| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 33.11.163...327.1 |
$ x^{33} - 3 x^{32} - 3 x^{31} + 28 x^{30} - 58 x^{29} + 22 x^{28} + \cdots - 1 $ |
$33$ |
[11,11] |
$-\,23^{31}$ |
$1$ |
$19.01949039124947$ |
|
|
not computed |
$S_3\times C_{11}$ (as 33T2) |
trivial |
$2$ |
$21$ |
$255776199.8931762$ |
| 33.1.127...537.1 |
$ x^{33} - x - 1 $ |
$33$ |
[1,16] |
$461\cdot 37057\cdot 74\!\cdots\!81$ |
$3$ |
$32.9886175927$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$477092908754.3794$ |
| 33.1.130...489.1 |
$ x^{33} + x - 1 $ |
$33$ |
[1,16] |
$17\cdot 43\cdot 1579\cdot 2609\cdot 13153817\cdot 216865282965193\cdot 15199633537674804809$ |
$7$ |
$33.0112581443$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$794597544869.8735$ |
| 33.1.125...305.1 |
$ x^{33} + 2 x - 1 $ |
$33$ |
[1,16] |
$5\cdot 25\!\cdots\!61$ |
$2$ |
$57.6194845298$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$12254017574219786$ |
| 33.33.271...161.1 |
$ x^{33} - x^{32} - 32 x^{31} + 31 x^{30} + 465 x^{29} - 435 x^{28} + \cdots - 1 $ |
$33$ |
[33,0] |
$67^{32}$ |
$1$ |
$58.9846766001$ |
|
✓ |
✓ |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$3985748844865106400$ |
| 33.1.135...753.1 |
$ x^{33} - 3 $ |
$33$ |
[1,16] |
$3^{65}\cdot 11^{27}$ |
$2$ |
$61.9202712528$ |
|
|
not computed |
$S_3\times F_{11}$ (as 33T11) |
trivial |
$2$ |
$16$ |
$62662652284763790$ |
| 33.33.277...001.1 |
$ x^{33} - x^{32} - 52 x^{31} + 47 x^{30} + 1159 x^{29} - 945 x^{28} + \cdots - 1 $ |
$33$ |
[33,0] |
$7^{22}\cdot 23^{30}$ |
$2$ |
$63.2897076721$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$15716532070591353000$ |
| 33.1.529...264.1 |
$ x^{33} - 4 x - 4 $ |
$33$ |
[1,16] |
$2^{32}\cdot 677\cdot 4266637\cdot 48046836047629\cdot 888172284811267871458394629$ |
$5$ |
$64.5374805481$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$80551974751644370$ |
| 33.1.541...056.1 |
$ x^{33} - 2 x - 2 $ |
$33$ |
[1,16] |
$2^{32}\cdot 17881556731651\cdot 70\!\cdots\!11$ |
$3$ |
$64.5833312616$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$88168911953428100$ |
| 33.1.554...872.1 |
$ x^{33} - x - 2 $ |
$33$ |
[1,16] |
$2^{32}\cdot 31\cdot 491\cdot 35603\cdot 23\!\cdots\!39$ |
$5$ |
$64.6281634182$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$133008702440587730$ |
| 33.1.554...392.1 |
$ x^{33} - x - 4 $ |
$33$ |
[1,16] |
$2^{32}\cdot 1621\cdot 3527\cdot 195457\cdot 11716761181\cdot 14330054499223\cdot 688121128326241$ |
$7$ |
$64.6281634182$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.554...848.1 |
$ x^{33} - 2 $ |
$33$ |
[1,16] |
$2^{32}\cdot 3^{33}\cdot 11^{33}$ |
$3$ |
$64.6281634182$ |
|
|
✓ |
$S_3\times F_{11}$ (as 33T11) |
trivial |
$2$ |
$16$ |
$95573511152749460$ |
| 33.1.567...640.1 |
$ x^{33} + 2 x - 2 $ |
$33$ |
[1,16] |
$2^{32}\cdot 5\cdot 53\cdot 3229\cdot 6433737122028757573993\cdot 23983104676408544038373$ |
$6$ |
$64.6720219514$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$96056886306925100$ |
| 33.1.579...432.1 |
$ x^{33} + 4 x - 4 $ |
$33$ |
[1,16] |
$2^{32}\cdot 7\cdot 127\cdot 361279\cdot 459803\cdot 149099734067\cdot 6129135169246811499255607$ |
$7$ |
$64.7149488714$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$84037986779048380$ |
| 33.33.700...569.1 |
$ x^{33} - 63 x^{31} - 4 x^{30} + 1710 x^{29} + 204 x^{28} - 26254 x^{27} + \cdots + 1 $ |
$33$ |
[33,0] |
$3^{44}\cdot 23^{30}$ |
$2$ |
$74.8335019768$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$176588774716401650000$ |
| 33.1.174...153.1 |
$ x^{33} - x - 3 $ |
$33$ |
[1,16] |
$32159\cdot 1547725797949519945333\cdot 35\!\cdots\!99$ |
$3$ |
$76.9368579483$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.3.812...935.1 |
$ x^{33} - 3 x - 1 $ |
$33$ |
[3,15] |
$-\,3^{33}\cdot 5\cdot 40739\cdot 11781157\cdot 3137660461139\cdot 194099782564469344251877$ |
$6$ |
$86.4292267677$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$17$ |
$10925780584629996000$ |
| 33.1.812...961.1 |
$ x^{33} + 3 x - 1 $ |
$33$ |
[1,16] |
$3^{34}\cdot 647\cdot 52009\cdot 14\!\cdots\!03$ |
$4$ |
$86.4292267677$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.812...296.1 |
$ x^{33} + 3 x - 2 $ |
$33$ |
[1,16] |
$2^{32}\cdot 3^{34}\cdot 5273\cdot 13873073\cdot 79403245997\cdot 19528960698348533$ |
$6$ |
$86.4294055199$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$22262502678802630000$ |
| 33.33.228...681.1 |
$ x^{33} - 8 x^{32} - 48 x^{31} + 488 x^{30} + 889 x^{29} + \cdots + 1013 $ |
$33$ |
[33,0] |
$13^{22}\cdot 23^{30}$ |
$2$ |
$95.6232054578$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$22765796489209540000000$ |
| 33.1.231...985.1 |
$ x^{33} - 3 x - 3 $ |
$33$ |
[1,16] |
$3^{33}\cdot 5\cdot 7\cdot 29264269\cdot 40\!\cdots\!33$ |
$5$ |
$95.6582185472$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.239...641.1 |
$ x^{33} - 2 x - 3 $ |
$33$ |
[1,16] |
$131009\cdot 18\!\cdots\!49$ |
$2$ |
$95.7584205303$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$91796156039521290000$ |
| 33.1.239...409.1 |
$ x^{33} + x - 3 $ |
$33$ |
[1,16] |
$7\cdot 17\cdot 59\cdot 34\!\cdots\!29$ |
$4$ |
$95.7584206826$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.247...881.1 |
$ x^{33} + 3 x - 3 $ |
$33$ |
[1,16] |
$3^{33}\cdot 251\cdot 6097463\cdot 19738007\cdot 14\!\cdots\!17$ |
$5$ |
$95.8553759516$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$64586856090532960000$ |
| 33.1.238...848.1 |
$ x^{33} + 2 x - 4 $ |
$33$ |
[1,16] |
$2^{62}\cdot 7\cdot 13\cdot 131\cdot 331\cdot 373\cdot 16487\cdot 339517\cdot 72016601\cdot 8704317240727202644261$ |
$10$ |
$110.083854703$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.486...440.1 |
$ x^{33} - 3 x - 4 $ |
$33$ |
[1,16] |
$2^{64}\cdot 3^{33}\cdot 5\cdot 7\cdot 211\cdot 47701\cdot 56203340663\cdot 23939822997841$ |
$8$ |
$112.489395024$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.3.107...016.1 |
$ x^{33} - 4 x - 2 $ |
$33$ |
[3,15] |
$-\,2^{32}\cdot 131\cdot 1332938071\cdot 25239878589041\cdot 56\!\cdots\!31$ |
$5$ |
$115.238969006$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
| 33.3.107...351.1 |
$ x^{33} - 4 x - 1 $ |
$33$ |
[3,15] |
$-\,157\cdot 862680509293\cdot 8877052066229\cdot 395644289235529\cdot 226702188673068757097323811$ |
$5$ |
$115.238969024$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
| 33.1.107...712.1 |
$ x^{33} + 4 x - 2 $ |
$33$ |
[1,16] |
$2^{32}\cdot 717559\cdot 45863269\cdot 561933804328655053279\cdot 1357723639278128039889733$ |
$5$ |
$115.238969042$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.108...297.1 |
$ x^{33} + 4 x - 3 $ |
$33$ |
[1,16] |
$7\cdot 383\cdot 9151\cdot 44\!\cdots\!87$ |
$4$ |
$115.246707935$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.3.177...432.1 |
$ x^{33} - 5 x - 2 $ |
$33$ |
[3,15] |
$-\,2^{32}\cdot 28938953909\cdot 14\!\cdots\!63$ |
$3$ |
$116.983287009$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
| 33.1.595...304.1 |
$ x^{33} - 2 x - 4 $ |
$33$ |
[1,16] |
$2^{62}\cdot 41\cdot 5227\cdot 495043\cdot 2489722643\cdot 103976867383\cdot 4701030158746705429$ |
$7$ |
$121.362760665$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.33.964...489.1 |
$ x^{33} - 8 x^{32} - 70 x^{31} + 734 x^{30} + 1439 x^{29} + \cdots - 470213 $ |
$33$ |
[33,0] |
$19^{22}\cdot 23^{30}$ |
$2$ |
$123.150675121$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$859641744829651100000000$ |
| 33.1.102...432.1 |
$ x^{33} + 5 x - 4 $ |
$33$ |
[1,16] |
$2^{64}\cdot 163\cdot 181\cdot 50551\cdot 28444257707\cdot 13\!\cdots\!87$ |
$6$ |
$123.361773147$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.238...984.1 |
$ x^{33} + x - 4 $ |
$33$ |
[1,16] |
$2^{64}\cdot 7\cdot 17\cdot 19\cdot 157\cdot 33211\cdot 277757\cdot 4264681\cdot 80479969\cdot 114878428009485623479$ |
$10$ |
$126.569682025$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.425...712.1 |
$ x^{33} + 5 x - 2 $ |
$33$ |
[1,16] |
$2^{30}\cdot 41\cdot 179\cdot 1579\cdot 2236133\cdot 39308148498265324319\cdot 38891111153367554795380843499$ |
$7$ |
$138.122724111$ |
|
|
|
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.3.170...487.1 |
$ x^{33} - 5 x - 1 $ |
$33$ |
[3,15] |
$-\,40857347\cdot 123238837\cdot 33\!\cdots\!33$ |
$3$ |
$144.04871128$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
| 33.1.170...513.1 |
$ x^{33} + 5 x - 1 $ |
$33$ |
[1,16] |
$59\cdot 107\cdot 113\cdot 167\cdot 9170594383\cdot 510233763264227\cdot 1295992890923813\cdot 235510051675084013415407$ |
$8$ |
$144.04871128$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.170...433.1 |
$ x^{33} + 5 x - 3 $ |
$33$ |
[1,16] |
$1297\cdot 12431057\cdot 17435333\cdot 170510057517160450557111079\cdot 3549619313840451585263090411$ |
$5$ |
$144.048717417$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.334...897.1 |
$ x^{33} + 3 x - 5 $ |
$33$ |
[1,16] |
$3^{33}\cdot 37\cdot 643\cdot 390353972345549\cdot 2624049677604259\cdot 2465544740666077701019$ |
$6$ |
$147.023445198$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.283...625.1 |
$ x^{33} - 5 x - 5 $ |
$33$ |
[1,16] |
$5^{32}\cdot 20333\cdot 35554829\cdot 26184343821271\cdot 6434496458277638628370639$ |
$5$ |
$156.86868509$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.300...177.1 |
$ x^{33} - 3 x - 5 $ |
$33$ |
[1,16] |
$3^{33}\cdot 79\cdot 263\cdot 465137788789\cdot 55\!\cdots\!83$ |
$5$ |
$157.145892898$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.300...625.1 |
$ x^{33} - 5 $ |
$33$ |
[1,16] |
$3^{33}\cdot 5^{32}\cdot 11^{33}$ |
$3$ |
$157.145892911$ |
|
|
✓ |
$S_3\times F_{11}$ (as 33T11) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.300...601.1 |
$ x^{33} + x - 5 $ |
$33$ |
[1,16] |
$17\cdot 947963\cdot 2718169\cdot 899817429526243\cdot 49025681184056655667\cdot 1555626574856691502779379$ |
$6$ |
$157.145892911$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.300...417.1 |
$ x^{33} + 2 x - 5 $ |
$33$ |
[1,16] |
$347\cdot 21709529\cdot 39\!\cdots\!59$ |
$3$ |
$157.145892911$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.1.317...625.1 |
$ x^{33} + 5 x - 5 $ |
$33$ |
[1,16] |
$5^{32}\cdot 271\cdot 5918259675491\cdot 101848657603787\cdot 835125266081452453199$ |
$5$ |
$157.408285012$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
| 33.33.236...601.1 |
$ x^{33} - 8 x^{32} - 86 x^{31} + 690 x^{30} + 3527 x^{29} + \cdots + 90889 $ |
$33$ |
[33,0] |
$7^{22}\cdot 67^{30}$ |
$2$ |
$167.288734484$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$503657750536712100000000000$ |
| 33.33.365...601.1 |
$ x^{33} - x^{32} - 96 x^{31} + 217 x^{30} + 3795 x^{29} + \cdots - 2947097 $ |
$33$ |
[33,0] |
$199^{32}$ |
$1$ |
$169.508258478$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$194708110268326050000000000$ |
| 33.33.458...889.1 |
$ x^{33} - 8 x^{32} - 114 x^{31} + 1061 x^{30} + \cdots + 8460460991 $ |
$33$ |
[33,0] |
$23^{30}\cdot 31^{22}$ |
$2$ |
$170.677206312$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$478444878328119400000000000$ |
| 33.33.225...481.1 |
$ x^{33} - 8 x^{32} - 136 x^{31} + 1010 x^{30} + \cdots + 3109630591 $ |
$33$ |
[33,0] |
$23^{30}\cdot 37^{22}$ |
$2$ |
$192.044649724$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
$$ |
