| 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 |
| 31.1.168...431.1 |
$x^{31} - x - 1$ |
$31$ |
[1,15] |
$-\,4211\cdot 107951341831\cdot 1040542609867\cdot 35650774802780191673$ |
$4$ |
$30.9878668755$ |
$1.2985870397716353e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$42212973871.16097$ |
| 31.1.172...431.1 |
$x^{31} + x - 1$ |
$31$ |
[1,15] |
$-\,107\cdot 349\cdot 46\!\cdots\!17$ |
$3$ |
$31.0119923122$ |
$1.3143464255217451e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$60402933903.83712$ |
| 31.1.365...111.1 |
$x^{31} + 2 x - 1$ |
$31$ |
[1,15] |
$-\,71\cdot 6073\cdot 84\!\cdots\!17$ |
$3$ |
$46.0591112201$ |
$6.044927225878627e+25$ |
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$38986878555233.18$ |
| 31.1.174...144.1 |
$x^{31} - 4 x - 4$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 29161973\cdot 14898732471895043\cdot 37391233052164359356929$ |
$4$ |
$60.5324503205$ |
$2.492799546000918e+23$ |
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$2698409433385651.0$ |
| 31.1.178...144.1 |
$x^{31} - 2 x - 2$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 937\cdot 17\!\cdots\!63$ |
$3$ |
$60.5813478258$ |
$2.5241947084706398e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$3069030481487575.5$ |
| 31.1.183...144.1 |
$x^{31} - x - 2$ |
$31$ |
[1,15] |
$-\,2^{31}\cdot 1433\cdot 3653617274537267\cdot 1630096334391835835360875373$ |
$4$ |
$60.6290892528$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$6213208850652677.0$ |
| 31.1.183...519.1 |
$x^{31} - x - 4$ |
$31$ |
[1,15] |
$-\,23\cdot 1693\cdot 3697\cdot 19843\cdot 14132537\cdot 75771043\cdot 5991663366536301415229073661$ |
$7$ |
$60.6290892528$ |
$4.28110805344789e+27$ |
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$4169052629874545.0$ |
| 31.1.183...144.1 |
$x^{31} - 2$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 31^{31}$ |
$2$ |
$60.6290892528$ |
$67.48167773073806$ |
|
|
✓ |
$F_{31}$ (as 31T8) |
trivial |
$2$ |
$15$ |
$5190129910021260.0$ |
| 31.1.187...144.1 |
$x^{31} + 2 x - 2$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 11\cdot 1489\cdot 1499\cdot 23334601\cdot 28850169461\cdot 1057614572100224186051$ |
$7$ |
$60.6757288558$ |
$2.5858417634744722e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$5116384966428125.0$ |
| 31.1.192...144.1 |
$x^{31} + 4 x - 4$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 7\cdot 90373\cdot 161611\cdot 54687761\cdot 3200213985295117341572815151$ |
$6$ |
$60.7213171385$ |
$2.6161205965049783e+23$ |
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$3952566540405579.5$ |
| 31.3.127...569.1 |
$x^{31} - 3 x - 1$ |
$31$ |
[3,14] |
$7\cdot 17\cdot 23\cdot 15726392777460683\cdot 29\!\cdots\!39$ |
$5$ |
$80.6479693545$ |
$3.5661390161578326e+29$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$16$ |
$227786011641746100$ |
| 31.1.127...431.1 |
$x^{31} + 3 x - 1$ |
$31$ |
[1,15] |
$-\,43\cdot 39047\cdot 455317\cdot 317197259\cdot 45044106017368643\cdot 11642845821394330173359$ |
$6$ |
$80.6479693545$ |
$3.566139016158311e+29$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$253630612977039870$ |
| 31.1.127...144.1 |
$x^{31} + 3 x - 2$ |
$31$ |
[1,15] |
$-\,2^{31}\cdot 59\cdot 316799009\cdot 31\!\cdots\!63$ |
$4$ |
$80.6483442561$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$1049301058301323900$ |
| 31.1.338...719.1 |
$x^{31} - 3 x - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 7\cdot 2713\cdot 14387\cdot 3413878991\cdot 72413150415649\cdot 243568924508677$ |
$7$ |
$89.655221097$ |
$3.7139239555445536e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$1235026277671475000$ |
| 31.1.351...719.1 |
$x^{31} - 2 x - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 1069\cdot 745011551\cdot 21\!\cdots\!49$ |
$4$ |
$89.7618797049$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$2083870736834916600$ |
| 31.1.351...719.1 |
$x^{31} - x - 3$ |
$31$ |
[1,15] |
$-\,3^{31}\cdot 571\cdot 99\!\cdots\!87$ |
$3$ |
$89.7618800692$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$1630733111771600400$ |
| 31.1.351...719.1 |
$x^{31} - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 31^{31}$ |
$2$ |
$89.7618800692$ |
$99.90719534111327$ |
|
|
✓ |
$F_{31}$ (as 31T8) |
trivial |
$2$ |
$15$ |
$2584759353644243000$ |
| 31.1.351...719.1 |
$x^{31} + x - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 19\cdot 3539\cdot 25\!\cdots\!91$ |
$4$ |
$89.7618800692$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$1038806063023256300$ |
| 31.1.364...719.1 |
$x^{31} + 3 x - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 678106210770691935341\cdot 26082709826393492021802491$ |
$3$ |
$89.8648674064$ |
$3.850839894720458e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$980243888323008500$ |
| 31.1.194...831.1 |
$x^{31} + 4 x - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 59\cdot 10709\cdot 14\!\cdots\!49$ |
$4$ |
$94.8552726221$ |
|
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$4933387750736738000$ |
| 31.3.949...856.1 |
$x^{31} - 4 x - 2$ |
$31$ |
[3,14] |
$2^{30}\cdot 2383\cdot 37\!\cdots\!43$ |
$3$ |
$107.530625739$ |
$1.839154007745496e+27$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$16$ |
$36948458623552070000$ |
| 31.3.949...569.1 |
$x^{31} - 4 x - 1$ |
$31$ |
[3,14] |
$24365060088671\cdot 38\!\cdots\!39$ |
$2$ |
$107.530625806$ |
$3.0814043149172737e+31$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$16$ |
$38197936820101820000$ |
| 31.1.949...431.1 |
$x^{31} + 4 x - 1$ |
$31$ |
[1,15] |
$-\,7\cdot 13\!\cdots\!33$ |
$2$ |
$107.530625806$ |
$3.0814043149172737e+31$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
$[2]$ |
$2$ |
$15$ |
$20750959184225810000$ |
| 31.1.949...144.1 |
$x^{31} + 4 x - 2$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 7\cdot 195469\cdot 212031575390627\cdot 30\!\cdots\!91$ |
$5$ |
$107.530625873$ |
$1.839154043245885e+27$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$26578047987565236000$ |
| 31.1.491...664.1 |
$x^{31} - 2 x - 4$ |
$31$ |
[1,15] |
$-\,2^{58}\cdot 18637\cdot 91\!\cdots\!13$ |
$3$ |
$113.391135691$ |
|
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$210828920582287920000$ |
| 31.1.491...664.1 |
$x^{31} + 2 x - 4$ |
$31$ |
[1,15] |
$-\,2^{58}\cdot 11\cdot 15\!\cdots\!71$ |
$3$ |
$113.391135691$ |
|
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$94153833123094710000$ |
| 31.1.196...656.1 |
$x^{31} - 3 x - 4$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 7\cdot 81987621103882733\cdot 1994715371164304797\cdot 16009667507940703067$ |
$5$ |
$118.576957979$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.196...656.1 |
$x^{31} + x - 4$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 103\cdot 1946342156463328037\cdot 91\!\cdots\!79$ |
$4$ |
$118.576982698$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$367578496614054170000$ |
| 31.1.106...191.1 |
$x^{31} + 5 x - 3$ |
$31$ |
[1,15] |
$-\,3^{30}\cdot 43\cdot 16293623473\cdot 73\!\cdots\!81$ |
$4$ |
$125.216113893$ |
|
|
|
? |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.239...536.1 |
$x^{31} + 5 x - 2$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 13\cdot 17\cdot 27768997\cdot 113656553679773909591\cdot 320037570123859568648600917$ |
$6$ |
$128.534850359$ |
|
|
|
? |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$1487371382989533200000$ |
| 31.3.958...281.1 |
$x^{31} - 5 x - 3$ |
$31$ |
[3,14] |
$3^{30}\cdot 13\cdot 16690100963\cdot 21\!\cdots\!51$ |
$4$ |
$134.413266364$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$16$ |
$1258080429033531000000$ |
| 31.3.958...856.1 |
$x^{31} - 5 x - 2$ |
$31$ |
[3,14] |
$2^{31}\cdot 15619263033943\cdot 55942004669294094613\cdot 510951109592180719533133$ |
$4$ |
$134.413282257$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$16$ |
$4907974822306732000000$ |
| 31.3.958...569.1 |
$x^{31} - 5 x - 1$ |
$31$ |
[3,14] |
$13\cdot 1877\cdot 25841\cdot 202437701896105219\cdot 75\!\cdots\!11$ |
$5$ |
$134.413282257$ |
$9.791605058234429e+32$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$16$ |
$1341618162426672300000$ |
| 31.1.958...431.1 |
$x^{31} + 5 x - 1$ |
$31$ |
[1,15] |
$-\,59\cdot 18439\cdot 88\!\cdots\!31$ |
$3$ |
$134.413282257$ |
$9.791605058234429e+32$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.978...656.1 |
$x^{31} + 5 x - 4$ |
$31$ |
[1,15] |
$-\,2^{30}\cdot 105767\cdot 86\!\cdots\!07$ |
$3$ |
$134.501409014$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.149...375.1 |
$x^{31} - 5 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 443\cdot 26931473971\cdot 13\!\cdots\!27$ |
$4$ |
$146.863137605$ |
$6.0120274587273514e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.158...375.1 |
$x^{31} - 4 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 139\cdot 162071227763491\cdot 757645147032594015522973305823$ |
$4$ |
$147.157852638$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.158...375.1 |
$x^{31} - 3 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 7\cdot 43132069\cdot 56\!\cdots\!73$ |
$4$ |
$147.158136144$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.158...375.1 |
$x^{31} - 2 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 17\!\cdots\!83$ |
$2$ |
$147.158136182$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.158...375.1 |
$x^{31} - x - 5$ |
$31$ |
[1,15] |
$-\,5^{31}\cdot 34\!\cdots\!31$ |
$2$ |
$147.158136182$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.158...375.1 |
$x^{31} - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 31^{31}$ |
$2$ |
$147.158136182$ |
$163.79064973019854$ |
|
|
✓ |
$F_{31}$ (as 31T8) |
not computed |
$2$ |
$15$ |
|
| 31.1.158...375.1 |
$x^{31} + x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 19\cdot 173\cdot 2149711\cdot 24\!\cdots\!51$ |
$5$ |
$147.158136182$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$4634927539611405600000$ |
| 31.1.158...375.1 |
$x^{31} + 2 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 11\cdot 71\cdot 311\cdot 1667\cdot 209394034439\cdot 201326610321383981030559113$ |
$7$ |
$147.158136182$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
trivial |
$2$ |
$15$ |
$4536078693224075000000$ |
| 31.1.158...375.1 |
$x^{31} + 3 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 190717\cdot 89\!\cdots\!59$ |
$3$ |
$147.15813622$ |
|
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.1.168...375.1 |
$x^{31} + 5 x - 5$ |
$31$ |
[1,15] |
$-\,5^{30}\cdot 13\cdot 23\cdot 863\cdot 91923297263327\cdot 763023859796690773329733469$ |
$6$ |
$147.436395264$ |
$6.386242904186628e+23$ |
|
|
✓ |
$S_{31}$ (as 31T12) |
not computed |
$2$ |
$15$ |
|
| 31.31.606...801.1 |
$x^{31} - x^{30} - 150 x^{29} + 117 x^{28} + 9434 x^{27} - 4958 x^{26} - 328880 x^{25} + 78328 x^{24} + 7098810 x^{23} + 507925 x^{22} - 100297691 x^{21} - 39217806 x^{20} + 950942678 x^{19} + 677567200 x^{18} - 6056859921 x^{17} - 6293114670 x^{16} + 25303767350 x^{15} + 35315191500 x^{14} - 65145555320 x^{13} - 122001770825 x^{12} + 87706314807 x^{11} + 253609179978 x^{10} - 19776440614 x^{9} - 299693882286 x^{8} - 98200795275 x^{7} + 175359843704 x^{6} + 113820457794 x^{5} - 30260338943 x^{4} - 38729335872 x^{3} - 5811762482 x^{2} + 1056847214 x - 26458109$ |
$31$ |
[31,0] |
$311^{30}$ |
$1$ |
$258.433472772$ |
$258.43347277162707$ |
|
✓ |
|
$C_{31}$ (as 31T1) |
not computed |
$2$ |
$30$ |
|
| 31.31.141...449.1 |
$x^{31} - x^{30} - 180 x^{29} + 381 x^{28} + 13354 x^{27} - 40454 x^{26} - 531040 x^{25} + 2069355 x^{24} + 12295300 x^{23} - 60883682 x^{22} - 164683595 x^{21} + 1114070344 x^{20} + 1058778882 x^{19} - 13103530537 x^{18} + 1853849258 x^{17} + 99224120479 x^{16} - 91885359548 x^{15} - 467511308511 x^{14} + 762650059488 x^{13} + 1229830733203 x^{12} - 3225889300699 x^{11} - 1095874556276 x^{10} + 7495923118841 x^{9} - 2504773526476 x^{8} - 8920808783994 x^{7} + 7437366186489 x^{6} + 3836259163454 x^{5} - 6642200925120 x^{4} + 1200673450587 x^{3} + 1711910811444 x^{2} - 967097412303 x + 151576217389$ |
$31$ |
[31,0] |
$373^{30}$ |
$1$ |
$308.141705804$ |
$308.14170580366806$ |
|
✓ |
|
$C_{31}$ (as 31T1) |
trivial |
$2$ |
$30$ |
$65100477933366770000000000000$ |
| 31.31.107...849.1 |
$x^{31} - x^{30} - 330 x^{29} + 852 x^{28} + 43784 x^{27} - 173944 x^{26} - 2923572 x^{25} + 15562316 x^{24} + 100635650 x^{23} - 707709554 x^{22} - 1616621784 x^{21} + 17266725972 x^{20} + 7046247776 x^{19} - 243865756432 x^{18} + 142454592564 x^{17} + 2084163747748 x^{16} - 2521472241195 x^{15} - 10836712986085 x^{14} + 18499228115810 x^{13} + 32698257976552 x^{12} - 74538290301632 x^{11} - 47884603550112 x^{10} + 168256221920320 x^{9} + 4878741111552 x^{8} - 195294436805376 x^{7} + 62882730299136 x^{6} + 92885896276480 x^{5} - 43440624908288 x^{4} - 15171034030080 x^{3} + 6823763935232 x^{2} + 786648006656 x + 5192548352$ |
$31$ |
[31,0] |
$683^{30}$ |
$1$ |
$553.334536638$ |
$553.3345366377058$ |
|
✓ |
|
$C_{31}$ (as 31T1) |
trivial |
$2$ |
$30$ |
$588096262939769340000000000000000000000000$ |
| 31.31.303...801.1 |
$x^{31} - 465 x^{29} - 341 x^{28} + 91078 x^{27} + 119908 x^{26} - 9914451 x^{25} - 18008892 x^{24} + 666449563 x^{23} + 1538774528 x^{22} - 28934386579 x^{21} - 83032233092 x^{20} + 817351924162 x^{19} + 2943382779538 x^{18} - 14471455469735 x^{17} - 68751097280499 x^{16} + 137645143880654 x^{15} + 1028543867187214 x^{14} - 144266178422457 x^{13} - 9110738641752719 x^{12} - 11199776062831713 x^{11} + 37846129267859005 x^{10} + 105950708850677777 x^{9} + 9682358886535270 x^{8} - 290542929220278846 x^{7} - 437492517497239584 x^{6} - 201727405103545942 x^{5} + 73256081844015542 x^{4} + 87563225965427030 x^{3} + 7669633084320922 x^{2} - 7522164033404415 x - 310695313260929$ |
$31$ |
[31,0] |
$31^{60}$ |
$1$ |
$770.027976566$ |
$770.0279765662414$ |
|
✓ |
|
$C_{31}$ (as 31T1) |
not computed |
$2$ |
$30$ |
|
