| 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 |
| 15.1.723352547563839.1 |
$x^{15} - x^{14} - 2 x^{13} + 2 x^{12} - 2 x^{11} + 2 x^{10} + 5 x^{9} - 5 x^{8} + 4 x^{7} - 5 x^{6} - 4 x^{5} + 5 x^{4} - 2 x^{3} + x^{2} + x + 1$ |
$15$ |
[1,7] |
$-\,3^{3}\cdot 6653\cdot 4026880369$ |
$3$ |
$9.78640837431$ |
$8965071.404337559$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$11.7410590074$ |
| 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 |
$2$ |
$7$ |
$39.9823344692$ |
| 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 |
$2$ |
$7$ |
$50.8430332143$ |
| 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 |
$2$ |
$7$ |
$46.8775403574$ |
| 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 |
$2$ |
$7$ |
$81.1679989991$ |
| 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 |
$2$ |
$7$ |
$124.657592501$ |
| 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 |
$2$ |
$7$ |
$145.805581456$ |
| 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 |
$2$ |
$7$ |
$146.289665433$ |
| 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 |
$2$ |
$7$ |
$158.627231153$ |
| 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 |
$2$ |
$7$ |
$185.949282778$ |
| 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 |
$2$ |
$7$ |
$226.323474369$ |
| 15.1.154669958288795403.1 |
$x^{15} - x^{12} + 2 x^{9} - 3 x^{6} + 3 x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.9945970392$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$255.941349852$ |
| 15.1.154669958288795403.2 |
$x^{15} - 2 x^{12} + 2 x^{9} - x^{6} + 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.9945970392$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$288.777984962$ |
| 15.1.154669958288795403.3 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
| 15.1.154669958288795403.4 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
| 15.1.154669958288795403.5 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
| 15.1.154669958288795403.6 |
$x^{15} - 3 x^{12} + 4 x^{9} - 3 x^{6} + x^{3} - 1$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 47^{6}$ |
$2$ |
$13.994597039155481$ |
$35.143128879205776$ |
|
|
✓ |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$7$ |
$291.92845219900784$ |
| 15.1.196421600341796875.1 |
$x^{15} - x^{10} + 1$ |
$15$ |
[1,7] |
$-\,5^{15}\cdot 23^{5}$ |
$2$ |
$14.2193348993$ |
$34.72138363576141$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$358.947276162$ |
| 15.1.426781883555301359.1 |
$x^{15} - x - 1$ |
$15$ |
[1,7] |
$-\,52489\cdot 418511\cdot 19428121$ |
$3$ |
$14.9743184596$ |
$653285453.3473873$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$501.532588967$ |
| 15.1.449005897206417391.1 |
$x^{15} + x - 1$ |
$15$ |
[1,7] |
$-\,7334881\cdot 61215157711$ |
$2$ |
$15.0250803442$ |
$670079023.1057956$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$548.874139448$ |
| 15.1.677952124826430464.1 |
$x^{15} - x^{14} + 4 x^{13} + 4 x^{11} - 2 x^{10} - 6 x^{9} - 12 x^{8} - 25 x^{7} + 19 x^{6} - 6 x^{5} + 28 x^{4} + 32 x^{3} - 36 x^{2} + 4 x + 4$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 131^{7}$ |
$2$ |
$15.4435309131$ |
$18.168635476349255$ |
|
|
|
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$1343.20606196$ |
| 15.1.873692352294921875.1 |
$x^{15} + x^{5} - 1$ |
$15$ |
[1,7] |
$-\,5^{15}\cdot 31^{5}$ |
$2$ |
$15.706903262$ |
$40.310107120236324$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$890.572745674$ |
| 15.1.957206371560558183.1 |
$x^{15} - x^{14} + x^{13} - 6 x^{12} - 4 x^{11} + 5 x^{10} + 18 x^{9} + 23 x^{8} - 4 x^{5} + 4 x^{4} + 10 x^{3} - 5 x^{2} + 1$ |
$15$ |
[1,7] |
$-\,3^{12}\cdot 23^{9}$ |
$2$ |
$15.8027876891$ |
$49.13768144738915$ |
|
|
? |
$A_5 \times S_3$ (as 15T23) |
trivial |
$2$ |
$7$ |
$627.503289611$ |
| 15.1.957834337125359375.1 |
$x^{15} - 6 x^{14} + 23 x^{13} - 67 x^{12} + 156 x^{11} - 307 x^{10} + 523 x^{9} - 771 x^{8} + 994 x^{7} - 1103 x^{6} + 1049 x^{5} - 854 x^{4} + 579 x^{3} - 288 x^{2} + 89 x - 13$ |
$15$ |
[1,7] |
$-\,5^{6}\cdot 11^{2}\cdot 47^{7}$ |
$3$ |
$15.8034786282$ |
$99.14954417983068$ |
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
trivial |
$2$ |
$7$ |
$738.167831427$ |
| 15.1.957834337125359375.2 |
$x^{15} - 5 x^{14} + 15 x^{13} - 37 x^{12} + 74 x^{11} - 137 x^{10} + 207 x^{9} - 292 x^{8} + 353 x^{7} - 407 x^{6} + 396 x^{5} - 334 x^{4} + 222 x^{3} - 121 x^{2} + 44 x - 11$ |
$15$ |
[1,7] |
$-\,5^{6}\cdot 11^{2}\cdot 47^{7}$ |
$3$ |
$15.8034786282$ |
$99.14954417983068$ |
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
trivial |
$2$ |
$7$ |
$722.408081993$ |
| 15.1.100...407.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 8 x^{12} + 4 x^{11} - 19 x^{10} + 3 x^{9} + 33 x^{8} - 23 x^{7} - 47 x^{6} + 39 x^{5} + 43 x^{4} - 13 x^{3} - 23 x^{2} - 8 x - 1$ |
$15$ |
[1,7] |
$-\,3^{6}\cdot 11^{8}\cdot 23^{5}$ |
$3$ |
$15.8550352766$ |
$56.56381504121475$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$7$ |
$824.556928356$ |
| 15.1.108...475.1 |
$x^{15} - x^{14} + 6 x^{13} - 8 x^{12} + 25 x^{11} - 40 x^{10} + 61 x^{9} - 74 x^{8} + 78 x^{7} - 83 x^{6} + 82 x^{5} - 36 x^{4} - 14 x^{3} + 35 x^{2} - 20 x + 5$ |
$15$ |
[1,7] |
$-\,5^{2}\cdot 17^{4}\cdot 43\cdot 2297^{3}$ |
$4$ |
$15.9384398951$ |
$6075.667650690129$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$7$ |
$786.568254332$ |
| 15.1.115...192.1 |
$x^{15} - 7 x^{14} + 29 x^{13} - 83 x^{12} + 185 x^{11} - 323 x^{10} + 445 x^{9} - 463 x^{8} + 341 x^{7} - 143 x^{6} + 3 x^{5} + 35 x^{4} - 15 x^{3} + x^{2} + 3 x - 1$ |
$15$ |
[1,7] |
$-\,2^{23}\cdot 13^{10}$ |
$2$ |
$16.0032514171$ |
$25.551388539968485$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
$2$ |
$7$ |
$2478.48165826$ |
| 15.1.127...000.1 |
$x^{15} - x^{14} + 3 x^{13} - x^{12} + 3 x^{11} + 5 x^{10} + 11 x^{9} + 11 x^{8} + 17 x^{7} + 19 x^{6} + 11 x^{5} + 11 x^{4} + 9 x^{3} + 3 x^{2} + x + 1$ |
$15$ |
[1,7] |
$-\,2^{22}\cdot 5^{6}\cdot 11^{7}$ |
$3$ |
$16.1094945821$ |
$30.788817184393896$ |
|
|
? |
$A_5 \times S_3$ (as 15T23) |
trivial |
$2$ |
$7$ |
$2664.19773281$ |
| 15.1.219...096.1 |
$x^{15} - 2 x^{14} + 5 x^{12} - 8 x^{11} + 2 x^{10} + 9 x^{9} - 11 x^{8} + 11 x^{6} - 7 x^{5} - 3 x^{4} + 7 x^{3} - x^{2} - 2 x + 1$ |
$15$ |
[1,7] |
$-\,2^{6}\cdot 34304987175946939$ |
$2$ |
$16.7020257541$ |
$523870115.0166666$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$7$ |
$2000.14922252$ |
| 15.1.267...712.1 |
$x^{15} - 6 x^{13} - 6 x^{12} + 8 x^{9} + 24 x^{8} + 22 x^{7} - 16 x^{5} - 28 x^{4} - 42 x^{3} - 40 x^{2} - 20 x - 4$ |
$15$ |
[1,7] |
$-\,2^{37}\cdot 11^{7}$ |
$2$ |
$16.9248141739$ |
$25.04381555535815$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
$2$ |
$7$ |
$3756.48041139$ |
| 15.1.314...479.1 |
$x^{15} - 5 x^{14} + 11 x^{13} - 9 x^{12} - 7 x^{11} + 17 x^{10} - x^{9} - 29 x^{8} + 38 x^{7} - 13 x^{6} - 20 x^{5} + 24 x^{4} + 7 x^{3} - 23 x^{2} + 13 x - 1$ |
$15$ |
[1,7] |
$-\,439^{7}$ |
$1$ |
$17.1060646655$ |
$20.952326839756964$ |
|
|
|
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$2414.83246229$ |
| 15.1.386...075.1 |
$x^{15} - 4 x^{12} + 5 x^{9} - 4 x^{6} + 6 x^{3} - 5$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 5^{2}\cdot 47^{6}$ |
$3$ |
$17.3442848906$ |
$103.69250158786609$ |
|
|
? |
$C_3^5:D_{10}$ (as 15T55) |
trivial |
$2$ |
$7$ |
$1561.00493818$ |
| 15.1.386...075.2 |
$x^{15} - 5 x^{12} + 10 x^{9} - 13 x^{6} + 13 x^{3} - 5$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 5^{2}\cdot 47^{6}$ |
$3$ |
$17.3442848906$ |
$103.69250158786609$ |
|
|
? |
$C_3^5:D_{10}$ (as 15T55) |
trivial |
$2$ |
$7$ |
$1346.00590418$ |
| 15.1.494...375.1 |
$x^{15} - 6 x^{12} + 9 x^{11} + 20 x^{10} + 57 x^{9} + 29 x^{8} + 27 x^{7} - 53 x^{6} - 44 x^{5} - 84 x^{4} - 43 x^{3} - 100 x^{2} - 75 x - 55$ |
$15$ |
[1,7] |
$-\,5^{10}\cdot 47^{7}$ |
$2$ |
$17.6316248441$ |
$20.046055658633293$ |
|
|
? |
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$1727.98179688$ |
| 15.1.503...000.1 |
$x^{15} - x^{10} + x^{5} + 1$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 5^{15}\cdot 11^{5}$ |
$3$ |
$17.651741676630316$ |
$38.11677176459088$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$7$ |
$2893.5472483909075$ |
| 15.1.602...616.1 |
$x^{15} - 3 x^{14} + 10 x^{13} - 18 x^{12} + 41 x^{11} - 61 x^{10} + 57 x^{9} - 103 x^{8} + 29 x^{7} - 57 x^{6} + 17 x^{5} - 31 x^{4} + 12 x^{3} - 2 x^{2} + 3 x - 1$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 179^{7}$ |
$2$ |
$17.8656194193$ |
$21.237978619971454$ |
|
|
|
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$4800.51400574$ |
| 15.1.640...000.1 |
$x^{15} - 5 x^{14} + 15 x^{13} - 35 x^{12} + 65 x^{11} - 93 x^{10} + 125 x^{9} - 125 x^{8} + 115 x^{7} - 55 x^{6} + 43 x^{5} + 5 x^{4} + 15 x^{3} + 5 x^{2} + 5 x - 1$ |
$15$ |
[1,7] |
$-\,2^{23}\cdot 5^{17}$ |
$2$ |
$17.9368151132$ |
$25.065218619440312$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
$2$ |
$7$ |
$6944.116640269703$ |
| 15.1.723...163.1 |
$x^{15} - x^{12} + 3 x^{9} + 5 x^{6} - 6 x^{3} + 11$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 11^{2}\cdot 1609^{3}$ |
$3$ |
$18.083597063$ |
$1026.2619620797323$ |
|
|
? |
$C_3^4:(S_3\times S_5)$ (as 15T83) |
trivial |
$2$ |
$7$ |
$1927.40173417$ |
| 15.1.172...067.1 |
$x^{15} - 5 x^{12} + 4 x^{9} + 11 x^{6} - 5 x^{3} - 17$ |
$15$ |
[1,7] |
$-\,3^{15}\cdot 17^{2}\cdot 1609^{3}$ |
$3$ |
$19.164271714$ |
$1359.4674047310777$ |
|
|
? |
$C_3^4:(S_3\times S_5)$ (as 15T83) |
trivial |
$2$ |
$7$ |
$2783.08897213$ |
| 15.1.318...272.1 |
$x^{15} - 3 x^{14} - 4 x^{13} + 6 x^{12} + 20 x^{11} - 8 x^{10} + 10 x^{9} + 50 x^{8} - 45 x^{7} - 65 x^{6} + 106 x^{5} + 80 x^{4} - 20 x^{3} - 40 x^{2} - 20 x - 4$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 227^{7}$ |
$2$ |
$19.9602233732$ |
$23.916608385226205$ |
|
|
|
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$13535.3893625$ |
| 15.1.612...591.1 |
$x^{15} - 3 x^{14} + 6 x^{13} - x^{12} - 20 x^{11} + 56 x^{10} - 81 x^{9} + 46 x^{8} + 90 x^{7} - 299 x^{6} + 481 x^{5} - 522 x^{4} + 403 x^{3} - 201 x^{2} + 44 x + 11$ |
$15$ |
[1,7] |
$-\,11^{7}\cdot 61^{7}$ |
$2$ |
$20.8514939353$ |
$25.903667693977237$ |
|
|
? |
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$8053.72361025$ |
| 15.1.707...875.1 |
$x^{15} - 3 x^{10} + 4 x^{5} - 3$ |
$15$ |
[1,7] |
$-\,3^{4}\cdot 5^{15}\cdot 31^{5}$ |
$3$ |
$21.0534320777$ |
|
|
|
✓ |
$C_9^2\times C_{54}$ (as 15T49) |
trivial |
$2$ |
$7$ |
$12190.0988389$ |
| 15.1.707...875.2 |
$x^{15} - 4 x^{10} + 5 x^{5} - 3$ |
$15$ |
[1,7] |
$-\,3^{4}\cdot 5^{15}\cdot 31^{5}$ |
$3$ |
$21.0534320777$ |
|
|
|
✓ |
$C_9^2\times C_{54}$ (as 15T49) |
trivial |
$2$ |
$7$ |
$8578.13846341$ |
| 15.1.821...375.1 |
$x^{15} - 5 x^{12} + 10 x^{11} - 12 x^{10} + 10 x^{9} - 20 x^{8} + 40 x^{7} - 60 x^{6} + 73 x^{5} - 65 x^{4} + 35 x^{3} - 35 x^{2} + 30 x - 9$ |
$15$ |
[1,7] |
$-\,5^{16}\cdot 7^{5}\cdot 179^{2}$ |
$3$ |
$21.2641366944$ |
|
|
|
? |
$D_5\wr S_3$ (as 15T60) |
trivial |
$2$ |
$7$ |
$11224.8164015$ |
| 15.1.134...751.1 |
$x^{15} - 5 x^{14} + 9 x^{13} - 6 x^{12} + 7 x^{11} - 12 x^{10} + 17 x^{9} - 29 x^{8} + 2 x^{7} - 4 x^{6} + 21 x^{5} - 9 x^{4} + 53 x^{3} + 12 x^{2} + 25 x - 1$ |
$15$ |
[1,7] |
$-\,751^{7}$ |
$1$ |
$21.9768429136$ |
$27.40437921208944$ |
|
|
|
$D_{15}$ (as 15T2) |
$[2]$ |
$2$ |
$7$ |
$10575.7740384$ |
| 15.1.136...072.1 |
$x^{15} - 5 x^{14} + 10 x^{13} - 10 x^{12} + 5 x^{11} - x^{10} - 4 x^{9} + 12 x^{8} - 12 x^{7} - 12 x^{6} + 32 x^{5} - 16 x^{4} - 32 x^{3} + 32 x^{2} - 32$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 47^{6}\cdot 179\cdot 257\cdot 269$ |
$5$ |
$21.9969112494$ |
$88460.4996368941$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$7$ |
$8878.38126725$ |
| 15.1.143...287.1 |
$x^{15} - x^{14} + 3 x^{13} - 21 x^{12} + 23 x^{11} + 8 x^{10} + 39 x^{9} - 113 x^{8} - 64 x^{7} + 132 x^{6} + 251 x^{5} + 261 x^{4} - 646 x^{3} + 393 x^{2} - 110 x + 13$ |
$15$ |
[1,7] |
$-\,7^{10}\cdot 47^{7}$ |
$2$ |
$22.0653604887$ |
$25.086936025192795$ |
|
|
? |
$D_{15}$ (as 15T2) |
$[3]$ |
$2$ |
$7$ |
$3725.0006398$ |
| 15.1.147...048.1 |
$x^{15} - 2 x^{13} - 4 x^{12} + 2 x^{11} + 8 x^{10} + 7 x^{9} - 6 x^{8} - 12 x^{7} - 8 x^{6} + x^{5} + 10 x^{4} + 40 x^{3} + 80 x^{2} + 80 x + 32$ |
$15$ |
[1,7] |
$-\,2^{10}\cdot 11\cdot 47^{6}\cdot 1211333$ |
$4$ |
$22.1056296236$ |
$91792.73030079878$ |
|
|
? |
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$7$ |
$11514.2059793$ |
| 15.1.151...431.1 |
$x^{15} - 3 x^{14} + 12 x^{13} - 5 x^{12} + 21 x^{11} + 15 x^{10} + 43 x^{9} + 54 x^{8} + 60 x^{7} + 93 x^{6} + 96 x^{5} + 108 x^{4} + 105 x^{3} + 72 x^{2} + 36 x + 9$ |
$15$ |
[1,7] |
$-\,3^{17}\cdot 53^{7}$ |
$2$ |
$22.151314058$ |
$26.228859011337757$ |
|
|
? |
$D_{15}$ (as 15T2) |
trivial |
$2$ |
$7$ |
$22591.3171442$ |
