| 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 |
| 15.5.8565893077528823.1 |
$x^{15} - 6 x^{13} + 9 x^{11} - 18 x^{10} + x^{9} + 32 x^{8} - 17 x^{7} - 19 x^{6} + 24 x^{5} + 3 x^{4} - 15 x^{3} + 3 x^{2} + 4 x - 1$ |
$15$ |
[5,5] |
$-\,23^{5}\cdot 191^{4}$ |
$2$ |
$11.5394429204$ |
$320.39860152359097$ |
|
|
? |
$C_5\wr S_3$ (as 15T32) |
trivial |
$2$ |
$9$ |
$87.8024975924$ |
| 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 |
$2$ |
$9$ |
$99.2990074596$ |
| 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 |
$2$ |
$9$ |
$211.33204879$ |
| 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 |
$2$ |
$9$ |
$416.964032767$ |
| 15.5.154972454814106259.1 |
$x^{15} - x^{14} - 2 x^{13} + x^{12} + x^{11} - x^{10} + 2 x^{9} - 15 x^{8} + 8 x^{7} + 28 x^{6} - 34 x^{5} - 7 x^{4} + 27 x^{3} - 7 x^{2} - 3 x + 1$ |
$15$ |
[5,5] |
$-\,11^{13}\cdot 67^{2}$ |
$2$ |
$13.9964200427$ |
$142.76988787487005$ |
|
|
? |
$C_7^3:C_6$ (as 15T44) |
trivial |
$2$ |
$9$ |
$492.79424719$ |
| 15.5.388863829589238784.1 |
$x^{15} - 3 x^{14} + 2 x^{13} - x^{12} + 5 x^{11} - 22 x^{9} + 33 x^{8} - 22 x^{7} + 22 x^{6} - 22 x^{5} - 9 x^{4} + 38 x^{3} - 29 x^{2} + 9 x - 1$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{14}$ |
$2$ |
$14.8817214018$ |
$18.749794052793643$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$803.578266232599$ |
| 15.5.982108001708984375.1 |
$x^{15} - 4 x^{13} - 11 x^{12} + 9 x^{11} + 30 x^{10} + 5 x^{9} + 7 x^{8} - 32 x^{7} - 7 x^{6} - 78 x^{5} - 120 x^{4} + 36 x^{3} + 154 x^{2} + 134 x + 43$ |
$15$ |
[5,5] |
$-\,5^{16}\cdot 23^{5}$ |
$2$ |
$15.8298676303$ |
$105.41109538118516$ |
|
|
? |
$C_5\wr S_3$ (as 15T32) |
trivial |
$2$ |
$9$ |
$1326.38565727$ |
| 15.5.109...839.1 |
$x^{15} - 4 x^{14} + 9 x^{13} - 7 x^{12} - 10 x^{11} + 31 x^{10} - 21 x^{9} - 32 x^{8} + 45 x^{7} + 13 x^{6} - 35 x^{5} - 2 x^{4} + 12 x^{3} - 3 x^{2} - 5 x - 1$ |
$15$ |
[5,5] |
$-\,3^{2}\cdot 121558348928602871$ |
$2$ |
$15.9441664713$ |
$603883305.6028364$ |
|
|
? |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$2377.94441595$ |
| 15.5.237...184.1 |
$x^{15} - 5 x^{14} + 7 x^{13} - 2 x^{12} + 11 x^{11} - 42 x^{10} + 54 x^{9} - 28 x^{8} + 39 x^{7} - 96 x^{6} + 36 x^{5} + 3 x^{4} + 7 x^{3} + 54 x^{2} + 19 x + 1$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 3^{9}\cdot 4903^{3}$ |
$3$ |
$16.7900424924$ |
$1233.5165266905358$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$9$ |
$2173.28422663$ |
| 15.5.952...571.1 |
$x^{15} - 2 x^{14} - 8 x^{13} + 17 x^{12} + 27 x^{11} - 63 x^{10} - 46 x^{9} + 131 x^{8} + 31 x^{7} - 154 x^{6} + 7 x^{5} + 95 x^{4} - 10 x^{3} - 31 x^{2} + 2 x + 4$ |
$15$ |
[5,5] |
$-\,23^{4}\cdot 32411^{3}$ |
$2$ |
$18.4189941141$ |
$1456.011391346678$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T91) |
trivial |
$2$ |
$9$ |
$7166.94578377$ |
| 15.5.202...303.1 |
$x^{15} - x^{14} - 4 x^{13} + 7 x^{12} + 24 x^{11} - 26 x^{10} - 57 x^{9} + 76 x^{8} + 79 x^{7} - 88 x^{6} - 97 x^{5} + 35 x^{4} + 42 x^{3} - 15 x^{2} + 1$ |
$15$ |
[5,5] |
$-\,11^{12}\cdot 23^{5}$ |
$2$ |
$19.3652642162$ |
$32.65713384043754$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$7020.68605475$ |
| 15.5.244...591.1 |
$x^{15} - 4 x^{14} + 7 x^{13} - 17 x^{12} + 51 x^{11} - 87 x^{10} - 7 x^{9} + 172 x^{8} - 100 x^{7} - 69 x^{6} - 17 x^{5} + 62 x^{4} + 50 x^{3} - 22 x^{2} - 18 x - 1$ |
$15$ |
[5,5] |
$-\,31^{13}$ |
$1$ |
$19.61161992504764$ |
$21.990014941549536$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$6179.9389969906615$ |
| 15.5.245...375.1 |
$x^{15} - 15 x^{13} - 20 x^{12} + 70 x^{11} + 199 x^{10} + 50 x^{9} - 440 x^{8} - 740 x^{7} - 400 x^{6} + 200 x^{5} + 425 x^{4} + 275 x^{3} + 90 x^{2} + 15 x + 1$ |
$15$ |
[5,5] |
$-\,5^{18}\cdot 23^{5}$ |
$2$ |
$19.6188381268$ |
$50.27593132583481$ |
|
|
? |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
trivial |
$2$ |
$9$ |
$9764.00443856$ |
| 15.5.340...000.1 |
$x^{15} - 3 x^{14} - 5 x^{13} + 25 x^{12} - 16 x^{11} - 46 x^{10} + 94 x^{9} - 29 x^{8} - 96 x^{7} + 107 x^{6} + 51 x^{5} - 191 x^{4} + 173 x^{3} - 78 x^{2} + 15 x - 1$ |
$15$ |
[5,5] |
$-\,2^{6}\cdot 5^{6}\cdot 32411^{3}$ |
$3$ |
$20.0511130768$ |
$835.6278043400864$ |
|
|
? |
$C_3:S_3^4:S_5$ (as 15T91) |
trivial |
$2$ |
$9$ |
$14284.5326369$ |
| 15.5.450...947.1 |
$x^{15} - 2 x^{12} - 5 x^{9} + 13 x^{6} - 7 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.4284493826$ |
$34.90644688215396$ |
|
|
✓ |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$9289.39400206$ |
| 15.5.450...947.2 |
$x^{15} - 10 x^{12} + 29 x^{9} - 25 x^{6} + 3 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.4284493826$ |
$34.90644688215396$ |
|
|
? |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$8686.79947771$ |
| 15.5.450...947.3 |
$x^{15} - 3 x^{12} - 3 x^{9} + 15 x^{6} - 10 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.428449382566903$ |
$34.90644688215396$ |
|
|
✓ |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$10031.504095520013$ |
| 15.5.450...947.4 |
$x^{15} - 3 x^{12} - 3 x^{9} + 15 x^{6} - 10 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.428449382566903$ |
$34.90644688215396$ |
|
|
✓ |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$10031.504095520013$ |
| 15.5.709...875.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 374 x^{5} + 100 x^{4} + 120 x^{3} - 50 x^{2} + 5 x - 1$ |
$15$ |
[5,5] |
$-\,5^{15}\cdot 19^{2}\cdot 23^{5}$ |
$3$ |
$21.0561886589$ |
|
|
|
✓ |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$9$ |
$18096.7724472$ |
| 15.5.785...696.1 |
$x^{15} - 4 x^{13} - 4 x^{12} + 13 x^{11} + 4 x^{10} - 43 x^{9} + 89 x^{8} - 67 x^{7} - 64 x^{6} + 90 x^{5} - 9 x^{4} - 26 x^{3} + 13 x^{2} - 1$ |
$15$ |
[5,5] |
$-\,2^{9}\cdot 31^{6}\cdot 557^{3}$ |
$3$ |
$21.1998951967$ |
$371.6665171898055$ |
|
|
|
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$9$ |
$16240.684335$ |
| 15.5.810...091.1 |
$x^{15} - 5 x^{14} + 9 x^{13} - 8 x^{12} + 14 x^{11} - 37 x^{10} + 67 x^{9} - 149 x^{8} + 274 x^{7} - 274 x^{6} + 183 x^{5} - 117 x^{4} - 51 x^{3} + 171 x^{2} - 70 x - 7$ |
$15$ |
[5,5] |
$-\,7^{3}\cdot 53\cdot 1217^{3}\cdot 2473633$ |
$4$ |
$21.2447585369$ |
$1056817.20980073$ |
|
|
? |
$S_3^5.S_5$ (as 15T93) |
trivial |
$2$ |
$9$ |
$13521.7991305$ |
| 15.5.898...871.1 |
$x^{15} + 9 x^{13} - 4 x^{12} + 28 x^{11} - 20 x^{10} + 4 x^{9} - 32 x^{8} - 71 x^{7} + 48 x^{6} - 57 x^{5} + 28 x^{4} + 38 x^{3} + 3 x^{2} + 3 x - 1$ |
$15$ |
[5,5] |
$-\,11^{12}\cdot 31^{5}$ |
$2$ |
$21.39117854958419$ |
$37.91359748671099$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$14230.552479105852$ |
| 15.5.914...359.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 18 x^{12} + 16 x^{11} - 40 x^{10} - 33 x^{9} + 101 x^{8} + 52 x^{7} - 96 x^{6} - 59 x^{5} + 32 x^{4} + 23 x^{3} - 12 x^{2} + 1$ |
$15$ |
[5,5] |
$-\,23^{5}\cdot 61^{3}\cdot 397^{3}$ |
$3$ |
$21.4157528907$ |
$746.3182967072428$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$9$ |
$15648.0000591$ |
| 15.5.944...512.1 |
$x^{15} - 5 x^{14} + 8 x^{13} + 8 x^{12} - 52 x^{11} + 77 x^{10} - 22 x^{9} + 11 x^{8} - 121 x^{7} - 44 x^{6} + 275 x^{5} - 26 x^{4} - 101 x^{3} - 43 x^{2} - 10 x + 43$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 3^{5}\cdot 11^{14}$ |
$3$ |
$21.463156297174642$ |
$25.77589757199556$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$14815.91735059762$ |
| 15.5.103...875.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 3 x^{10} - 275 x^{9} + 30 x^{8} + 450 x^{7} - 105 x^{6} - 373 x^{5} + 150 x^{4} + 115 x^{3} - 75 x^{2} + 10 x + 1$ |
$15$ |
[5,5] |
$-\,5^{15}\cdot 23^{7}$ |
$2$ |
$21.5994650145$ |
$34.72138363576141$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$9$ |
$21869.311632$ |
| 15.5.105...875.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 376 x^{5} + 100 x^{4} + 130 x^{3} - 50 x^{2} - 5 x + 3$ |
$15$ |
[5,5] |
$-\,5^{15}\cdot 11^{2}\cdot 31^{5}$ |
$3$ |
$21.6243432764$ |
|
|
|
✓ |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$9$ |
$27392.8465071$ |
| 15.5.108...168.1 |
$x^{15} - 2 x^{14} - 3 x^{13} + 7 x^{12} + 16 x^{11} - 34 x^{10} - 54 x^{9} + 176 x^{8} - 65 x^{7} - 238 x^{6} + 291 x^{5} - 31 x^{4} - 119 x^{3} + 46 x^{2} + 17 x - 7$ |
$15$ |
[5,5] |
$-\,2^{12}\cdot 23^{6}\cdot 563^{3}$ |
$3$ |
$21.657923227753585$ |
$198.12629214590953$ |
|
|
? |
$S_5 \times S_3$ (as 15T29) |
trivial |
$2$ |
$9$ |
$19767.717157909436$ |
| 15.5.140...031.1 |
$x^{15} - 4 x^{14} + 2 x^{13} + 25 x^{12} - 77 x^{11} + 56 x^{10} + 46 x^{9} + 26 x^{8} - 157 x^{7} + 71 x^{6} - 67 x^{5} + 95 x^{4} + 26 x^{3} - 34 x^{2} - 11 x + 1$ |
$15$ |
[5,5] |
$-\,3^{5}\cdot 7^{5}\cdot 11^{13}$ |
$3$ |
$22.04347667383534$ |
$39.66094555677728$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$18274.701264234773$ |
| 15.5.203...891.1 |
$x^{15} - 2 x^{12} - 3 x^{9} + 6 x^{6} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 61^{3}\cdot 397^{3}$ |
$3$ |
$22.5915132906$ |
$797.7221794318356$ |
|
|
✓ |
$C_3^4:(C_2\times S_5)$ (as 15T70) |
trivial |
$2$ |
$9$ |
$24855.5233084$ |
| 15.5.203...891.2 |
$x^{15} - 5 x^{9} - x^{6} + 3 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 61^{3}\cdot 397^{3}$ |
$3$ |
$22.5915132906$ |
$797.7221794318356$ |
|
|
✓ |
$C_3^4:(C_2\times S_5)$ (as 15T70) |
trivial |
$2$ |
$9$ |
$25221.9106564$ |
| 15.5.288...375.1 |
$x^{15} - 3 x^{14} + 2 x^{13} - x^{12} - 17 x^{11} + 22 x^{10} + 99 x^{7} + 154 x^{6} + 132 x^{5} + 321 x^{4} + 643 x^{3} - 84 x^{2} - 343 x + 197$ |
$15$ |
[5,5] |
$-\,3^{5}\cdot 5^{5}\cdot 11^{14}$ |
$3$ |
$23.12048424210466$ |
$36.308820055644325$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$19806.507558070312$ |
| 15.5.405...643.1 |
$x^{15} - 3 x^{14} - x^{13} - 4 x^{12} + 10 x^{11} + 25 x^{10} + 36 x^{9} - 46 x^{8} - 111 x^{7} - 151 x^{6} + 138 x^{5} + 181 x^{4} - 15 x^{3} - 52 x^{2} - 24 x + 3$ |
$15$ |
[5,5] |
$-\,3^{5}\cdot 401^{7}$ |
$2$ |
$23.6505434997$ |
$34.68429039204925$ |
|
|
|
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$9$ |
$77823.7688685$ |
| 15.5.608...000.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - x^{10} - 275 x^{9} + 10 x^{8} + 450 x^{7} - 35 x^{6} - 376 x^{5} + 50 x^{4} + 130 x^{3} - 25 x^{2} - 5 x - 1$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 5^{15}\cdot 11^{7}$ |
$3$ |
$24.3018827503$ |
$38.11677176459088$ |
|
|
✓ |
$C_5^2:(C_4\times S_3)$ (as 15T27) |
trivial |
$2$ |
$9$ |
$93323.0722574$ |
| 15.5.695...651.1 |
$x^{15} - x^{14} - 6 x^{13} + 29 x^{12} - 66 x^{11} - 32 x^{10} + 34 x^{9} + 100 x^{8} + 122 x^{7} + 56 x^{6} + 12 x^{5} + 11 x^{4} - 9 x^{3} + 7 x^{2} - 6 x + 1$ |
$15$ |
[5,5] |
$-\,11^{13}\cdot 67^{4}$ |
$2$ |
$24.5184836613$ |
$142.76988787487005$ |
|
|
? |
$C_7^3:C_6$ (as 15T44) |
trivial |
$2$ |
$9$ |
$47044.8303705$ |
| 15.5.804...000.1 |
$x^{15} - 15 x^{13} + 90 x^{11} - 2 x^{10} - 275 x^{9} + 20 x^{8} + 450 x^{7} - 70 x^{6} - 375 x^{5} + 100 x^{4} + 125 x^{3} - 50 x^{2} + 8$ |
$15$ |
[5,5] |
$-\,2^{12}\cdot 5^{15}\cdot 23^{5}$ |
$3$ |
$24.757300012490276$ |
|
|
|
? |
$D_5^3.D_6$ (as 15T68) |
trivial |
$2$ |
$9$ |
$59566.61941447335$ |
| 15.5.121...000.1 |
$x^{15} - 6 x^{14} + 19 x^{13} - 52 x^{12} + 91 x^{11} - 165 x^{10} + 209 x^{9} - 396 x^{8} + 1034 x^{7} - 1397 x^{6} + 1749 x^{5} - 1998 x^{4} + 1109 x^{3} - 826 x^{2} + 848 x - 197$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 5^{5}\cdot 11^{14}$ |
$3$ |
$25.447385642214737$ |
$41.92581406616787$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
trivial |
$2$ |
$9$ |
$60043.03877172378$ |
| 15.5.145...951.1 |
$x^{15} - 4 x^{14} + x^{13} + 10 x^{12} - 18 x^{11} + 78 x^{10} - 154 x^{9} + 13 x^{8} + 122 x^{7} + 108 x^{6} - 197 x^{5} - 61 x^{4} + 98 x^{3} + 38 x^{2} - 21 x - 7$ |
$15$ |
[5,5] |
$-\,7^{6}\cdot 199^{7}$ |
$2$ |
$25.7535627774$ |
$37.322915213043046$ |
|
|
|
$D_5\times S_3$ (as 15T7) |
trivial |
$2$ |
$9$ |
$145057.542197$ |
| 15.5.205...000.1 |
$x^{15} - 10 x^{13} + 10 x^{11} - 74 x^{10} - 90 x^{9} + 50 x^{8} - 80 x^{7} - 160 x^{6} + 124 x^{5} + 140 x^{4} - 60 x^{3} - 60 x^{2} + 4$ |
$15$ |
[5,5] |
$-\,2^{14}\cdot 5^{16}\cdot 7^{7}$ |
$3$ |
$26.3577551473$ |
$32.16072676113696$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
$2$ |
$9$ |
$204986.499805$ |
| 15.5.257...000.1 |
$x^{15} - 5 x^{13} - 5 x^{12} - 20 x^{11} - 10 x^{10} + 30 x^{9} + 70 x^{8} + 95 x^{7} + 110 x^{6} + 85 x^{5} + 185 x^{4} + 45 x^{3} + 50 x^{2} - 25 x - 5$ |
$15$ |
[5,5] |
$-\,2^{12}\cdot 5^{17}\cdot 7^{7}$ |
$3$ |
$26.7527903869$ |
$30.937664227835434$ |
|
|
? |
$F_5 \times S_3$ (as 15T11) |
trivial |
$2$ |
$9$ |
$184544.05094$ |
| 15.5.320...247.1 |
$x^{15} - 4 x^{14} + 13 x^{12} + 10 x^{11} - 70 x^{10} - 29 x^{9} + 226 x^{8} + 13 x^{7} - 454 x^{6} + 76 x^{5} + 499 x^{4} - 78 x^{3} - 183 x^{2} + 46 x + 23$ |
$15$ |
[5,5] |
$-\,3^{12}\cdot 11^{6}\cdot 23^{7}$ |
$3$ |
$27.1473266107$ |
$102.63308446066065$ |
|
|
? |
$A_5 \times S_3$ (as 15T23) |
trivial |
$2$ |
$9$ |
$110150.048352$ |
| 15.5.509...275.1 |
$x^{15} - 7 x^{12} + 15 x^{9} - 7 x^{6} - 8 x^{3} + 5$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 5^{2}\cdot 61^{3}\cdot 397^{3}$ |
$4$ |
$27.9989228362$ |
$2353.7405744869748$ |
|
|
✓ |
$C_3^4:(S_3\times S_5)$ (as 15T83) |
trivial |
$2$ |
$9$ |
$109168.983075$ |
| 15.5.544...587.1 |
$x^{15} - 22 x^{12} + 66 x^{9} - 33 x^{6} - 22 x^{3} + 11$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{14}$ |
$2$ |
$28.124691079190463$ |
$33.77598086990868$ |
|
|
? |
$S_3 \times C_5$ (as 15T4) |
$[2]$ |
$2$ |
$9$ |
$56600.06558827911$ |
| 15.5.662...523.1 |
$x^{15} - 2 x^{12} - 6 x^{9} + 15 x^{6} - 8 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{13}\cdot 401^{6}$ |
$2$ |
$28.4946178223$ |
|
|
|
? |
$C_3^4:D_{10}$ (as 15T43) |
trivial |
$2$ |
$9$ |
$276624.713435$ |
| 15.5.662...523.2 |
$x^{15} - 9 x^{12} + 27 x^{9} - 30 x^{6} + 7 x^{3} + 3$ |
$15$ |
[5,5] |
$-\,3^{13}\cdot 401^{6}$ |
$2$ |
$28.4946178223$ |
$191.56732377614063$ |
|
|
? |
$C_3^5:D_{10}$ (as 15T55) |
trivial |
$2$ |
$9$ |
$176156.941662$ |
| 15.5.836...871.1 |
$x^{15} - x^{14} - x^{13} - x^{12} - x^{11} + 6 x^{10} - 3 x^{9} + 5 x^{8} - 8 x^{7} + 4 x^{6} - x^{5} + x^{4} + x^{3} - 2 x^{2} + 3 x - 1$ |
$15$ |
[5,5] |
$-\,61\cdot 443437\cdot 309247046331703$ |
$3$ |
$28.9399530034$ |
$91460518976.96445$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$424231.084588$ |
| 15.5.136...456.1 |
$x^{15} - x^{14} - 6 x^{13} + 5 x^{12} + 13 x^{11} - 8 x^{10} - 15 x^{9} + 11 x^{8} + 7 x^{7} - 16 x^{6} - x^{5} + 17 x^{4} + 2 x^{3} - 7 x^{2} - x + 1$ |
$15$ |
[5,5] |
$-\,2^{3}\cdot 1999922317\cdot 853738824721$ |
$3$ |
$29.9016538528$ |
$116872967907.85727$ |
|
|
✓ |
$S_{15}$ (as 15T104) |
trivial |
$2$ |
$9$ |
$474668.432119$ |
| 15.5.279...064.1 |
$x^{15} + 4 x^{13} - 19 x^{12} + 15 x^{11} - 95 x^{10} + 119 x^{9} - 195 x^{8} + 703 x^{7} - 390 x^{6} + 615 x^{5} - 946 x^{4} - 186 x^{3} - 384 x^{2} - 146 x + 157$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 3^{8}\cdot 401^{6}$ |
$3$ |
$31.3623850115$ |
$398.5654832175406$ |
|
|
|
$S_3\wr D_5$ (as 15T86) |
trivial |
$2$ |
$9$ |
$567079.72413$ |
| 15.5.281...072.1 |
$x^{15} - 5 x^{14} + 10 x^{13} + 2 x^{12} - 43 x^{11} + 71 x^{10} - 52 x^{9} + 24 x^{8} - 12 x^{7} - 76 x^{6} + 160 x^{5} - 80 x^{4} - 96 x^{3} + 96 x^{2} - 32$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{12}\cdot 43\cdot 197\cdot 1033$ |
$5$ |
$31.3764023494$ |
$73886.12521996467$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$9$ |
$183908.779975$ |
| 15.5.364...104.1 |
$x^{15} - 6 x^{13} - 12 x^{12} + 10 x^{11} + 40 x^{10} + 39 x^{9} - 6 x^{8} - 18 x^{7} - 56 x^{6} - 143 x^{5} - 182 x^{4} - 56 x^{3} + 80 x^{2} + 80 x + 32$ |
$15$ |
[5,5] |
$-\,2^{10}\cdot 11^{12}\cdot 11356201$ |
$3$ |
$31.9263803534$ |
$45894.503845687716$ |
|
|
? |
$S_3\wr C_5$ (as 15T81) |
trivial |
$2$ |
$9$ |
$302797.187809$ |
| 15.5.588...499.1 |
$x^{15} - 12 x^{12} + 53 x^{9} - 104 x^{6} + 84 x^{3} - 17$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 17^{2}\cdot 61^{3}\cdot 397^{3}$ |
$4$ |
$32.9613643022$ |
$5274.131429093919$ |
|
|
✓ |
$C_3^4:(S_3\times S_5)$ (as 15T83) |
trivial |
$2$ |
$9$ |
$431347.778673$ |
