{11} + 7 x^{10} + 16 x^{9} - 24 x^{8} - 62 x^{7} + 125 x^{6} + 80 x^{5} - 54 x^{4} - 94 x^{3} + 9 x^{2} + 16 x + 9$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{8}$ |
$2$ |
$22.6057572718$ |
$40.85985846931865$ |
|
|
? |
$C_2^5:S_4$ (as 12T191) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$809.379670123$ |
$0$ |
$19$ |
| 12.0.17808556599279616.14 |
$x^{12} - 9 x^{10} + 44 x^{8} - 133 x^{6} + 304 x^{4} - 361 x^{2} + 361$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{8}$ |
$2$ |
$22.6057572718$ |
$40.85985846931865$ |
|
|
? |
$C_2^2:S_4$ (as 12T69) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$411.154074895$ |
$0$ |
$19$ |
| 12.0.17808556599279616.15 |
$x^{12} - x^{10} + 24 x^{8} - 209 x^{6} + 456 x^{4} - 361 x^{2} + 361$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{8}$ |
$2$ |
$22.6057572718$ |
$40.85985846931865$ |
|
|
|
$S_4$ (as 12T9) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$564.193174968$ |
$0$ |
$19$ |
| 12.0.17808556599279616.17 |
$x^{12} + 3 x^{10} + 20 x^{8} + 29 x^{6} - 10 x^{4} + 133 x^{2} + 361$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{8}$ |
$2$ |
$22.6057572718$ |
$40.85985846931865$ |
|
|
? |
$C_2^5:S_4$ (as 12T191) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$776.978802702$ |
$0$ |
$19$ |
| 12.0.17808556599279616.21 |
$x^{12} - 9 x^{10} + 28 x^{8} - 61 x^{6} + 64 x^{4} + 399 x^{2} + 361$ |
$12$ |
(0, 6) |
$2^{20}\cdot 19^{8}$ |
$2$ |
$22.6057572718$ |
$40.85985846931865$ |
|
|
|
$C_2^2:S_4$ (as 12T68) |
$[4]$ |
$[4]$ |
$2$ |
$5$ |
$1509.62128666$ |
$0$ |
$19$ |
| 12.12.30706253824000000.1 |
$x^{12} - 15 x^{10} + 78 x^{8} - 183 x^{6} + 196 x^{4} - 77 x^{2} + 1$ |
$12$ |
(12, 0) |
$2^{20}\cdot 5^{6}\cdot 37^{4}$ |
$3$ |
$23.6556872417$ |
$61.06853778901886$ |
|
|
? |
$C_2 \times S_4$ (as 12T23) |
trivial |
$[2]$ |
$2$ |
$11$ |
$18639.8138968$ |
$11$ |
$37$ |
| 12.0.32905425960566784.22 |
$x^{12} - 6 x^{10} + 24 x^{8} - 80 x^{6} + 168 x^{4} + 48 x^{2} + 16$ |
$12$ |
(0, 6) |
$2^{20}\cdot 3^{22}$ |
$2$ |
$23.792438739$ |
$33.64758954662642$ |
|
|
? |
$S_4$ (as 12T9) |
trivial |
trivial |
$6$ |
$5$ |
$14717.4100799$ |
$0$ |
$3$ |
| 12.4.160000000000000000.4 |
$x^{12} - 2 x^{11} - 14 x^{10} + 30 x^{9} + 55 x^{8} - 120 x^{7} - 120 x^{6} + 340 x^{5} - 225 x^{4} + 50 x^{3} + 30 x^{2} - 10 x + 5$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{16}$ |
$2$ |
$27.1441761659$ |
$54.404542678012895$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
trivial |
$2$ |
$7$ |
$14985.7093727$ |
$4$ |
$5$ |
| 12.12.184...000.1 |
$x^{12} - 24 x^{10} + 192 x^{8} - 664 x^{6} + 992 x^{4} - 512 x^{2} + 16$ |
$12$ |
(12, 0) |
$2^{20}\cdot 5^{6}\cdot 103^{4}$ |
$3$ |
$33.2772479889$ |
$101.89087030315206$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$160256.354359$ |
$10$ |
$103$ |
| 12.4.184...000.1 |
$x^{12} - 4 x^{11} - 3 x^{10} + 8 x^{9} + 6 x^{8} - 4 x^{7} - 9 x^{6} - 4 x^{5} + 6 x^{4} + 8 x^{3} - 3 x^{2} - 4 x + 1$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{6}\cdot 103^{4}$ |
$3$ |
$33.27724798893153$ |
$101.89087030315206$ |
|
|
✓ |
$C_2^5:S_5$ (as 12T257) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$10571.128267552353$ |
$4$ |
$103$ |
| 12.4.400...000.3 |
$x^{12} - 14 x^{10} + 55 x^{8} - 205 x^{4} - 146 x^{2} + 9$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{18}$ |
$2$ |
$35.4953665976$ |
$103.56742195303535$ |
|
|
? |
$C_2^5:S_5$ (as 12T257) |
trivial |
trivial |
$2$ |
$7$ |
$204986.892267$ |
$4$ |
$5$ |
| 12.4.400...000.6 |
$x^{12} - x^{10} - 25 x^{6} - 25 x^{2} + 25$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{18}$ |
$2$ |
$35.4953665976$ |
$103.56742195303535$ |
|
|
? |
$C_2^5:S_5$ (as 12T257) |
trivial |
trivial |
$2$ |
$7$ |
$120856.029241$ |
$4$ |
$5$ |
| 12.4.100...000.1 |
$x^{12} - 6 x^{11} + 19 x^{10} + 30 x^{9} - 460 x^{8} + 2226 x^{7} - 6881 x^{6} + 14994 x^{5} - 23860 x^{4} + 26670 x^{3} - 17661 x^{2} + 4866 x - 209$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{20}$ |
$2$ |
$46.4158883361$ |
$103.56742195303535$ |
|
|
? |
$S_5$ (as 12T74) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$130986.30254$ |
$4$ |
$5$ |
| 12.4.100...000.2 |
$x^{12} - 2 x^{11} - 9 x^{10} + 20 x^{9} + 20 x^{8} - 86 x^{7} + 47 x^{6} - 396 x^{5} + 890 x^{4} + 90 x^{3} + 549 x^{2} - 648 x - 81$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{20}$ |
$2$ |
$46.4158883361$ |
$103.56742195303535$ |
|
|
|
$S_5$ (as 12T74) |
trivial |
trivial |
$2$ |
$7$ |
$613626.435741$ |
$4$ |
$5$ |
| 12.4.100...000.6 |
$x^{12} - 4 x^{11} - 21 x^{10} + 30 x^{9} + 160 x^{8} - 28 x^{7} - 423 x^{6} - 2 x^{5} + 830 x^{4} + 460 x^{3} - 459 x^{2} - 274 x + 149$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{20}$ |
$2$ |
$46.4158883361$ |
$103.56742195303535$ |
|
|
? |
$S_5$ (as 12T74) |
trivial |
trivial |
$2$ |
$7$ |
$373026.28497$ |
$4$ |
$5$ |
| 12.4.100...000.7 |
$x^{12} - 5 x^{10} - 125 x^{6} - 125 x^{2} + 625$ |
$12$ |
(4, 4) |
$2^{20}\cdot 5^{20}$ |
$2$ |
$46.4158883361$ |
$103.56742195303535$ |
|
|
? |
$C_2^5:S_5$ (as 12T257) |
$[2, 2]$ |
$[2, 4]$ |
$2$ |
$7$ |
$189699.20629$ |
$3$ |
$5$ |
| 12.0.999...000.3 |
$x^{12} + 33 x^{10} + 454 x^{8} + 3417 x^{6} + 15596 x^{4} + 45335 x^{2} + 81225$ |
$12$ |
(0, 6) |
$2^{20}\cdot 5^{6}\cdot 83^{2}\cdot 97^{4}$ |
$4$ |
$68.124802322$ |
$900.8273695976882$ |
✓ |
|
|
$C_2^2\wr S_3$ (as 12T139) |
$[8, 32]$ |
$[8, 32]$ |
$2$ |
$5$ |
$19531.044449839992$ |
$0$ |
$97$ |
| 12.0.135...000.1 |
$x^{12} + 25 x^{10} + 238 x^{8} + 1065 x^{6} + 2208 x^{4} + 1755 x^{2} + 441$ |
$12$ |
(0, 6) |
$2^{20}\cdot 3^{6}\cdot 5^{8}\cdot 7^{2}\cdot 31^{4}$ |
$5$ |
$69.8598305093$ |
$440.8414966325568$ |
✓ |
|
? |
$C_2^2\wr S_3$ (as 12T139) |
$[280]$ |
$[280]$ |
$2$ |
$5$ |
$19642.574084041036$ |
$0$ |
$31$ |
| 12.0.147...624.3 |
$x^{12} + 27 x^{10} + 280 x^{8} + 1377 x^{6} + 3142 x^{4} + 2553 x^{2} + 81$ |
$12$ |
(0, 6) |
$2^{20}\cdot 3^{4}\cdot 23^{2}\cdot 757^{4}$ |
$4$ |
$70.3736932303$ |
$1026.1341526265182$ |
✓ |
|
? |
$C_2^2\wr S_3$ (as 12T139) |
$[8, 16]$ |
$[8, 16]$ |
$2$ |
$5$ |
$22034.731245965657$ |
$0$ |
$757$ |
| 14.6.449152684508839936.1 |
$x^{14} - 7 x^{13} + 23 x^{12} - 47 x^{11} + 54 x^{10} - 6 x^{9} - 81 x^{8} + 129 x^{7} - 78 x^{6} - 26 x^{5} + 71 x^{4} - 43 x^{3} + x^{2} + 9 x - 4$ |
$14$ |
(6, 4) |
$2^{20}\cdot 809^{4}$ |
$2$ |
$18.2341400313$ |
$127.70441679847741$ |
|
|
? |
$C_2^6:\GL(3,2)$ (as 14T50) |
trivial |
trivial |
$2$ |
$9$ |
$11443.5024238$ |
$6$ |
$809$ |
| 14.6.359...488.1 |
$x^{14} - 2 x^{13} - 8 x^{12} + 22 x^{11} - 11 x^{10} - 13 x^{8} + 26 x^{7} - 13 x^{6} - 11 x^{4} + 22 x^{3} - 8 x^{2} - 2 x + 1$ |
$14$ |
(6, 4) |
$2^{23}\cdot 809^{4}$ |
$2$ |
$21.1539616817$ |
$170.46494509614888$ |
|
|
? |
$C_2^7.\PSL(2,7)$ (as 14T51) |
trivial |
$[2]$ |
$2$ |
$9$ |
$17505.5082711$ |
$5$ |
$809$ |
| 14.8.853...784.1 |
$x^{14} - 3 x^{13} - 5 x^{12} + 18 x^{11} - 7 x^{10} + x^{9} + 3 x^{8} + 71 x^{6} - 193 x^{5} - 59 x^{4} + 34 x^{3} + 35 x^{2} + 11 x + 1$ |
$14$ |
(8, 3) |
$-\,2^{20}\cdot 19\cdot 809^{4}$ |
$3$ |
$22.5021921366$ |
$556.6506474683611$ |
|
|
|
$C_2^7.\PSL(2,7)$ (as 14T51) |
trivial |
$[2]$ |
$2$ |
$10$ |
$29284.3445382$ |
$7$ |
$809$ |
| 14.6.130...144.1 |
$x^{14} - 5 x^{13} + 6 x^{12} + 3 x^{11} - 9 x^{10} + 6 x^{9} - 5 x^{8} + 7 x^{7} - 5 x^{6} + 6 x^{5} - 9 x^{4} + 3 x^{3} + 6 x^{2} - 5 x + 1$ |
$14$ |
(6, 4) |
$2^{20}\cdot 29\cdot 809^{4}$ |
$3$ |
$23.1922180501$ |
$687.7093310587969$ |
|
|
|
$C_2^7.\PSL(2,7)$ (as 14T51) |
trivial |
$[2]$ |
$2$ |
$9$ |
$25868.8843749$ |
$5$ |
$809$ |
| 16.0.767656345600000000.3 |
$x^{16} - 2 x^{14} + 4 x^{12} - 10 x^{10} + 15 x^{8} - 10 x^{6} + 4 x^{4} - 2 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{8}\cdot 37^{4}$ |
$3$ |
$13.1166499283$ |
$61.06853778901886$ |
|
|
|
$C_2^4:S_4$ (as 16T747) |
trivial |
trivial |
$2$ |
$7$ |
$308.729862622$ |
$0$ |
$37$ |
| 16.0.162...896.1 |
$x^{16} - x^{15} + 6 x^{14} - 15 x^{13} + 25 x^{12} - 50 x^{11} + 89 x^{10} - 125 x^{9} + 165 x^{8} - 202 x^{7} + 225 x^{6} - 253 x^{5} + 264 x^{4} - 205 x^{3} + 103 x^{2} - 30 x + 4$ |
$16$ |
(0, 8) |
$2^{20}\cdot 19^{2}\cdot 809^{4}$ |
$3$ |
$18.3281582118$ |
$556.6506474683611$ |
|
|
|
$C_2^4.C_2^6:\GL(3,2)$ (as 16T1902) |
trivial |
trivial |
$2$ |
$7$ |
$6573.74087177$ |
$0$ |
$809$ |
| 16.0.105...000.1 |
$x^{16} - x^{15} - x^{14} + 4 x^{13} + 34 x^{12} - 60 x^{10} + 24 x^{9} + 392 x^{8} + 320 x^{7} - 540 x^{6} - 888 x^{5} + 252 x^{4} + 1412 x^{3} + 916 x^{2} + 128 x + 16$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{8}\cdot 37^{6}$ |
$3$ |
$20.5990951312$ |
$150.61490509961556$ |
|
|
|
$C_2^3\wr C_2:S_4$ (as 16T1523) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$6671.57648833$ |
$0$ |
$37$ |
| 16.0.285...000.1 |
$x^{16} - 3 x^{14} + 11 x^{12} - 18 x^{10} + 34 x^{8} - 18 x^{6} + 11 x^{4} - 3 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{8}\cdot 17^{8}$ |
$3$ |
$21.9278957314$ |
$66.37674328962952$ |
|
|
|
$C_2^3:S_4$ (as 16T442) |
trivial |
trivial |
$2$ |
$7$ |
$18710.8931651$ |
$0$ |
$17$ |
| 16.0.285...000.2 |
$x^{16} + 7 x^{12} - 12 x^{10} - x^{8} - 12 x^{6} + 49 x^{4} + 52 x^{2} + 16$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{8}\cdot 17^{8}$ |
$3$ |
$21.9278957314$ |
$66.37674328962952$ |
|
|
|
$C_2^4:S_4$ (as 16T772) |
trivial |
trivial |
$2$ |
$7$ |
$26710.5244108$ |
$0$ |
$17$ |
| 16.0.117...736.2 |
$x^{16} + 13 x^{14} + 52 x^{12} + 43 x^{10} - 122 x^{8} - 233 x^{6} + 112 x^{4} + 193 x^{2} + 49$ |
$16$ |
(0, 8) |
$2^{20}\cdot 3^{16}\cdot 127^{4}$ |
$3$ |
$23.9529870417$ |
$182.29509428866749$ |
|
|
|
$C_2^6:S_4$ (as 16T1318) |
trivial |
trivial |
$6$ |
$7$ |
$554716.65958$ |
$0$ |
$127$ |
| 16.0.714...000.1 |
$x^{16} + 6 x^{14} + 20 x^{12} + 48 x^{10} + 99 x^{8} + 180 x^{6} + 160 x^{4} + 25$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{10}\cdot 17^{8}$ |
$3$ |
$26.8144076783$ |
$99.25638217958134$ |
|
|
|
$C_2^6:S_4$ (as 16T1327) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$67608.3888587$ |
$0$ |
$17$ |
| 16.4.178...000.1 |
$x^{16} + 14 x^{14} + 64 x^{12} + 58 x^{10} - 266 x^{8} - 354 x^{6} + 416 x^{4} + 2 x^{2} + 1$ |
$16$ |
(4, 6) |
$2^{20}\cdot 5^{12}\cdot 17^{8}$ |
$3$ |
$32.7898521567$ |
$99.25638217958134$ |
|
|
|
$C_2^6:S_4$ (as 16T1318) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$662084.852402$ |
$3$ |
$17$ |
| 16.0.178...000.2 |
$x^{16} - x^{14} - 10 x^{12} + 21 x^{10} - 46 x^{8} + 101 x^{6} + 190 x^{4} + 59 x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{12}\cdot 17^{8}$ |
$3$ |
$32.7898521567$ |
$99.25638217958134$ |
|
|
|
$C_2^6:S_4$ (as 16T1318) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$144415.380468$ |
$0$ |
$17$ |
| 16.8.178...000.2 |
$x^{16} - 11 x^{14} + 50 x^{12} - 119 x^{10} + 144 x^{8} - 129 x^{6} + 125 x^{4} - 76 x^{2} + 16$ |
$16$ |
(8, 4) |
$2^{20}\cdot 5^{12}\cdot 17^{8}$ |
$3$ |
$32.7898521567$ |
$99.25638217958134$ |
|
|
|
$C_2^6:S_4$ (as 16T1318) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$3837527.73261$ |
$6$ |
$17$ |
| 16.0.178...000.3 |
$x^{16} + 16 x^{14} + 95 x^{12} + 324 x^{10} + 559 x^{8} + 564 x^{6} + 345 x^{4} + 116 x^{2} + 16$ |
$16$ |
(0, 8) |
$2^{20}\cdot 5^{12}\cdot 17^{8}$ |
$3$ |
$32.7898521567$ |
$99.25638217958134$ |
|
|
|
$C_2^6:S_4$ (as 16T1318) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$7$ |
$198645.385927$ |
$0$ |
$17$ |
| 16.4.178...000.4 |
$x^{16} + 9 x^{14} + 9 x^{12} - 112 x^{10} - 256 x^{8} + 176 x^{6} + 176 x^{4} - 1088 x^{2} + 16$ |
$16$ |
(4, 6) |
$2^{20}\cdot 5^{12}\cdot 17^{8}$ |
$3$ |
$32.7898521567$ |
$99.25638217958134$ |
|
|
|
$Q_8^2:S_4$ (as 16T1321) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$996092.397687$ |
$3$ |
$17$ |
| 16.4.178...000.5 |
$x^{16} + 2 x^{14} - 44 x^{12} + 26 x^{10} + 534 x^{8} - 1462 x^{6} + 1524 x^{4} - 1166 x^{2} + 841$ |
$16$ |
(4, 6) |
$2^{20}\cdot 5^{12}\cdot 17^{8}$ |
$3$ |
$32.78985215668483$ |
$99.25638217958134$ |
|
|
|
$Q_8^2:S_4$ (as 16T1321) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$703083.0013373039$ |
$3$ |
$17$ |
| 18.2.557...504.1 |
$x^{18} - 6 x^{16} + 6 x^{14} + 21 x^{12} - 30 x^{10} - 24 x^{8} + 27 x^{6} + 18 x^{4} - 1$ |
$18$ |
(2, 8) |
$2^{24}\cdot 3^{24}\cdot 7^{6}$ |
$3$ |
$20.8561598693$ |
$54.632249942518804$ |
|
|
? |
$S_4^2$ (as 18T186) |
trivial |
trivial |
$2$ |
$9$ |
$289175.083953$ |
$2$ |
$7$ |
| 18.4.167...512.1 |
$x^{18} - 3 x^{16} - 9 x^{14} - 9 x^{12} + 12 x^{10} - 24 x^{8} + 48$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 3^{25}\cdot 7^{6}$ |
$3$ |
$22.1687437592$ |
$54.632249942518804$ |
|
|
|
$S_4^2$ (as 18T187) |
trivial |
$[2]$ |
$2$ |
$10$ |
$203743.896943$ |
$3$ |
$7$ |
| 18.2.251...136.1 |
$x^{18} + 18 x^{14} + 3 x^{12} + 108 x^{10} + 36 x^{8} + 165 x^{6} + 54 x^{4} - 1$ |
$18$ |
(2, 8) |
$2^{24}\cdot 3^{36}$ |
$2$ |
$22.6785788981$ |
$42.951753948724544$ |
|
|
? |
$\PSOPlus(4,3)$ (as 18T117) |
trivial |
trivial |
$2$ |
$9$ |
$746710.479421$ |
$2$ |
$3$ |
| 18.0.755...408.1 |
$x^{18} + 9 x^{16} + 27 x^{14} + 27 x^{12} - 36 x^{8} - 24 x^{6} + 144 x^{4} + 144 x^{2} + 48$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 3^{37}$ |
$2$ |
$24.1058568579$ |
$42.951753948724544$ |
|
|
|
$\PSOPlus(4,3)$ (as 18T116) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$138970.206657$ |
$0$ |
$3$ |
| 18.2.179...856.1 |
$x^{18} - 3 x^{12} - 16 x^{9} + 27 x^{6} - 12 x^{3} + 1$ |
$18$ |
(2, 8) |
$2^{30}\cdot 3^{34}$ |
$2$ |
$25.2898175463$ |
$58.67590245029688$ |
|
|
? |
$C_3^4:S_4$ (as 18T359) |
trivial |
trivial |
$2$ |
$9$ |
$882836.958932$ |
$2$ |
$3$ |
| 18.2.353...184.1 |
$x^{18} - x^{17} - x^{16} + 11 x^{15} + 2 x^{14} - 40 x^{13} + 122 x^{12} + 4 x^{11} - 412 x^{10} + 972 x^{9} - 1896 x^{8} + 2344 x^{7} - 5492 x^{6} + 9308 x^{5} - 6716 x^{4} + 2780 x^{3} - 576 x^{2} - 8 x - 8$ |
$18$ |
(2, 8) |
$2^{24}\cdot 11^{9}\cdot 19^{7}$ |
$3$ |
$26.2641129343$ |
$64.90898235874951$ |
|
|
? |
$S_4^2$ (as 18T181) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1526218.00774$ |
$1$ |
$19$ |
