| 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 |
| 15.1.723352547563839.1 |
$x^{15} - x^{14} - 2 x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} + 5 x^{9} - 5 x^{8} + 4 x^{7} - 5 x^{6} - 4 x^{5} + 5 x^{4} - 2 x^{3} + x^{2} + x + 1$ |
$15$ |
[1,7] |
$-\,3^{3}\cdot 6653\cdot 4026880369$ |
$3$ |
$9.78640837431$ |
$8965071.404337559$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$7$ |
$11.7410590074$ |
| 15.3.1788527348449625.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 9 x^{12} + 13 x^{11} - 15 x^{10} + 18 x^{9} - 23 x^{8} + 33 x^{7} - 44 x^{6} + 48 x^{5} - 44 x^{4} + 30 x^{3} - 16 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$5^{3}\cdot 7^{10}\cdot 37^{3}$ |
$3$ |
$10.3952045383$ |
$49.77193869732466$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
trivial |
$2$ |
$8$ |
$26.5068203244$ |
| 15.3.2164169497031757.1 |
$x^{15} - 7 x^{14} + 23 x^{13} - 45 x^{12} + 54 x^{11} - 32 x^{10} - 14 x^{9} + 55 x^{8} - 72 x^{7} + 69 x^{6} - 57 x^{5} + 39 x^{4} - 21 x^{3} + 9 x^{2} - 4 x + 1$ |
$15$ |
[3,6] |
$3^{3}\cdot 69593\cdot 1151759887$ |
$3$ |
$10.5281666665$ |
$15506878.391474314$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$8$ |
$29.6657425505$ |
| 15.3.2354315214908549.1 |
$x^{15} - x^{14} + x^{13} - x^{12} - x^{11} + 3 x^{10} - 2 x^{9} + 2 x^{8} - 2 x^{7} - x^{6} + 2 x^{3} - x^{2} + 2 x - 1$ |
$15$ |
[3,6] |
$27765763\cdot 84792023$ |
$2$ |
$10.5874402875$ |
$48521286.204186186$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$8$ |
$31.1653663197$ |
| 15.3.2432060458605625.1 |
$x^{15} - x^{14} - 2 x^{13} + x^{12} + 2 x^{11} - 4 x^{10} - 4 x^{9} + 3 x^{8} + 4 x^{7} - 2 x^{6} - 3 x^{5} + 5 x^{4} + 5 x^{3} - x^{2} - 4 x - 1$ |
$15$ |
[3,6] |
$5^{4}\cdot 19^{2}\cdot 47^{6}$ |
$3$ |
$10.6103967712$ |
$142.7352803864651$ |
|
|
? |
$C_3\wr D_5$ (as 15T46) |
trivial |
trivial |
$2$ |
$8$ |
$32.0155843928$ |
| 15.3.2581408254768721.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 11 x^{12} - 4 x^{11} - 19 x^{10} + 24 x^{9} + 6 x^{8} - 29 x^{7} + 13 x^{6} + 13 x^{5} - 14 x^{4} - x^{3} + 5 x^{2} - x - 1$ |
$15$ |
[3,6] |
$7^{10}\cdot 3023^{2}$ |
$2$ |
$10.652636625745691$ |
$201.19527021937301$ |
|
|
✓ |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$33.36148075197536$ |
| 15.3.3187134619912369.1 |
$x^{15} - x^{14} - 3 x^{13} + 5 x^{12} + 3 x^{11} - 9 x^{10} - x^{9} + 8 x^{8} + 4 x^{7} - 7 x^{6} - 9 x^{5} + 5 x^{4} + 9 x^{3} - x^{2} - 4 x - 1$ |
$15$ |
[3,6] |
$7^{10}\cdot 3359^{2}$ |
$2$ |
$10.803389325352759$ |
$212.08194383428116$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$37.83417450489708$ |
| 15.3.3276367268581097.1 |
$x^{15} - 6 x^{13} - x^{12} + 16 x^{11} + 8 x^{10} - 20 x^{9} - 24 x^{8} + 4 x^{7} + 31 x^{6} + 15 x^{5} - 15 x^{4} - 14 x^{3} + x^{2} + 4 x + 1$ |
$15$ |
[3,6] |
$3276367268581097$ |
$1$ |
$10.8232952365$ |
$57239560.34580539$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$8$ |
$37.7909873347$ |
| 15.1.3703260525677583.1 |
$x^{15} - 2 x^{14} + x^{13} - x^{12} - 5 x^{11} + 4 x^{10} - 3 x^{9} + 2 x^{8} + 6 x^{7} - 3 x^{6} + 3 x^{5} - 4 x^{4} - 5 x^{3} - 3 x^{2} - 3 x - 1$ |
$15$ |
[1,7] |
$-\,3\cdot 13^{3}\cdot 561866260913$ |
$3$ |
$10.912031669$ |
$8888625.705547903$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$7$ |
$39.9823344692$ |
| 15.3.4864965285308625.1 |
$x^{15} - 3 x^{14} + 6 x^{13} - 12 x^{12} + 14 x^{11} - 17 x^{10} + 24 x^{9} - 28 x^{8} + 31 x^{7} - 21 x^{6} + 18 x^{5} - 15 x^{4} + 16 x^{3} - 11 x^{2} + 5 x - 1$ |
$15$ |
[3,6] |
$3^{9}\cdot 5^{3}\cdot 7^{11}$ |
$3$ |
$11.1123347675$ |
$40.77320330425099$ |
|
|
? |
$S_5 \times C_3$ (as 15T24) |
trivial |
trivial |
$2$ |
$8$ |
$50.4138149085$ |
| 15.3.5318139197378329.1 |
$x^{15} - 2 x^{14} + 5 x^{13} - 10 x^{12} + 12 x^{11} - 22 x^{10} + 20 x^{9} - 34 x^{8} + 27 x^{7} - 36 x^{6} + 22 x^{5} - 17 x^{4} + 5 x^{3} - x + 1$ |
$15$ |
[3,6] |
$7^{10}\cdot 4339^{2}$ |
$2$ |
$11.178511553825736$ |
$241.04244193574246$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$52.4584251761628$ |
| 15.1.5976545641547631.1 |
$x^{15} - 2 x^{14} + 5 x^{13} - 10 x^{12} + 13 x^{11} - 20 x^{10} + 23 x^{9} - 22 x^{8} + 22 x^{7} - 20 x^{6} + 18 x^{5} - 20 x^{4} + 21 x^{3} - 15 x^{2} + 6 x - 1$ |
$15$ |
[1,7] |
$-\,3\cdot 195479\cdot 10191283363$ |
$3$ |
$11.2658340433$ |
$77308121.44624671$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$7$ |
$50.8430332143$ |
| 15.3.6114596477365737.1 |
$x^{15} - 3 x^{14} + 5 x^{13} - 2 x^{12} - 8 x^{11} + 18 x^{10} - 18 x^{9} + 20 x^{7} - 27 x^{6} + 15 x^{5} + 3 x^{4} - 11 x^{3} + 10 x^{2} - 5 x + 1$ |
$15$ |
[3,6] |
$3^{4}\cdot 15601\cdot 4838718377$ |
$3$ |
$11.2829982327$ |
$15048805.141895186$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$8$ |
$53.4601866446$ |
| 15.3.6142020067423681.1 |
$x^{15} + x^{13} - 5 x^{12} - 4 x^{11} - 6 x^{10} + 6 x^{9} + 9 x^{8} + 12 x^{7} - 2 x^{6} - 6 x^{5} - 10 x^{4} + 2 x^{3} + x^{2} + 3 x - 1$ |
$15$ |
[3,6] |
$7^{10}\cdot 4663^{2}$ |
$2$ |
$11.286364762616902$ |
$249.8799446471716$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$57.94470615370426$ |
| 15.1.6401597515801839.1 |
$x^{15} - x^{14} - x^{13} + 2 x^{12} - 4 x^{11} - x^{10} + 3 x^{9} + 3 x^{8} + 12 x^{7} - 2 x^{6} - 14 x^{5} + 7 x^{4} + 11 x^{3} - 6 x^{2} + 1$ |
$15$ |
[1,7] |
$-\,3^{9}\cdot 13^{3}\cdot 23^{6}$ |
$3$ |
$11.3175535402$ |
$62.298423685493326$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
trivial |
$2$ |
$7$ |
$46.8775403574$ |
| 15.5.8565893077528823.1 |
$x^{15} - 6 x^{13} + 9 x^{11} - 18 x^{10} + x^{9} + 32 x^{8} - 17 x^{7} - 19 x^{6} + 24 x^{5} + 3 x^{4} - 15 x^{3} + 3 x^{2} + 4 x - 1$ |
$15$ |
[5,5] |
$-\,23^{5}\cdot 191^{4}$ |
$2$ |
$11.5394429204$ |
$320.39860152359097$ |
|
|
? |
$C_5\wr S_3$ (as 15T32) |
trivial |
trivial |
$2$ |
$9$ |
$87.8024975924$ |
| 15.3.9139423287309561.1 |
$x^{15} - 4 x^{12} + 6 x^{11} - 2 x^{9} - 6 x^{8} + 6 x^{7} + 12 x^{6} - 24 x^{5} + 12 x^{4} + 7 x^{3} - 12 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$3^{20}\cdot 1619^{2}$ |
$2$ |
$11.589408013714339$ |
$174.09451854004277$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$71.05008318791243$ |
| 15.5.10496055636998343.1 |
$x^{15} - 4 x^{14} + 6 x^{13} - x^{12} - 11 x^{11} + 18 x^{10} - 10 x^{9} - 9 x^{8} + 19 x^{7} - 12 x^{6} - 3 x^{5} + 9 x^{4} - 5 x^{3} - x^{2} + 3 x - 1$ |
$15$ |
[5,5] |
$-\,3^{5}\cdot 157\cdot 2377\cdot 115742009$ |
$4$ |
$11.6968362025$ |
$11383362.147893872$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$9$ |
$99.2990074596$ |
| 15.3.10544075126076649.1 |
$x^{15} - 6 x^{14} + 11 x^{13} - x^{12} - 10 x^{11} - 13 x^{10} + 18 x^{9} + 40 x^{8} - 30 x^{7} - 64 x^{6} + 42 x^{5} + 47 x^{4} - 27 x^{3} - 19 x^{2} + 9 x + 1$ |
$15$ |
[3,6] |
$37^{2}\cdot 43^{2}\cdot 1609^{3}$ |
$3$ |
$11.7003961458$ |
$5466.694549893152$ |
|
|
? |
$C_3\wr S_5$ (as 15T78) |
trivial |
trivial |
$2$ |
$8$ |
$73.2403388939$ |
| 15.3.11354350039657729.1 |
$x^{15} - 4 x^{14} + 5 x^{13} + x^{12} - 7 x^{11} + x^{10} + 7 x^{9} - 2 x^{8} - 8 x^{7} + 22 x^{6} - 37 x^{5} + 35 x^{4} - 20 x^{3} + 11 x^{2} - 7 x + 1$ |
$15$ |
[3,6] |
$13^{2}\cdot 127^{2}\cdot 1609^{3}$ |
$3$ |
$11.7582895867$ |
$5603.285322545042$ |
|
|
? |
$C_3\wr S_5$ (as 15T78) |
trivial |
trivial |
$2$ |
$8$ |
$79.4890458165$ |
| 15.3.12205980432301041.1 |
$x^{15} - 3 x^{14} + 7 x^{12} - 6 x^{11} + 4 x^{9} - 6 x^{8} + 6 x^{7} - 7 x^{6} + 6 x^{4} - 5 x^{3} + 3 x^{2} + 1$ |
$15$ |
[3,6] |
$3^{20}\cdot 1871^{2}$ |
$2$ |
$11.815121117231264$ |
$187.15376431258608$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$82.95238709015337$ |
| 15.3.12680211005112249.1 |
$x^{15} - 3 x^{14} + 3 x^{13} + 2 x^{12} - 6 x^{11} + 8 x^{9} - 9 x^{8} + 3 x^{7} + 4 x^{6} - 9 x^{5} + 9 x^{4} - 3 x^{3} - 3 x^{2} + 3 x - 1$ |
$15$ |
[3,6] |
$3^{20}\cdot 1907^{2}$ |
$2$ |
$11.845182746386993$ |
$188.94570292822178$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$86.83152808433424$ |
| 15.3.12853809661090929.1 |
$x^{15} - x^{14} - x^{13} + 3 x^{12} - x^{10} - 4 x^{9} + 4 x^{8} + 2 x^{7} - 7 x^{6} - x^{5} + 2 x^{4} - x^{3} + 2 x + 1$ |
$15$ |
[3,6] |
$3\cdot 4284603220363643$ |
$2$ |
$11.855925391$ |
$113374642.9369942$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$8$ |
$108.091851993$ |
| 15.3.15315650494266781.1 |
$x^{15} - 2 x^{14} + x^{13} - x^{12} + 7 x^{11} - 5 x^{10} - 10 x^{9} + 7 x^{8} + 16 x^{7} - 15 x^{6} - 19 x^{5} + 27 x^{4} - 2 x^{3} - 11 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$127^{2}\cdot 9829^{3}$ |
$2$ |
$11.9952424328$ |
$2504.9005119012204$ |
|
|
? |
$C_3\wr S_5$ (as 15T78) |
trivial |
trivial |
$2$ |
$8$ |
$87.5727798613$ |
| 15.3.16680932154277329.1 |
$x^{15} - 2 x^{14} + 6 x^{13} - 14 x^{12} + 23 x^{11} - 35 x^{10} + 44 x^{9} - 41 x^{8} + 25 x^{7} - 4 x^{6} - 20 x^{5} + 34 x^{4} - 30 x^{3} + 17 x^{2} - 6 x + 1$ |
$15$ |
[3,6] |
$3\cdot 47\cdot 103\cdot 11057\cdot 103878739$ |
$5$ |
$12.063722938$ |
$129154683.05205712$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$8$ |
$124.641970008$ |
| 15.3.19075922001903321.1 |
$x^{15} - 3 x^{14} + 7 x^{12} - 6 x^{11} + 3 x^{10} + 7 x^{9} - 24 x^{8} + 3 x^{7} + 32 x^{6} - 27 x^{5} + 12 x^{4} - 8 x^{3} + 3 x - 1$ |
$15$ |
[3,6] |
$3^{20}\cdot 2339^{2}$ |
$2$ |
$12.172105349935228$ |
$209.2554528777342$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$110.00465421038055$ |
| 15.3.19664802801826816.1 |
$x^{15} - 5 x^{14} + 14 x^{13} - 23 x^{12} + 19 x^{11} + 7 x^{10} - 41 x^{9} + 47 x^{8} - 10 x^{7} - 39 x^{6} + 50 x^{5} - 18 x^{4} - 16 x^{3} + 21 x^{2} - 9 x + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 79^{7}$ |
$2$ |
$12.1968019833$ |
$17.776388834631177$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
trivial |
$2$ |
$8$ |
$103.698212623$ |
| 15.3.21643467887730481.1 |
$x^{15} - x^{14} - x^{13} + x^{12} - 7 x^{11} - 2 x^{10} + 18 x^{9} + 12 x^{8} - 17 x^{7} + 7 x^{6} - 11 x^{5} - 21 x^{4} + 22 x^{3} - 11 x^{2} - 2 x - 1$ |
$15$ |
[3,6] |
$13^{2}\cdot 47^{6}\cdot 109^{2}$ |
$3$ |
$12.2750081706$ |
$864.8925624711881$ |
|
|
? |
$C_3\wr D_5$ (as 15T46) |
trivial |
trivial |
$2$ |
$8$ |
$116.633322592$ |
| 15.3.23713122135310336.1 |
$x^{15} - 5 x^{14} + 10 x^{13} - 5 x^{12} - 15 x^{11} + 29 x^{10} - 8 x^{9} - 31 x^{8} + 36 x^{7} - 24 x^{5} + 12 x^{4} + 9 x^{3} - 9 x^{2} + 1$ |
$15$ |
[3,6] |
$2^{18}\cdot 67^{6}$ |
$2$ |
$12.3499703768$ |
$23.15167380558045$ |
|
|
? |
$A_5$ (as 15T5) |
trivial |
trivial |
$2$ |
$8$ |
$133.707274982$ |
| 15.1.24118280788986467.1 |
$x^{15} - 2 x^{14} + 6 x^{12} - 13 x^{11} + 13 x^{10} - x^{9} - 21 x^{8} + 40 x^{7} - 41 x^{6} + 29 x^{5} - 18 x^{4} + 13 x^{3} - 7 x^{2} + x + 1$ |
$15$ |
[1,7] |
$-\,59^{6}\cdot 83^{3}$ |
$2$ |
$12.3639267417$ |
$69.97856814768362$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
trivial |
$2$ |
$7$ |
$81.1679989991$ |
| 15.3.25399833134309001.1 |
$x^{15} - 3 x^{13} - 5 x^{12} + 18 x^{10} + 25 x^{9} - 24 x^{8} - 60 x^{7} + 54 x^{5} + 21 x^{4} - 17 x^{3} - 12 x^{2} + 1$ |
$15$ |
[3,6] |
$3^{20}\cdot 2699^{2}$ |
$2$ |
$12.40667457485079$ |
$224.7828199524016$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$130.1617893792361$ |
| 15.3.28182454451958249.1 |
$x^{15} - 6 x^{14} + 18 x^{13} - 31 x^{12} + 30 x^{11} - 6 x^{10} - 24 x^{9} + 36 x^{8} - 24 x^{7} + 8 x^{6} - 1$ |
$15$ |
[3,6] |
$3^{20}\cdot 2843^{2}$ |
$2$ |
$12.492957261452485$ |
$230.70133242014245$ |
|
|
? |
$D_5\wr C_3$ (as 15T50) |
trivial |
trivial |
$2$ |
$8$ |
$138.52109299581252$ |
| 15.3.31123779291971584.1 |
$x^{15} + x^{13} - x^{12} - 5 x^{11} - 4 x^{10} - 5 x^{9} - x^{8} + 4 x^{7} + 2 x^{6} - 2 x^{5} - 4 x^{4} - 5 x^{3} - 4 x^{2} - 3 x - 1$ |
$15$ |
[3,6] |
$2^{18}\cdot 587^{4}$ |
$2$ |
$12.5759119634$ |
$81.49323216626063$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
trivial |
$2$ |
$8$ |
$152.23669177$ |
| 15.5.35351257235385344.1 |
$x^{15} - 3 x^{13} - 5 x^{12} + 8 x^{11} + x^{10} + 14 x^{9} - 13 x^{8} - 17 x^{7} + 4 x^{6} + x^{5} + 22 x^{4} - 2 x^{3} - 8 x^{2} - 3 x - 1$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{13}$ |
$2$ |
$12.6831459743$ |
$13.738524116073206$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
trivial |
$2$ |
$9$ |
$211.33204879$ |
| 15.3.39671359416303616.1 |
$x^{15} - 7 x^{14} + 24 x^{13} - 47 x^{12} + 46 x^{11} + 18 x^{10} - 150 x^{9} + 296 x^{8} - 383 x^{7} + 371 x^{6} - 282 x^{5} + 171 x^{4} - 83 x^{3} + 31 x^{2} - 8 x + 1$ |
$15$ |
[3,6] |
$2^{18}\cdot 73^{6}$ |
$2$ |
$12.7810089465$ |
$24.166091947189145$ |
|
|
? |
$A_5$ (as 15T5) |
trivial |
trivial |
$2$ |
$8$ |
$170.85154758$ |
| 15.1.44543599279432079.1 |
$x^{15} - 4 x^{14} + 4 x^{13} + 4 x^{12} - 5 x^{11} - 13 x^{10} + 20 x^{9} + 4 x^{8} - 15 x^{7} - 13 x^{6} + 27 x^{5} - 4 x^{4} - 8 x^{3} - 2 x^{2} + 6 x - 1$ |
$15$ |
[1,7] |
$-\,239^{7}$ |
$1$ |
$12.8800936408$ |
$15.459624833740307$ |
|
|
? |
$D_{15}$ (as 15T2) |
trivial |
trivial |
$2$ |
$7$ |
$124.657592501$ |
| 15.3.47090024679574321.1 |
$x^{15} - x^{12} - x^{11} - x^{8} - 2 x^{7} + 2 x^{5} + 3 x^{4} + 2 x^{3} - x - 1$ |
$15$ |
[3,6] |
$14731^{4}$ |
$1$ |
$12.9279181717$ |
$121.37133104650373$ |
|
|
✓ |
$S_6$ (as 15T28) |
trivial |
trivial |
$2$ |
$8$ |
$175.688399353$ |
| 15.3.57352136505929721.1 |
$x^{15} - 2 x^{14} + 4 x^{13} - 10 x^{12} + 22 x^{11} - 33 x^{10} + 40 x^{9} - 63 x^{8} + 81 x^{7} - 81 x^{6} + 63 x^{5} - 69 x^{4} + 57 x^{3} - 24 x^{2} + 3$ |
$15$ |
[3,6] |
$3^{18}\cdot 23^{6}$ |
$2$ |
$13.0989546953$ |
$58.192859749017636$ |
|
|
? |
$C_3^4:A_5$ (as 15T53) |
trivial |
trivial |
$2$ |
$8$ |
$279.393832589$ |
| 15.1.57477829056511319.1 |
$x^{15} - 2 x^{14} + 3 x^{13} - 3 x^{12} - 3 x^{11} + 6 x^{10} - 14 x^{9} + 4 x^{8} - 9 x^{7} - 7 x^{6} + 7 x^{5} - 15 x^{4} + 4 x^{3} - 4 x^{2} + 2 x - 1$ |
$15$ |
[1,7] |
$-\,1609^{3}\cdot 13798511$ |
$2$ |
$13.1008665794$ |
$149002.69862992415$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
trivial |
$2$ |
$7$ |
$145.805581456$ |
| 15.3.59463924292145152.1 |
$x^{15} - x^{14} - 6 x^{13} + 15 x^{12} - 9 x^{11} - 13 x^{10} + 30 x^{9} - 31 x^{8} + 24 x^{7} - 14 x^{6} + 10 x^{5} - 18 x^{4} + 27 x^{3} - 21 x^{2} + 8 x - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{9}\cdot 37^{2}$ |
$3$ |
$13.1305697532$ |
$132.357735064494$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
trivial |
$2$ |
$8$ |
$226.669584518$ |
| 15.1.59770508839234803.1 |
$x^{15} - 2 x^{12} + 3 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 1609^{3}$ |
$2$ |
$13.1350721761$ |
$205.62197122852638$ |
|
|
✓ |
$C_3^4:(C_2\times S_5)$ (as 15T70) |
trivial |
trivial |
$2$ |
$7$ |
$146.289665433$ |
| 15.1.59770508839234803.2 |
$x^{15} - x^{9} - x^{6} + x^{3} + 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 1609^{3}$ |
$2$ |
$13.1350721761$ |
$205.62197122852638$ |
|
|
✓ |
$C_3^4:(C_2\times S_5)$ (as 15T70) |
trivial |
trivial |
$2$ |
$7$ |
$158.627231153$ |
| 15.3.69184806150882304.1 |
$x^{15} + x^{13} - 3 x^{12} - 3 x^{11} - 5 x^{10} - 2 x^{9} + 3 x^{8} + 7 x^{7} + 4 x^{6} + x^{5} + x^{4} + 3 x^{3} + x^{2} - 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 47^{4}\cdot 61^{4}$ |
$3$ |
$13.2637822009$ |
$84.99639580651171$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
trivial |
$2$ |
$8$ |
$273.665310463$ |
| 15.1.69378727128301847.1 |
$x^{15} - 2 x^{14} + 2 x^{13} - 2 x^{12} + 2 x^{11} - 4 x^{10} + 3 x^{9} + 2 x^{8} + x^{7} - 5 x^{6} + 3 x^{5} + 3 x^{4} + 6 x^{3} + 2 x^{2} - 1$ |
$15$ |
[1,7] |
$-\,23^{5}\cdot 47^{6}$ |
$2$ |
$13.266257472$ |
$32.87856444554719$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
trivial |
$2$ |
$7$ |
$185.949282778$ |
| 15.5.77595502265817783.1 |
$x^{15} - 3 x^{13} - 2 x^{12} + x^{11} + 12 x^{10} + 3 x^{9} - 15 x^{8} - 10 x^{7} - 4 x^{6} + 20 x^{5} + 7 x^{4} - 3 x^{3} - 7 x^{2} - 4 x + 1$ |
$15$ |
[5,5] |
$-\,3\cdot 13^{3}\cdot 11772948303113$ |
$3$ |
$13.3656198083$ |
$40687476.96822902$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
trivial |
$2$ |
$9$ |
$416.964032767$ |
| 15.1.96318312824155136.1 |
$x^{15} - 6 x^{14} + 19 x^{13} - 39 x^{12} + 58 x^{11} - 67 x^{10} + 68 x^{9} - 69 x^{8} + 65 x^{7} - 52 x^{6} + 33 x^{5} - 20 x^{4} + 12 x^{3} - 4 x^{2} + 3 x - 1$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 11^{7}\cdot 13^{6}$ |
$3$ |
$13.5596118481$ |
$18.982555683309183$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
trivial |
$2$ |
$7$ |
$226.323474369$ |
| 15.3.98765528526263521.1 |
$x^{15} - 3 x^{14} + 7 x^{13} - 12 x^{12} + 8 x^{11} - 2 x^{10} - 17 x^{9} + 36 x^{8} - 49 x^{7} + 54 x^{6} - 41 x^{5} + 30 x^{4} - 17 x^{3} + 8 x^{2} - 5 x + 3$ |
$15$ |
[3,6] |
$13^{3}\cdot 31^{6}\cdot 37^{3}$ |
$3$ |
$13.5823116986$ |
$122.11060560000512$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
trivial |
$2$ |
$8$ |
$363.728980494$ |
| 15.3.126064044311049216.1 |
$x^{15} - 4 x^{14} + 3 x^{13} + 15 x^{12} - 40 x^{11} + 23 x^{10} + 52 x^{9} - 111 x^{8} + 83 x^{7} - 67 x^{5} + 86 x^{4} - 62 x^{3} + 26 x^{2} - 7 x + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 3^{5}\cdot 47^{7}$ |
$3$ |
$13.8050955127$ |
$18.849343120394256$ |
|
|
? |
$D_5\times S_3$ (as 15T7) |
trivial |
trivial |
$2$ |
$8$ |
$280.863045663$ |
| 15.3.137631064560062464.1 |
$x^{15} - x^{14} - 2 x^{13} + 3 x^{12} + 11 x^{11} - 5 x^{10} - 14 x^{9} - 5 x^{8} - 10 x^{7} + 22 x^{6} + 14 x^{5} + 2 x^{4} - 13 x^{3} - 5 x^{2} + 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 23^{6}\cdot 61^{3}$ |
$3$ |
$13.8861258816$ |
$65.21580088926439$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
trivial |
$2$ |
$8$ |
$381.090214491$ |
| 15.3.146928604515779584.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 9 x^{12} - x^{11} - 5 x^{10} + 4 x^{9} - x^{8} + x^{7} - x^{5} - x^{4} + 7 x^{3} - x^{2} + 1$ |
$15$ |
[3,6] |
$2^{10}\cdot 3461^{4}$ |
$2$ |
$13.9467737903$ |
$93.38722346966051$ |
|
|
? |
$S_6$ (as 15T28) |
trivial |
trivial |
$2$ |
$8$ |
$470.017972215$ |
