| 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 |
| 13.3.5570916369223.1 |
$x^{13} - x^{12} + x^{11} - 4 x^{10} + 5 x^{9} - 5 x^{8} + 6 x^{7} - 2 x^{6} - 5 x^{5} + 5 x^{4} - 7 x^{3} + 5 x^{2} - x + 1$ |
$13$ |
[3,5] |
$-\,5570916369223$ |
$1$ |
$9.55995604118$ |
$2360278.8753075344$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$9.61638823677$ |
| 13.3.5717814639679.1 |
$x^{13} - 2 x^{12} - 3 x^{11} + 7 x^{10} + 3 x^{9} - 7 x^{8} - 6 x^{7} + 4 x^{6} + 8 x^{5} - 3 x^{4} - 4 x^{3} + 2 x^{2} - 1$ |
$13$ |
[3,5] |
$-\,89\cdot 107\cdot 283\cdot 2121631$ |
$4$ |
$9.5791150674$ |
$2391195.2324473634$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$9.76540201266$ |
| 13.3.6855574490939.1 |
$x^{13} - x^{12} + 2 x^{11} + 2 x^{10} - 3 x^{9} + x^{8} - x^{7} - 8 x^{6} - 7 x^{5} - 6 x^{4} - 6 x^{3} - 6 x^{2} - 4 x - 1$ |
$13$ |
[3,5] |
$-\,1798333\cdot 3812183$ |
$2$ |
$9.71377386112$ |
$2618315.200837936$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$10.9027200388$ |
| 13.3.7805208559959.1 |
$x^{13} - 4 x^{12} + 6 x^{11} - 6 x^{10} + 7 x^{9} - 5 x^{8} - x^{7} + x^{6} + 5 x^{5} - 2 x^{4} - 3 x^{3} - x^{2} + 1$ |
$13$ |
[3,5] |
$-\,3^{3}\cdot 31\cdot 71\cdot 821\cdot 159977$ |
$5$ |
$9.81119450388$ |
$931260.111650338$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$11.7783503996$ |
| 13.3.9197165262683.1 |
$x^{13} - 2 x^{10} + 2 x^{9} - x^{8} - 3 x^{7} - 3 x^{6} + 9 x^{5} - 10 x^{4} + 7 x^{3} + 1$ |
$13$ |
[3,5] |
$-\,82163\cdot 111938041$ |
$2$ |
$9.93583002049$ |
$3032682.849010592$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$13.0679687985$ |
| 13.3.14047799762079.1 |
$x^{13} - 2 x^{12} + 2 x^{10} - 3 x^{9} + 4 x^{8} - 4 x^{7} + 4 x^{6} - 5 x^{5} + 3 x^{4} - 2 x^{3} + 3 x^{2} - x - 1$ |
$13$ |
[3,5] |
$-\,3^{3}\cdot 16103\cdot 32310059$ |
$3$ |
$10.2648943838$ |
$1249346.4852597937$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$16.6395085824$ |
| 13.3.18597951501632.1 |
$x^{13} - 2 x^{12} + x^{11} + x^{10} - 6 x^{9} + 3 x^{8} + 7 x^{7} - 4 x^{6} + 4 x^{4} - 4 x^{3} - 4 x^{2} + x + 1$ |
$13$ |
[3,5] |
$-\,2^{6}\cdot 67\cdot 43517\cdot 99667$ |
$4$ |
$10.4888550911$ |
$1078133.5579843528$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$20.8860106706$ |
| 13.3.21982001088443.1 |
$x^{13} - x^{12} + x^{11} + 3 x^{10} - 8 x^{9} + 10 x^{8} - 6 x^{7} - 5 x^{6} + 15 x^{5} - 19 x^{4} + 15 x^{3} - 9 x^{2} + 3 x - 1$ |
$13$ |
[3,5] |
$-\,11^{2}\cdot 71\cdot 2558724373$ |
$3$ |
$10.6246067266$ |
$1413634.937072864$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$22.4503389791$ |
| 13.3.21990353102339.1 |
$x^{13} - 2 x^{12} + 4 x^{11} - 5 x^{10} + 3 x^{9} + x^{8} - 4 x^{7} + 9 x^{6} - 7 x^{5} + 2 x^{4} - 4 x^{2} + 4 x - 1$ |
$13$ |
[3,5] |
$-\,157\cdot 3169\cdot 44198783$ |
$3$ |
$10.624917195$ |
$4689387.284319669$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$22.0576155446$ |
| 13.3.34372007159104.1 |
$x^{13} - x^{12} - 2 x^{11} + 5 x^{10} + x^{9} - 8 x^{8} + 5 x^{7} + 7 x^{6} - 2 x^{4} - 4 x - 1$ |
$13$ |
[3,5] |
$-\,2^{6}\cdot 29\cdot 239\cdot 77487031$ |
$4$ |
$10.9962987482$ |
$1465691.1159736216$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$29.7815563037$ |
| 13.3.49047631346319.1 |
$x^{13} - 2 x^{12} + 3 x^{11} + 2 x^{10} - 9 x^{9} + 12 x^{8} - 2 x^{7} - 19 x^{6} + 27 x^{5} - 19 x^{4} - x^{3} + 11 x^{2} - 6 x + 1$ |
$13$ |
[3,5] |
$-\,3\cdot 16349210448773$ |
$2$ |
$11.3011974948$ |
$7003401.412622226$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$44.4479338582$ |
| 13.3.53877019237375.1 |
$x^{13} - 2 x^{12} - 4 x^{11} + 7 x^{10} + 6 x^{9} - 6 x^{8} - 6 x^{7} - 8 x^{6} + 8 x^{5} + 15 x^{4} - 7 x^{3} - 7 x^{2} + x + 1$ |
$13$ |
[3,5] |
$-\,5^{3}\cdot 204793\cdot 2104643$ |
$3$ |
$11.3831330569$ |
$2195200.9241965474$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$39.9707034173$ |
| 13.3.60464861374756.1 |
$x^{13} - x^{11} - 3 x^{10} - x^{9} + 4 x^{8} + 5 x^{7} - x^{6} - 6 x^{5} - 5 x^{4} + x^{3} + 4 x^{2} + 3 x + 1$ |
$13$ |
[3,5] |
$-\,2^{2}\cdot 15116215343689$ |
$2$ |
$11.4845932957$ |
$7775915.46859635$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$66.5258088388$ |
| 13.3.69188908404875.1 |
$x^{13} - 3 x^{12} + 3 x^{11} - 3 x^{10} + 5 x^{9} + 2 x^{8} - 17 x^{7} + 10 x^{6} + 16 x^{5} - 16 x^{4} - 5 x^{3} + 7 x^{2} - 1$ |
$13$ |
[3,5] |
$-\,5^{3}\cdot 7^{5}\cdot 31\cdot 1062367$ |
$4$ |
$11.6042797679$ |
$97116.7192341759$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$49.3240960032$ |
| 13.3.96082590998375.1 |
$x^{13} - 4 x^{11} - 3 x^{10} + 9 x^{9} + 10 x^{8} - 4 x^{7} - 12 x^{6} - 13 x^{5} + 5 x^{4} + 12 x^{3} - x + 1$ |
$13$ |
[3,5] |
$-\,5^{3}\cdot 768660727987$ |
$2$ |
$11.9011260303$ |
$2931533.4207658344$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$61.9626233533$ |
| 13.3.105628246955776.1 |
$x^{13} - x^{12} + 3 x^{11} - x^{10} + 3 x^{9} + 6 x^{8} - 6 x^{7} + x^{6} + 6 x^{5} - 8 x^{4} - 9 x^{3} + 2 x^{2} + 4 x + 1$ |
$13$ |
[3,5] |
$-\,2^{8}\cdot 257\cdot 1605487703$ |
$3$ |
$11.9881539994$ |
$2569390.0900283707$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$94.5194105196$ |
| 13.3.114312593686528.1 |
$x^{13} - x^{12} - 5 x^{11} + 15 x^{9} + 9 x^{8} - 28 x^{7} - 20 x^{6} + 26 x^{5} + 20 x^{4} - 12 x^{3} - 10 x^{2} + 2 x + 2$ |
$13$ |
[3,5] |
$-\,2^{14}\cdot 6977087017$ |
$2$ |
$12.0612370249$ |
$417931.07479608984$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$95.7333582025$ |
| 13.3.134713017952000.1 |
$x^{13} - 5 x^{12} + 15 x^{11} - 34 x^{10} + 56 x^{9} - 79 x^{8} + 85 x^{7} - 78 x^{6} + 53 x^{5} - 25 x^{4} + 6 x^{3} + 4 x^{2} - 2 x + 1$ |
$13$ |
[3,5] |
$-\,2^{8}\cdot 5^{3}\cdot 4209781811$ |
$3$ |
$12.214555267$ |
$867795.2892169062$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$115.220069967$ |
| 13.3.156408138976000.1 |
$x^{13} - 3 x^{12} + 3 x^{11} - 4 x^{10} + 4 x^{9} + 7 x^{8} - 20 x^{7} + 27 x^{6} - 35 x^{5} + 41 x^{4} - 36 x^{3} + 24 x^{2} - 12 x + 4$ |
$13$ |
[3,5] |
$-\,2^{8}\cdot 5^{3}\cdot 137\cdot 599\cdot 59561$ |
$5$ |
$12.3556644027$ |
$935065.8145079553$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$127.407170199$ |
| 13.3.215762905145828.1 |
$x^{13} - 2 x^{12} + x^{11} + 5 x^{10} - 10 x^{9} + 4 x^{8} + 8 x^{7} - 13 x^{6} + 5 x^{5} + 10 x^{4} - 9 x^{3} - 3 x^{2} + 4 x + 1$ |
$13$ |
[3,5] |
$-\,2^{2}\cdot 953\cdot 10313\cdot 5488313$ |
$4$ |
$12.665245094$ |
$14688870.111272275$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$143.677539316$ |
| 13.3.509211272757248.1 |
$x^{13} - x^{12} - 2 x^{11} - 2 x^{10} + 3 x^{9} + 4 x^{8} + 8 x^{7} - 4 x^{6} - 13 x^{5} + 3 x^{4} + 2 x^{3} - 6 x^{2} + x + 2$ |
$13$ |
[3,5] |
$-\,2^{14}\cdot 31079789597$ |
$2$ |
$13.5300638744$ |
$882077.2661754743$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$379.340811006$ |
| 13.3.1990387975424000.1 |
$x^{13} - x^{12} - 4 x^{11} - 2 x^{10} + 6 x^{9} + 3 x^{8} - x^{7} - 6 x^{6} + x^{4} + x^{3} - 12 x^{2} - 3 x + 1$ |
$13$ |
[3,5] |
$-\,2^{11}\cdot 5^{3}\cdot 84089\cdot 92461$ |
$4$ |
$15.0259301129$ |
$1179332.8112017198$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$942.961496704$ |
| 13.3.71106764206294000.1 |
$x^{13} - 2 x^{12} - x^{11} + 4 x^{10} + 4 x^{9} + 5 x^{8} - 27 x^{7} - 6 x^{6} - 16 x^{5} + 80 x^{4} + 27 x^{3} - 13 x^{2} - 84 x - 36$ |
$13$ |
[3,5] |
$-\,2^{4}\cdot 5^{3}\cdot 241\cdot 147524407067$ |
$4$ |
$19.783395792$ |
$39874748.70457772$ |
|
|
|
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$12644.711746$ |
| 13.3.142...435.1 |
$x^{13} - 3 x - 1$ |
$13$ |
[3,5] |
$-\,5\cdot 226169\cdot 12570105664223$ |
$3$ |
$29.7363628145$ |
$3770257436.814926$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$45375.9232824$ |
| 13.3.597...896.1 |
$x^{13} - 4 x - 2$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 11546071\cdot 12625811381$ |
$3$ |
$39.6422192479$ |
$723970053.9470894$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$334935.266624$ |
| 13.3.598...931.1 |
$x^{13} - 4 x - 1$ |
$13$ |
[3,5] |
$-\,23\cdot 17579\cdot 1479900843934943$ |
$3$ |
$39.648547192$ |
$24461174737.065353$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$326795.8846$ |
| 13.3.119...080.1 |
$x^{13} - 8 x - 4$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 5\cdot 23\cdot 1993\cdot 1273413051689$ |
$5$ |
$41.8166077225$ |
$1024379927.742423$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$834014.333738$ |
| 13.3.237...827.1 |
$x^{13} - 6 x - 3$ |
$13$ |
[3,5] |
$-\,3^{12}\cdot 24749\cdot 180439539103$ |
$3$ |
$44.0815912468$ |
$184231675.62898946$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$1070286.79031$ |
| 13.3.553...256.1 |
$x^{13} - 9 x - 4$ |
$13$ |
[3,5] |
$-\,2^{14}\cdot 43\cdot 7852028154455813$ |
$3$ |
$47.0466257025$ |
|
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$2637773.12241$ |
| 13.3.107...427.1 |
$x^{13} - 5 x - 3$ |
$13$ |
[3,5] |
$-\,3^{12}\cdot 37\cdot 1033\cdot 527906776207$ |
$4$ |
$49.5039170754$ |
|
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$1649749.6598$ |
| 13.3.108...712.1 |
$x^{13} - 5 x - 2$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 1373\cdot 4079\cdot 93893\cdot 5052637$ |
$5$ |
$49.5602513542$ |
$4077794882.427895$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$7122148.48547$ |
| 13.3.108...747.1 |
$x^{13} - 5 x - 1$ |
$13$ |
[3,5] |
$-\,97\cdot 7489\cdot 14982677517575459$ |
$3$ |
$49.5606858137$ |
$104325986106.64983$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$1291193.99807$ |
| 13.3.278...112.1 |
$x^{13} - 6 x - 4$ |
$13$ |
[3,5] |
$-\,2^{22}\cdot 7\cdot 11\cdot 86209262103439$ |
$4$ |
$53.2740526035$ |
$374719603.7763133$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$9041727.04856$ |
| 13.3.959...291.1 |
$x^{13} - 7 x - 3$ |
$13$ |
[3,5] |
$-\,3^{11}\cdot 71\cdot 8627573\cdot 884392891$ |
$4$ |
$58.5943645771$ |
$5295991262.1649885$ |
|
|
|
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$12680428.6498$ |
| 13.3.116...808.1 |
$x^{13} - 6 x - 2$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 7\cdot 29\cdot 1601\cdot 10211\cdot 8566846531$ |
$6$ |
$59.4727743666$ |
$10110256144.00497$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$8920185.39416$ |
| 13.3.116...843.1 |
$x^{13} - 6 x - 1$ |
$13$ |
[3,5] |
$-\,7\cdot 106123\cdot 474647\cdot 330265270729$ |
$4$ |
$59.4728230918$ |
$341248383831.6556$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$7142691.32078$ |
| 13.3.196...483.1 |
$x^{13} - 8 x - 1$ |
$13$ |
[3,5] |
$-\,196067122333410552143483$ |
$1$ |
$61.9046744759$ |
$442794672882.8279$ |
|
|
? |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$9730179.4488$ |
| 13.3.215...976.1 |
$x^{13} - 7 x - 2$ |
$13$ |
[3,5] |
$-\,2^{10}\cdot 6311\cdot 33418789974864709$ |
$3$ |
$62.3667321902$ |
$35552886109.60805$ |
|
|
|
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$42431581.911$ |
| 13.3.789...067.1 |
$x^{13} - 7 x - 5$ |
$13$ |
[3,5] |
$-\,11\cdot 6389\cdot 11239887182523352373$ |
$3$ |
$68.9090025337$ |
$888778955252.9688$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$9653171.82944$ |
| 13.3.858...544.1 |
$x^{13} - 7 x - 4$ |
$13$ |
[3,5] |
$-\,2^{25}\cdot 397\cdot 64468409915761$ |
$3$ |
$69.3534800586$ |
$1279848959.502509$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$31843391.6113$ |
| 13.3.863...939.1 |
$x^{13} - 7 x - 1$ |
$13$ |
[3,5] |
$-\,1951\cdot 442784289501823599389$ |
$2$ |
$69.3849602858$ |
$929447227559.509$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$7312741.36675$ |
| 13.3.424...320.1 |
$x^{13} - 8 x - 6$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 3^{12}\cdot 5\cdot 11943947\cdot 32634517$ |
$5$ |
$78.4208496831$ |
$417620777.2365524$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$60261510.7411$ |
| 13.3.482...203.1 |
$x^{13} - 8 x - 5$ |
$13$ |
[3,5] |
$-\,521\cdot 1231\cdot 7527444318037649653$ |
$3$ |
$79.2044325299$ |
$2197210490785.4788$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$37847644.5934$ |
| 13.3.490...755.1 |
$x^{13} - 8 x - 3$ |
$13$ |
[3,5] |
$-\,3^{12}\cdot 5\cdot 11\cdot 59\cdot 103\cdot 27594564189113$ |
$6$ |
$79.2968971654$ |
$15151249753.105644$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$64236665.3802$ |
| 13.3.490...040.1 |
$x^{13} - 8 x - 2$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 5\cdot 239339688381919058023$ |
$3$ |
$79.2970959278$ |
$65594315580.91077$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$40345047.207$ |
| 13.3.184...371.1 |
$x^{13} - 9 x - 7$ |
$13$ |
[3,5] |
$-\,1531661\cdot 12059685344860216111$ |
$2$ |
$87.8166402922$ |
$4297830815073.337$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$52498509.9019$ |
| 13.3.220...216.1 |
$x^{13} - 9 x - 6$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 3^{12}\cdot 182029\cdot 55532949839$ |
$4$ |
$89.0068771627$ |
$693430406.7106662$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$287416139.261$ |
| 13.3.225...099.1 |
$x^{13} - 9 x - 5$ |
$13$ |
[3,5] |
$-\,23\cdot 101\cdot 9724316372600271793313$ |
$3$ |
$89.1868114664$ |
$4752850400922.633$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$87164987.1254$ |
| 13.3.226...651.1 |
$x^{13} - 9 x - 3$ |
$13$ |
[3,5] |
$-\,3^{12}\cdot 54469\cdot 16734163\cdot 46786013$ |
$4$ |
$89.2091859185$ |
$18003391961.32576$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$79898152.146$ |
| 13.3.226...936.1 |
$x^{13} - 9 x - 2$ |
$13$ |
[3,5] |
$-\,2^{12}\cdot 16519\cdot 334952983395693989$ |
$3$ |
$89.2092342799$ |
$186089299130.6508$ |
|
|
✓ |
$S_{13}$ (as 13T9) |
trivial |
$2$ |
$7$ |
$329492464.675$ |
