| 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 |
| 15.13.150...219.1 |
$x^{15} - 20 x^{13} - 9 x^{12} + 160 x^{11} + 144 x^{10} - 612 x^{9} - 864 x^{8} + 944 x^{7} + 2269 x^{6} + 320 x^{5} - 2024 x^{4} - 1777 x^{3} - 560 x^{2} - 60 x - 1$ |
$15$ |
[13,1] |
$-\,11^{13}\cdot 23\cdot 109\cdot 1738307$ |
$4$ |
$35.0880350376$ |
$571338.9379340672$ |
|
|
✓ |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$13$ |
$3498882.15493$ |
| 15.13.105...011.1 |
$x^{15} - 20 x^{13} - 10 x^{12} + 160 x^{11} + 160 x^{10} - 607 x^{9} - 960 x^{8} + 884 x^{7} + 2520 x^{6} + 560 x^{5} - 2240 x^{4} - 2100 x^{3} - 640 x^{2} - 48 x - 1$ |
$15$ |
[13,1] |
$-\,61^{3}\cdot 107\cdot 397^{3}\cdot 601\cdot 1158121$ |
$5$ |
$39.9599449059$ |
$42468435.6768518$ |
|
|
✓ |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$13$ |
$7821822.01554$ |
| 15.13.557...088.1 |
$x^{15} - 33 x^{13} - 22 x^{12} + 396 x^{11} + 528 x^{10} - 1903 x^{9} - 4158 x^{8} + 1683 x^{7} + 11264 x^{6} + 9207 x^{5} - 3630 x^{4} - 11000 x^{3} - 7920 x^{2} - 2640 x - 352$ |
$15$ |
[13,1] |
$-\,2^{10}\cdot 3^{15}\cdot 11^{14}$ |
$3$ |
$44.6451642054$ |
$177.8755140349851$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$13$ |
$22910503.5068$ |
| 15.13.264...643.1 |
$x^{15} - 20 x^{13} - 14 x^{12} + 160 x^{11} + 224 x^{10} - 589 x^{9} - 1344 x^{8} + 668 x^{7} + 3521 x^{6} + 1424 x^{5} - 3080 x^{4} - 3241 x^{3} - 1008 x^{2} - 92 x - 1$ |
$15$ |
[13,1] |
$-\,401^{6}\cdot 6369171443$ |
$2$ |
$49.5294241054$ |
$1598135.7103334498$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$13$ |
$54662801.9271$ |
| 15.13.274...699.1 |
$x^{15} - 20 x^{13} - 10 x^{12} + 160 x^{11} + 160 x^{10} - 609 x^{9} - 960 x^{8} + 908 x^{7} + 2525 x^{6} + 464 x^{5} - 2280 x^{4} - 1973 x^{3} - 560 x^{2} - 44 x - 1$ |
$15$ |
[13,1] |
$-\,13\cdot 59\cdot 1451\cdot 36497^{3}\cdot 507839$ |
$5$ |
$49.6513073921$ |
$143622670.2483992$ |
|
|
✓ |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$13$ |
$47479897.0022$ |
| 15.13.284...239.1 |
$x^{15} - 15 x^{13} - 17 x^{12} + 90 x^{11} + 204 x^{10} - 264 x^{9} - 918 x^{8} + 351 x^{7} + 1885 x^{6} - 81 x^{5} - 1671 x^{4} - 209 x^{3} + 441 x^{2} + 141 x + 9$ |
$15$ |
[13,1] |
$-\,3^{17}\cdot 53\cdot 401^{6}$ |
$3$ |
$49.7676226822$ |
|
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$13$ |
$106123713.261$ |
| 15.13.171...952.1 |
$x^{15} - 45 x^{13} - 30 x^{12} + 711 x^{11} + 948 x^{10} - 4436 x^{9} - 9504 x^{8} + 6300 x^{7} + 32288 x^{6} + 24948 x^{5} - 14184 x^{4} - 36384 x^{3} - 25920 x^{2} - 8640 x - 1152$ |
$15$ |
[13,1] |
$-\,2^{8}\cdot 3^{15}\cdot 881^{6}$ |
$3$ |
$65.412530328$ |
$2140.9695711335535$ |
|
|
|
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$13$ |
$4983572147.3$ |
| 15.13.310...216.1 |
$x^{15} - 15 x^{13} - 3 x^{12} + 90 x^{11} + 36 x^{10} - 278 x^{9} - 162 x^{8} + 477 x^{7} + 338 x^{6} - 459 x^{5} - 327 x^{4} + 232 x^{3} + 126 x^{2} - 48 x - 12$ |
$15$ |
[13,1] |
$-\,2^{16}\cdot 3^{15}\cdot 53^{9}$ |
$3$ |
$68.0433110341$ |
|
|
|
|
$S_3\wr F_5$ (as 15T87) |
trivial |
$2$ |
$13$ |
$1076875753.47$ |
| 15.13.806...032.1 |
$x^{15} - 46 x^{13} - 14 x^{12} + 744 x^{11} + 183 x^{10} - 5430 x^{9} + 2554 x^{8} + 27217 x^{7} - 28396 x^{6} - 115050 x^{5} + 36504 x^{4} + 215190 x^{3} + 47709 x^{2} - 118098 x - 55404$ |
$15$ |
[13,1] |
$-\,2^{8}\cdot 3^{3}\cdot 11^{6}\cdot 19^{4}\cdot 131^{6}$ |
$5$ |
$72.5170509851$ |
$7347.194099942892$ |
|
|
? |
$S_3\wr A_5$ (as 15T90) |
trivial |
$2$ |
$13$ |
$8604109121.98$ |
| 15.13.172...000.1 |
$x^{15} - 45 x^{13} - 75 x^{12} + 450 x^{11} + 1320 x^{10} + 1230 x^{9} - 90 x^{8} - 15165 x^{7} - 30560 x^{6} + 41355 x^{5} + 89985 x^{4} - 65975 x^{3} - 74970 x^{2} + 62925 x - 9587$ |
$15$ |
[13,1] |
$-\,2^{12}\cdot 3^{19}\cdot 5^{15}\cdot 7^{6}\cdot 101$ |
$5$ |
$103.707038154$ |
$2563.6914393831335$ |
|
|
? |
$S_3\wr F_5$ (as 15T87) |
trivial |
$2$ |
$13$ |
$30584458462.7$ |
| 15.13.315...951.1 |
$x^{15} - 2 x^{14} - 23 x^{13} + 42 x^{12} + 182 x^{11} - 300 x^{10} - 614 x^{9} + 885 x^{8} + 918 x^{7} - 1113 x^{6} - 525 x^{5} + 508 x^{4} + 60 x^{3} - 65 x^{2} + x + 1$ |
$15$ |
[13,1] |
$-\,13\cdot 17\cdot 23585458327\cdot 60\!\cdots\!53$ |
$4$ |
$1079.64391955$ |
$5.618288984389848e+22$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$13$ |
$1953101179450000000$ |
| 15.13.686...679.1 |
$x^{15} - 2 x^{14} - 23 x^{13} + 42 x^{12} + 182 x^{11} - 300 x^{10} - 614 x^{9} + 885 x^{8} + 918 x^{7} - 1112 x^{6} - 525 x^{5} + 508 x^{4} + 60 x^{3} - 66 x^{2} + x + 1$ |
$15$ |
[13,1] |
$-\,277\cdot 140891\cdot 1754444023\cdot 100190895611918899269402449839$ |
$4$ |
$1136.98670488$ |
$8.282575394661537e+22$ |
|
|
|
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$13$ |
$2184299502770000000$ |
| 15.13.771...000.1 |
$x^{15} - 1628 x^{13} - 5920 x^{12} + 1105179 x^{11} + 7903120 x^{10} - 388843381 x^{9} - 4223348520 x^{8} + 69563456700 x^{7} + 1121721226000 x^{6} - 4146108150000 x^{5} - 145380612000000 x^{4} - 422827275000000 x^{3} + 6657280500000000 x^{2} + 53977950000000000 x + 119951000000000000$ |
$15$ |
[13,1] |
$-\,2^{15}\cdot 5^{3}\cdot 7^{10}\cdot 13^{4}\cdot 1973^{2}\cdot 9227^{4}\cdot 9097717^{2}$ |
$7$ |
$5319.02041404$ |
$60316209129.16033$ |
|
|
|
$S_5\wr C_3$ (as 15T101) |
trivial |
$2$ |
$13$ |
$139335852303000000000000$ |
| 15.13.138...000.1 |
$x^{15} + 990 x^{13} - 37224 x^{12} - 1551408 x^{11} + 23094672 x^{10} + 394944750 x^{9} - 3242199744 x^{8} - 18669792904 x^{7} + 39296958832 x^{6} + 177645972320 x^{5} - 14676537600 x^{4} - 494313940000 x^{3} - 552000886400 x^{2} - 228301696000 x - 32614528000$ |
$15$ |
[13,1] |
$-\,2^{24}\cdot 5^{3}\cdot 37^{5}\cdot 67^{4}\cdot 709^{2}\cdot 3691^{2}\cdot 3803^{4}\cdot 57389^{2}$ |
$8$ |
$11913.665286557263$ |
$707298750086.3732$ |
|
|
|
$S_5^3.S_3$ (as 15T102) |
not computed |
$2$ |
$13$ |
|
