| 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 $p$ |
| 12.0.6728000000000.1 |
$x^{12} + 2 x^{10} - 2 x^{9} + 3 x^{8} - 2 x^{7} - 2 x^{5} + 3 x^{4} - 2 x^{3} + 2 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{9}\cdot 29^{2}$ |
$3$ |
$11.721697207017359$ |
$53.90488995872866$ |
|
|
? |
$S_4^2:C_4$ (as 12T237) |
trivial |
trivial |
$2$ |
$5$ |
$27.428544702659103$ |
$0$ |
$29$ |
| 12.4.39022400000000.1 |
$x^{12} - 3 x^{10} - 6 x^{9} + 2 x^{8} + 14 x^{7} + 9 x^{6} - 8 x^{5} - 12 x^{4} - 2 x^{3} + 7 x^{2} - 1$ |
$12$ |
(4, 4) |
$2^{12}\cdot 5^{8}\cdot 29^{3}$ |
$3$ |
$13.5709264894$ |
$102.2954725150871$ |
|
|
? |
$S_4^2:C_4$ (as 12T238) |
trivial |
trivial |
$2$ |
$7$ |
$162.271219918$ |
$4$ |
$29$ |
| 12.0.89549120000000.1 |
$x^{12} + 3 x^{10} - 2 x^{8} + 3 x^{6} + 26 x^{4} - 5 x^{2} + 5$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{7}\cdot 23^{4}$ |
$3$ |
$14.5435951592$ |
$39.257427049286115$ |
|
|
? |
$C_2^5.S_3^2$ (as 12T197) |
trivial |
trivial |
$2$ |
$5$ |
$133.615856052$ |
$0$ |
$23$ |
| 12.0.170061120000000.1 |
$x^{12} + 6 x^{10} - 4 x^{9} + 15 x^{8} - 12 x^{7} + 4 x^{6} - 12 x^{5} + 15 x^{4} - 4 x^{3} + 6 x^{2} + 1$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{12}\cdot 5^{7}$ |
$3$ |
$15.3420626867$ |
$37.646648893686574$ |
|
|
? |
$C_2^5.S_3^2$ (as 12T197) |
trivial |
trivial |
$2$ |
$5$ |
$174.67994942$ |
$0$ |
$5$ |
| 12.8.241875776000000.1 |
$x^{12} - 2 x^{11} - 2 x^{10} + 6 x^{9} - x^{8} - 16 x^{7} + 6 x^{6} + 40 x^{5} - 7 x^{4} - 30 x^{3} + 4 x^{2} + 6 x - 1$ |
$12$ |
(8, 2) |
$2^{12}\cdot 5^{6}\cdot 19^{4}\cdot 29$ |
$4$ |
$15.799112733228817$ |
$209.9021141342055$ |
|
|
? |
$A_4^2:D_4$ (as 12T208) |
trivial |
$[2]$ |
$2$ |
$9$ |
$662.2910309313443$ |
$7$ |
$29$ |
| 12.10.492092096000000.1 |
$x^{12} - 4 x^{11} - x^{10} + 20 x^{9} - 20 x^{8} - 16 x^{7} + 41 x^{6} - 8 x^{5} - 30 x^{4} + 10 x^{3} + 9 x^{2} - 2 x - 1$ |
$12$ |
(10, 1) |
$-\,2^{12}\cdot 5^{6}\cdot 19^{4}\cdot 59$ |
$4$ |
$16.7624385636$ |
$299.39450122576613$ |
|
|
? |
$A_4^2:D_4$ (as 12T208) |
trivial |
$[2]$ |
$2$ |
$10$ |
$1352.48458763$ |
$9$ |
$59$ |
| 12.8.1042568000000000.1 |
$x^{12} - 6 x^{11} + 7 x^{10} + 14 x^{9} - 14 x^{8} - 42 x^{7} + 31 x^{6} + 44 x^{5} - 42 x^{4} - 2 x^{3} + 17 x^{2} - 8 x + 1$ |
$12$ |
(8, 2) |
$2^{12}\cdot 5^{9}\cdot 19^{4}$ |
$3$ |
$17.8446773237$ |
$58.285471622057656$ |
|
|
✓ |
$A_4^2:C_4$ (as 12T159) |
trivial |
$[2]$ |
$2$ |
$9$ |
$1467.60599756$ |
$7$ |
$19$ |
| 12.0.5658248000000000.1 |
$x^{12} - 2 x^{11} + 12 x^{10} - 20 x^{9} + 76 x^{8} - 70 x^{7} + 198 x^{6} - 156 x^{5} + 236 x^{4} - 180 x^{3} + 120 x^{2} - 80 x + 20$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{9}\cdot 29^{4}$ |
$3$ |
$20.545820909933465$ |
$102.2954725150871$ |
|
|
? |
$S_4^2:C_4$ (as 12T237) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$5$ |
$377.38101499393036$ |
$0$ |
$29$ |
| 12.4.481964313920000000.1 |
$x^{12} - 6 x^{11} + x^{10} + 34 x^{9} - 6 x^{8} - 104 x^{7} - 47 x^{6} + 230 x^{5} + 206 x^{4} + 40 x^{3} - 235 x^{2} - 150 x - 25$ |
$12$ |
(4, 4) |
$2^{12}\cdot 5^{7}\cdot 197^{4}$ |
$3$ |
$29.7566867783$ |
$114.89232747123341$ |
|
|
? |
$C_2^5.S_3^2$ (as 12T197) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$11926.1465695$ |
$4$ |
$197$ |
| 12.4.481964313920000000.2 |
$x^{12} - 5 x^{10} - 46 x^{8} + 135 x^{6} + 514 x^{4} + 135 x^{2} + 5$ |
$12$ |
(4, 4) |
$2^{12}\cdot 5^{7}\cdot 197^{4}$ |
$3$ |
$29.7566867783$ |
$114.89232747123341$ |
|
|
? |
$C_2^5.S_3^2$ (as 12T197) |
trivial |
$[2]$ |
$2$ |
$7$ |
$16125.7755704$ |
$3$ |
$197$ |
| 12.0.634278221120000000.1 |
$x^{12} - 6 x^{11} + 13 x^{10} - 2 x^{9} - 16 x^{8} - 2 x^{7} + 35 x^{6} + 34 x^{5} - 72 x^{4} + 200 x^{3} + 451 x^{2} + 426 x + 269$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{7}\cdot 211^{4}$ |
$3$ |
$30.4455144308$ |
$290.1212574904409$ |
✓ |
|
? |
$A_4^2:C_4$ (as 12T159) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$4694.7779163$ |
$0$ |
$211$ |
| 12.12.392...000.1 |
$x^{12} - 2 x^{11} - 26 x^{10} + 42 x^{9} + 236 x^{8} - 320 x^{7} - 950 x^{6} + 1020 x^{5} + 1820 x^{4} - 1300 x^{3} - 1600 x^{2} + 500 x + 500$ |
$12$ |
(12, 0) |
$2^{12}\cdot 5^{8}\cdot 19^{3}\cdot 71^{3}$ |
$4$ |
$35.4415727616$ |
$300.6518559684287$ |
|
|
? |
$S_4^2:C_4$ (as 12T238) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$340865.534851$ |
$10$ |
$71$ |
| 12.12.733...000.1 |
$x^{12} - 2 x^{11} - 26 x^{10} + 58 x^{9} + 182 x^{8} - 488 x^{7} - 186 x^{6} + 964 x^{5} - 136 x^{4} - 584 x^{3} + 172 x^{2} + 60 x - 4$ |
$12$ |
(12, 0) |
$2^{12}\cdot 5^{9}\cdot 19^{2}\cdot 71^{4}$ |
$4$ |
$45.23443970538952$ |
$300.6518559684287$ |
|
|
? |
$S_4^2:C_4$ (as 12T237) |
trivial |
$[2, 2, 2]$ |
$2$ |
$11$ |
$2015681.2637384525$ |
$9$ |
$71$ |
| 12.0.165...000.1 |
$x^{12} - 2 x^{11} + 8 x^{10} - 54 x^{9} + 150 x^{8} - 474 x^{7} + 1038 x^{6} - 792 x^{5} - 184 x^{4} + 1980 x^{3} - 2980 x^{2} - 2380 x + 6220$ |
$12$ |
(0, 6) |
$2^{12}\cdot 5^{9}\cdot 379^{4}$ |
$3$ |
$48.39537977215163$ |
$428.69727304791195$ |
✓ |
|
? |
$A_4^2:C_4$ (as 12T159) |
$[2, 2, 6]$ |
$[2, 2, 6]$ |
$2$ |
$5$ |
$8639.508839391267$ |
$0$ |
$379$ |
| 12.0.166...000.1 |
$x^{12} - 144 x^{7} + 240 x^{6} + 2304 x^{2} - 7680 x + 6400$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{12}\cdot 5^{17}$ |
$3$ |
$58.6622554203$ |
|
|
|
? |
$A_6^2:C_4$ (as 12T298) |
trivial |
trivial |
$2$ |
$5$ |
$664799.123079$ |
$0$ |
$5$ |
| 12.0.415...000.1 |
$x^{12} - 240 x^{7} + 400 x^{6} + 11520 x^{2} - 38400 x + 32000$ |
$12$ |
(0, 6) |
$2^{12}\cdot 3^{12}\cdot 5^{19}$ |
$3$ |
$76.7103134334$ |
$344.5116357004392$ |
|
|
? |
$A_6^2:C_4$ (as 12T298) |
$[2]$ |
$[2]$ |
$2$ |
$5$ |
$1564443.97899$ |
$0$ |
$5$ |
| 16.0.330...000.2 |
$x^{16} - 9 x^{14} + 38 x^{12} - 99 x^{10} + 158 x^{8} - 131 x^{6} + 58 x^{4} - x^{2} + 1$ |
$16$ |
(0, 8) |
$2^{12}\cdot 5^{8}\cdot 379^{4}$ |
$3$ |
$16.5927091808036$ |
$286.6871451206211$ |
|
|
? |
$Q_8^2.A_4\wr C_2$ (as 16T1791) |
trivial |
trivial |
$2$ |
$7$ |
$1426.256246608487$ |
$0$ |
$379$ |
| 16.4.145...000.1 |
$x^{16} - x^{15} - 5 x^{14} + 5 x^{13} + 7 x^{12} - 8 x^{11} - 6 x^{10} - 9 x^{9} + 12 x^{8} + 28 x^{7} - 34 x^{6} - 21 x^{5} + 27 x^{4} + 5 x^{3} - 5 x^{2} - 2 x + 1$ |
$16$ |
(4, 6) |
$2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 61^{4}$ |
$4$ |
$18.203319217$ |
$146.92507822159706$ |
|
|
? |
$Q_8^2.A_4\wr C_2$ (as 16T1791) |
trivial |
$[2]$ |
$2$ |
$9$ |
$8833.53771546$ |
$3$ |
$61$ |
| 16.4.145...000.2 |
$x^{16} + x^{14} - 3 x^{12} - 6 x^{10} - 6 x^{8} + 34 x^{6} - 43 x^{4} - 155 x^{2} + 1$ |
$16$ |
(4, 6) |
$2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 61^{4}$ |
$4$ |
$18.203319217$ |
$146.92507822159706$ |
|
|
? |
$Q_8^2.A_4\wr C_2$ (as 16T1791) |
trivial |
$[2]$ |
$2$ |
$9$ |
$8146.18259885$ |
$3$ |
$61$ |
| 16.12.414...000.2 |
$x^{16} - 15 x^{14} + 37 x^{12} + 194 x^{10} - 806 x^{8} + 474 x^{6} + 477 x^{4} - 459 x^{2} + 81$ |
$16$ |
(12, 2) |
$2^{12}\cdot 3^{4}\cdot 5^{8}\cdot 7^{4}\cdot 191^{4}$ |
$5$ |
$29.9275155005$ |
$831.9820798935591$ |
|
|
? |
$C_2^6.\POPlus(4,3)$ (as 16T1836) |
trivial |
trivial |
$2$ |
$13$ |
$2232567.79272$ |
$12$ |
$191$ |
| 16.4.540...000.1 |
$x^{16} - x^{15} - 2 x^{14} - 12 x^{13} + 47 x^{12} - 120 x^{11} + 212 x^{10} - 172 x^{9} + 12 x^{8} + 368 x^{7} - 700 x^{6} + 792 x^{5} - 608 x^{4} - 320 x^{3} + 912 x^{2} - 976 x + 16$ |
$16$ |
(4, 6) |
$2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 61^{6}$ |
$4$ |
$30.4310413667$ |
$291.5082854596327$ |
|
|
? |
$C_2^7.A_4\wr C_2$ (as 16T1824) |
trivial |
$[2]$ |
$2$ |
$9$ |
$458811.274339$ |
$3$ |
$61$ |
| 16.8.540...000.2 |
$x^{16} - x^{15} - 6 x^{14} + 4 x^{13} - 5 x^{12} + 62 x^{11} - 6 x^{10} - 118 x^{9} - 162 x^{8} + 58 x^{7} + 330 x^{6} - 612 x^{5} + 1800 x^{4} + 1564 x^{3} - 2888 x^{2} - 2040 x - 236$ |
$16$ |
(8, 4) |
$2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 61^{6}$ |
$4$ |
$30.4310413667$ |
$291.5082854596327$ |
|
|
? |
$C_2^7.A_4\wr C_2$ (as 16T1824) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1808686.92251$ |
$7$ |
$61$ |
| 16.0.540...000.2 |
$x^{16} - 6 x^{15} + 16 x^{14} - 29 x^{13} + 44 x^{12} - 118 x^{11} + 558 x^{10} - 2025 x^{9} + 5460 x^{8} - 11560 x^{7} + 19668 x^{6} - 27501 x^{5} + 31336 x^{4} - 27360 x^{3} + 16750 x^{2} - 6401 x + 1171$ |
$16$ |
(0, 8) |
$2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 61^{6}$ |
$4$ |
$30.4310413667$ |
$291.5082854596327$ |
|
|
? |
$C_2^7.A_4\wr C_2$ (as 16T1824) |
$[2]$ |
$[2]$ |
$2$ |
$7$ |
$60470.337919$ |
$0$ |
$61$ |
| 16.12.613...000.1 |
$x^{16} - 12 x^{14} + 14 x^{12} + 220 x^{10} - 517 x^{8} - 68 x^{6} + 626 x^{4} - 160 x^{2} + 5$ |
$16$ |
(12, 2) |
$2^{12}\cdot 5^{9}\cdot 11^{4}\cdot 269^{4}$ |
$4$ |
$30.6711009543$ |
$445.27713729133035$ |
|
|
|
$C_2^7.\POPlus(4,3)$ (as 16T1863) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$4612911.92362$ |
$9$ |
$269$ |
| 16.10.196...000.1 |
$x^{16} - 5 x^{14} - 35 x^{12} + 164 x^{10} - 116 x^{8} - 180 x^{6} + 199 x^{4} - 47 x^{2} - 1$ |
$16$ |
(10, 3) |
$-\,2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{4}$ |
$4$ |
$32.98384182469852$ |
$430.3383803700806$ |
|
|
|
$C_2^8.\POPlus(4,3)$ (as 16T1887) |
trivial |
$[2, 2]$ |
$2$ |
$12$ |
$4707666.714215823$ |
$8$ |
$269$ |
| 16.12.186...000.1 |
$x^{16} - 7 x^{15} + 3 x^{14} + 124 x^{13} - 525 x^{12} + 589 x^{11} + 1798 x^{10} - 6599 x^{9} + 5776 x^{8} + 8041 x^{7} - 19954 x^{6} + 8593 x^{5} + 7251 x^{4} - 3880 x^{3} - 1265 x^{2} - 15 x + 5$ |
$16$ |
(12, 2) |
$2^{12}\cdot 3^{6}\cdot 5^{9}\cdot 7^{4}\cdot 191^{4}$ |
$5$ |
$37.966140145$ |
$1637.3321399084546$ |
|
|
|
$C_2^7.\POPlus(4,3)$ (as 16T1863) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$31571108.4711$ |
$10$ |
$191$ |
| 16.8.596...000.2 |
$x^{16} - 9 x^{14} - 6 x^{13} - 78 x^{12} + 34 x^{11} + 465 x^{10} + 48 x^{9} + 1112 x^{8} - 1040 x^{7} - 5221 x^{6} + 1778 x^{5} - 4564 x^{4} - 10258 x^{3} + 5185 x^{2} + 3488 x - 1051$ |
$16$ |
(8, 4) |
$2^{16}\cdot 3^{6}\cdot 5^{8}\cdot 7^{4}\cdot 191^{4}$ |
$5$ |
$40.8289602353$ |
$1399.616571532276$ |
|
|
|
$C_2^7.\POPlus(4,3)$ (as 16T1867) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$13035158.9689$ |
$6$ |
$191$ |
| 16.4.527...000.1 |
$x^{16} - 2 x^{15} + 2 x^{14} - 14 x^{13} - 44 x^{12} - 2 x^{11} + 122 x^{10} + 332 x^{9} + 708 x^{8} - 3096 x^{7} + 648 x^{6} - 5152 x^{5} + 10956 x^{4} + 4544 x^{3} - 6080 x^{2} - 4304$ |
$16$ |
(4, 6) |
$2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5}$ |
$4$ |
$46.7908308211$ |
$1541.4901570344189$ |
|
|
|
$C_2^7.\POPlus(4,3)$ (as 16T1870) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$3571279.01469$ |
$3$ |
$269$ |
| 16.12.527...000.1 |
$x^{16} - 18 x^{14} + 104 x^{12} - 168 x^{10} - 339 x^{8} + 1212 x^{6} - 672 x^{4} - 538 x^{2} + 269$ |
$16$ |
(12, 2) |
$2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 269^{5}$ |
$4$ |
$46.7908308211$ |
$1541.4901570344189$ |
|
|
|
$C_2^7.\POPlus(4,3)$ (as 16T1870) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$156144938.185$ |
$9$ |
$269$ |
| 16.12.887...000.1 |
$x^{16} - 6 x^{15} - 8 x^{14} + 136 x^{13} - 216 x^{12} - 982 x^{11} + 2814 x^{10} + 2368 x^{9} - 11179 x^{8} + 84 x^{7} + 15888 x^{6} - 3986 x^{5} - 6530 x^{4} + 2466 x^{3} - 836 x^{2} - 80 x + 445$ |
$16$ |
(12, 2) |
$2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 269^{6}$ |
$4$ |
$55.8165224709$ |
$1205.940736510186$ |
|
|
? |
$Q_8^2.\POPlus(4,3)$ (as 16T1837) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$373070895.801$ |
$9$ |
$269$ |
| 16.4.887...000.2 |
$x^{16} + 45 x^{14} + 637 x^{12} + 2594 x^{10} - 7206 x^{8} - 46806 x^{6} - 34163 x^{4} + 72361 x^{2} + 72361$ |
$16$ |
(4, 6) |
$2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 269^{6}$ |
$4$ |
$55.8165224709$ |
$1205.940736510186$ |
|
|
? |
$Q_8^2.\POPlus(4,3)$ (as 16T1837) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$34628793.7702$ |
$2$ |
$269$ |
| 16.0.620...000.1 |
$x^{16} - 4 x^{15} + 22 x^{14} - 56 x^{13} + 192 x^{12} - 452 x^{11} + 650 x^{10} - 860 x^{9} - 1097 x^{8} - 2610 x^{7} + 11994 x^{6} + 100836 x^{5} + 304526 x^{4} + 559836 x^{3} + 784068 x^{2} + 607774 x + 421219$ |
$16$ |
(0, 8) |
$2^{16}\cdot 3^{4}\cdot 5^{8}\cdot 7^{6}\cdot 191^{5}$ |
$5$ |
$63.0274887823$ |
$4693.349490473681$ |
✓ |
|
|
$C_2^8.\POPlus(4,3)$ (as 16T1887) |
$[2, 2, 128]$ |
$[2, 2, 128]$ |
$2$ |
$7$ |
$179538.402106$ |
$0$ |
$191$ |
| 18.2.107...368.1 |
$x^{18} - 6 x^{17} + 16 x^{16} - 24 x^{15} + 30 x^{14} - 58 x^{13} + 111 x^{12} - 144 x^{11} + 150 x^{10} - 200 x^{9} + 261 x^{8} - 260 x^{7} + 196 x^{6} - 114 x^{5} + 35 x^{4} + 8 x^{3} - 9 x^{2} + 2 x + 1$ |
$18$ |
(2, 8) |
$2^{18}\cdot 3^{9}\cdot 113^{6}$ |
$3$ |
$16.7475045397$ |
$91.15625121211103$ |
|
|
? |
$C_2^3:A_4^2.S_4$ (as 18T662) |
trivial |
trivial |
$2$ |
$9$ |
$5702.74607772$ |
$2$ |
$113$ |
| 18.10.922...736.1 |
$x^{18} - 3 x^{16} - 72 x^{15} - 261 x^{14} + 402 x^{13} + 2613 x^{12} + 8082 x^{11} + 870 x^{10} - 31370 x^{9} - 19386 x^{8} - 135510 x^{7} - 269838 x^{6} - 1037592 x^{5} - 3147576 x^{4} + 970692 x^{3} + 8472564 x^{2} + 5771352 x + 504580$ |
$18$ |
(10, 4) |
$2^{16}\cdot 3^{24}\cdot 163^{8}$ |
$3$ |
$77.0794100817$ |
$335.96230842210707$ |
|
|
|
$C_2^8:\PU(3,2)$ (as 18T735) |
trivial |
trivial |
$2$ |
$13$ |
$269793141260$ |
$10$ |
$163$ |
| 18.8.276...208.1 |
$x^{18} - 9 x^{16} - 204 x^{14} + 1488 x^{12} + 8070 x^{10} - 18930 x^{8} - 17004 x^{6} + 792 x^{4} + 2097 x^{2} + 147$ |
$18$ |
(8, 5) |
$-\,2^{16}\cdot 3^{25}\cdot 163^{8}$ |
$3$ |
$81.9304081824$ |
|
|
|
? |
$C_2^9.\PU(3,2)$ (as 18T799) |
trivial |
$[2]$ |
$2$ |
$12$ |
$458362648114$ |
$7$ |
$163$ |
| 18.8.276...208.2 |
$x^{18} + 12 x^{16} - 216 x^{14} - 2043 x^{12} + 14652 x^{10} + 89208 x^{8} - 315333 x^{6} - 792072 x^{4} + 242028 x^{2} + 477603$ |
$18$ |
(8, 5) |
$-\,2^{16}\cdot 3^{25}\cdot 163^{8}$ |
$3$ |
$81.9304081824$ |
|
|
|
? |
$C_2^9.\PU(3,2)$ (as 18T799) |
trivial |
$[2]$ |
$2$ |
$12$ |
$488205745931$ |
$7$ |
$163$ |
| 18.2.908...000.1 |
$x^{18} - 8 x^{17} - 3 x^{16} + 64 x^{15} + 499 x^{14} - 1636 x^{13} - 2945 x^{12} - 6700 x^{11} + 54188 x^{10} + 72560 x^{9} - 239980 x^{8} - 842056 x^{7} + 750448 x^{6} + 10043024 x^{5} - 30472560 x^{4} + 37964448 x^{3} - 22856640 x^{2} + 6092736 x - 677056$ |
$18$ |
(2, 8) |
$2^{16}\cdot 5^{10}\cdot 23^{6}\cdot 1429^{2}\cdot 216661^{2}$ |
$5$ |
$113.039916928$ |
$17966513.73383935$ |
|
|
|
$C_3^6.(C_2^5.S_3^2)$ (as 18T918) |
trivial |
trivial |
$2$ |
$9$ |
$556261265169$ |
$2$ |
$216661$ |
| 18.14.330...000.1 |
$x^{18} - x^{17} - 158 x^{16} - 21 x^{15} + 10314 x^{14} + 7747 x^{13} - 350947 x^{12} - 364128 x^{11} + 6622068 x^{10} + 7273400 x^{9} - 69358036 x^{8} - 65624432 x^{7} + 394931316 x^{6} + 203199136 x^{5} - 1235751560 x^{4} + 170623280 x^{3} + 1653608944 x^{2} - 1395919856 x + 329875984$ |
$18$ |
(14, 2) |
$2^{16}\cdot 5^{12}\cdot 19^{6}\cdot 211^{2}\cdot 7621^{2}\cdot 41221^{2}$ |
$6$ |
$230.246287932$ |
$954631165.3641257$ |
|
|
|
$C_3^6:(A_4^2:C_4)$ (as 18T892) |
trivial |
trivial |
$2$ |
$15$ |
$1898618467090000$ |
$14$ |
$41221$ |
| 18.10.224...000.1 |
$x^{18} - 6 x^{17} - 247 x^{16} + 1480 x^{15} + 22194 x^{14} - 153430 x^{13} - 868106 x^{12} + 8055028 x^{11} + 9383936 x^{10} - 213867114 x^{9} + 311681384 x^{8} + 2363004752 x^{7} - 9009599142 x^{6} + 1179065318 x^{5} + 54444101326 x^{4} - 133271543204 x^{3} + 138996861211 x^{2} - 60965672856 x + 5318837731$ |
$18$ |
(10, 4) |
$2^{16}\cdot 5^{10}\cdot 17^{4}\cdot 19^{2}\cdot 197^{6}\cdot 3391^{2}\cdot 13171^{2}$ |
$7$ |
$485.547642547$ |
$680858821.3412019$ |
|
|
|
$C_3^6.(C_2^5.S_3^2)$ (as 18T918) |
trivial |
trivial |
$2$ |
$13$ |
$1145162453050000000$ |
$10$ |
$13171$ |
| 18.10.353...000.1 |
$x^{18} - 6 x^{17} - 408 x^{16} + 3480 x^{15} + 54090 x^{14} - 663650 x^{13} - 1912646 x^{12} + 51983360 x^{11} - 113004592 x^{10} - 1566983916 x^{9} + 9143280664 x^{8} + 3360102400 x^{7} - 170299619268 x^{6} + 502730516856 x^{5} + 105388977984 x^{4} - 3627737769480 x^{3} + 8481685631360 x^{2} - 8456304656320 x + 3183400636720$ |
$18$ |
(10, 4) |
$2^{16}\cdot 5^{10}\cdot 151^{2}\cdot 197^{6}\cdot 20363090971^{2}$ |
$5$ |
$643.067543161$ |
$24294322550.748955$ |
|
|
|
$C_3^6.(C_2^5.S_3^2)$ (as 18T918) |
trivial |
trivial |
$2$ |
$13$ |
$14445842973400000000$ |
$10$ |
$20363090971$ |
| 20.10.976...056.1 |
$x^{20} - 2 x^{18} - 4 x^{16} + 7 x^{14} + x^{12} + 3 x^{10} + 3 x^{8} - 11 x^{6} + 4 x^{2} - 1$ |
$20$ |
(10, 5) |
$-\,2^{20}\cdot 30516826559^{2}$ |
$2$ |
$22.360624706$ |
$677645.9190796186$ |
|
|
? |
$C_2^{10}.S_{10}$ (as 20T1110) |
trivial |
trivial |
$2$ |
$14$ |
$1334502.89974$ |
$10$ |
$30516826559$ |
| 20.2.976...056.1 |
$x^{20} + 12 x^{18} + 59 x^{16} + 153 x^{14} + 218 x^{12} + 136 x^{10} - 60 x^{8} - 168 x^{6} - 106 x^{4} - 21 x^{2} - 1$ |
$20$ |
(2, 9) |
$-\,2^{20}\cdot 30516826559^{2}$ |
$2$ |
$22.360624706$ |
$677645.9190796186$ |
|
|
? |
$C_2^{10}.S_{10}$ (as 20T1110) |
trivial |
trivial |
$2$ |
$10$ |
$222620.403565$ |
$2$ |
$30516826559$ |
| 20.8.344...000.1 |
$x^{20} - 120 x^{17} - 405 x^{16} + 2076 x^{15} + 1800 x^{14} + 8700 x^{13} - 67515 x^{12} + 147540 x^{11} + 273906 x^{10} - 2771100 x^{9} + 4175100 x^{8} - 11125260 x^{7} + 84132660 x^{6} - 236877744 x^{5} + 322399800 x^{4} - 224890800 x^{3} + 50829520 x^{2} + 6736080 x - 2092464$ |
$20$ |
(8, 6) |
$2^{20}\cdot 3^{24}\cdot 5^{33}$ |
$3$ |
$106.383924767$ |
|
|
|
|
$A_6^2:C_4$ (as 20T937) |
$[2]$ |
$[2, 2]$ |
$2$ |
$13$ |
$6522944287310$ |
$7$ |
$5$ |
| 20.8.511...000.1 |
$x^{20} - 4 x^{19} + 1647 x^{18} - 6444 x^{17} - 260452 x^{16} + 5844148 x^{15} - 1573874230 x^{14} + 12009884328 x^{13} - 486113795285 x^{12} + 1454493380180 x^{11} + 310647299614074 x^{10} - 3583749168654180 x^{9} + 138706292339072455 x^{8} - 1146508155372235668 x^{7} - 2737860248140861370 x^{6} - 25363257788242872288 x^{5} - 3105200580343332192552 x^{4} + 8715616052401155296304 x^{3} + 29585189944050767132407 x^{2} - 117999388104537362338856 x + 896756648962153116185641$ |
$20$ |
(8, 6) |
$2^{20}\cdot 5^{16}\cdot 41^{4}\cdot 2543^{10}$ |
$4$ |
$768.1321637506203$ |
$8673.887158304547$ |
|
|
? |
$C_2^9.A_5^2.C_4$ (as 20T1025) |
not computed |
not computed |
$2$ |
$13$ |
|
|
$2543$ |
