| 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 |
| 47.1.384...167.1 |
$x^{47} - x - 1$ |
$47$ |
[1,23] |
$-\,11\cdot 199\cdot 227153\cdot 393351713\cdot 3297807724117\cdot 73745876125109\cdot 80\!\cdots\!59$ |
$7$ |
$46.9920576706$ |
$1.961439246360604e+39$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.312...512.1 |
$x^{47} + 4 x - 4$ |
$47$ |
[1,23] |
$-\,2^{46}\cdot 3\cdot 521\cdot 11213\cdot 282143\cdot 89\!\cdots\!99$ |
$6$ |
$88.452032442$ |
$1.3139199004859982e+39$ |
|
|
? |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.264...456.1 |
$x^{47} - 4 x - 4$ |
$47$ |
[1,23] |
$-\,2^{46}\cdot 1630520977\cdot 36906152269379\cdot 62\!\cdots\!13$ |
$4$ |
$92.5605257743$ |
$3.818930938814277e+39$ |
|
|
? |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.268...744.1 |
$x^{47} - 2 x - 2$ |
$47$ |
[1,23] |
$-\,2^{46}\cdot 3\cdot 919\cdot 34591\cdot 40\!\cdots\!33$ |
$5$ |
$92.5924511038$ |
$3.850005522409575e+39$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.272...336.1 |
$x^{47} - x - 2$ |
$47$ |
[1,23] |
$-\,2^{47}\cdot 31\cdot 39010490269\cdot 2162799135849959\cdot 1173213609967733880077131\cdot 631877578695978213816509977$ |
$6$ |
$92.6238779755$ |
|
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.277...320.1 |
$x^{47} + 2 x - 2$ |
$47$ |
[1,23] |
$-\,2^{46}\cdot 5\cdot 13\cdot 17\cdot 89\cdot 361179289\cdot 582997712425903553\cdot 19\!\cdots\!87$ |
$8$ |
$92.6548218769$ |
$3.911414135180125e+39$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.3.815...889.1 |
$x^{47} - 3 x - 1$ |
$47$ |
[3,22] |
$45361\cdot 5090740900405619\cdot 35\!\cdots\!71$ |
$3$ |
$127.204144117$ |
$2.856140809309561e+49$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$24$ |
|
| 47.1.815...784.1 |
$x^{47} + 3 x - 2$ |
$47$ |
[1,23] |
$-\,2^{47}\cdot 151\cdot 4406810867\cdot 798813369105083\cdot 10\!\cdots\!23$ |
$5$ |
$127.204145023$ |
|
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.343...439.1 |
$x^{47} - 2 x - 3$ |
$47$ |
[1,23] |
$-\,13\cdot 19051\cdot 13\!\cdots\!53$ |
$3$ |
$137.742384398$ |
$1.8539094577531702e+50$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.351...479.1 |
$x^{47} + 3 x - 3$ |
$47$ |
[1,23] |
$-\,3^{46}\cdot 19\cdot 41\cdot 2593\cdot 95957\cdot 371957\cdot 523877\cdot 221163397457\cdot 47\!\cdots\!53$ |
$9$ |
$137.81114769$ |
$5.839331005779363e+39$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.607...327.1 |
$x^{47} + 4 x - 1$ |
$47$ |
[1,23] |
$-\,3\cdot 161387\cdot 659693\cdot 1442983\cdot 48897948557\cdot 5667513832583\cdot 47737985627803\cdot 1031694803012501\cdot 1239335306776487\cdot 77947030248288422983$ |
$10$ |
$169.60552549$ |
$2.465130555727849e+52$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.480...384.1 |
$x^{47} + 2 x - 4$ |
$47$ |
[1,23] |
$-\,2^{90}\cdot 7\cdot 11\cdot 1983262109989\cdot 9629954559409\cdot 26\!\cdots\!33$ |
$6$ |
$177.230423466$ |
|
|
|
? |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.192...496.1 |
$x^{47} - 3 x - 4$ |
$47$ |
[1,23] |
$-\,2^{46}\cdot 503\cdot 12399061109599\cdot 43\!\cdots\!37$ |
$4$ |
$182.535803478$ |
|
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.192...944.1 |
$x^{47} + x - 4$ |
$47$ |
[1,23] |
$-\,2^{46}\cdot 3\cdot 90\!\cdots\!07$ |
$3$ |
$182.535803643$ |
|
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.588...375.1 |
$x^{47} - 5 x - 5$ |
$47$ |
[1,23] |
$-\,5^{46}\cdot 101\cdot 40\!\cdots\!87$ |
$3$ |
$216.531047325$ |
$3.1082242924364957e+39$ |
|
|
? |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.551...911.1 |
$x^{47} - 4 x - 5$ |
$47$ |
[1,23] |
$-\,11\cdot 887\cdot 56\!\cdots\!23$ |
$3$ |
$227.089027186$ |
$2.34752119342858e+55$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.551...663.1 |
$x^{47} + 2 x - 5$ |
$47$ |
[1,23] |
$-\,19\cdot 43\cdot 97694879\cdot 33279582301451\cdot 20\!\cdots\!91$ |
$5$ |
$227.089032514$ |
$2.3475224877442604e+55$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
| 47.1.551...127.1 |
$x^{47} + 3 x - 5$ |
$47$ |
[1,23] |
$-\,769\cdot 204367\cdot 1847903553389\cdot 18\!\cdots\!41$ |
$4$ |
$227.089032514$ |
$2.347522487745998e+55$ |
|
|
✓ |
$S_{47}$ (as 47T6) |
not computed |
$2$ |
$23$ |
|
