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 |
x33 - 3x32 - 3x31 + 28x30 - 58x29 + 22x28 + 191x27 - 526x26 + 330x25 + 728x24 - 1012x23 + 413x22 - 2524x21 + 3437x20 + 6311x19 - 13555x18 - 573x17 + 14501x16 - 6805x15 - 2479x14 + 5007x13 - 7594x12 - 344x11 + 8602x10 - 626x9 - 5041x8 + 15x7 + 1789x6 + 121x5 - 352x4 - 33x3 + 32x2 + 2x - 1 |
$33$ |
[11,11] |
$-\,23^{31}$ |
$$ |
$19.01949039124947$ |
|
|
not computed |
$C_{11}\times S_3$ (as 33T2) |
trivial |
$2$ |
$21$ |
$255776199.8931762$ |
33.1.127...537.1 |
x33 - x - 1 |
$33$ |
[1,16] |
$461\cdot 37057\cdot 74\!\cdots\!81$ |
$$ |
$32.9886175927$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$477092908754.3794$ |
33.1.130...489.1 |
x33 + x - 1 |
$33$ |
[1,16] |
$17\cdot 43\cdot 1579\cdot 2609\cdot 13153817\cdot 216865282965193\cdot 15199633537674804809$ |
$$ |
$33.0112581443$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$794597544869.8735$ |
33.1.125...305.1 |
x33 + 2x - 1 |
$33$ |
[1,16] |
$5\cdot 25\!\cdots\!61$ |
$$ |
$57.6194845298$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$12254017574219786$ |
33.33.271...161.1 |
x33 - x32 - 32x31 + 31x30 + 465x29 - 435x28 - 4060x27 + 3654x26 + 23751x25 - 20475x24 - 98280x23 + 80730x22 + 296010x21 - 230230x20 - 657800x19 + 480700x18 + 1081575x17 - 735471x16 - 1307504x15 + 817190x14 + 1144066x13 - 646646x12 - 705432x11 + 352716x10 + 293930x9 - 125970x8 - 77520x7 + 27132x6 + 11628x5 - 3060x4 - 816x3 + 136x2 + 17x - 1 |
$33$ |
[33,0] |
$67^{32}$ |
$$ |
$58.9846766001$ |
|
✓ |
✓ |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$3985748844865106400$ |
33.1.135...753.1 |
x33 - 3 |
$33$ |
[1,16] |
$3^{65}\cdot 11^{27}$ |
$$ |
$61.9202712528$ |
|
|
not computed |
$S_3\times F_{11}$ (as 33T11) |
trivial |
$2$ |
$16$ |
$62662652284763790$ |
33.33.277...001.1 |
x33 - x32 - 52x31 + 47x30 + 1159x29 - 945x28 - 14589x27 + 10741x26 + 115099x25 - 76770x24 - 597580x23 + 362822x22 + 2088771x21 - 1160546x20 - 4956062x19 + 2531215x18 + 7980244x17 - 3753538x16 - 8674935x15 + 3750773x14 + 6304834x13 - 2497276x12 - 3006793x11 + 1087323x10 + 908614x9 - 298518x8 - 163557x7 + 48112x6 + 15777x5 - 3955x4 - 691x3 + 126x2 + 12x - 1 |
$33$ |
[33,0] |
$7^{22}\cdot 23^{30}$ |
$$ |
$63.2897076721$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$15716532070591353000$ |
33.1.529...264.1 |
x33 - 4x - 4 |
$33$ |
[1,16] |
$2^{32}\cdot 677\cdot 4266637\cdot 48046836047629\cdot 888172284811267871458394629$ |
$$ |
$64.5374805481$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$80551974751644370$ |
33.1.541...056.1 |
x33 - 2x - 2 |
$33$ |
[1,16] |
$2^{32}\cdot 17881556731651\cdot 70\!\cdots\!11$ |
$$ |
$64.5833312616$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$88168911953428100$ |
33.1.554...872.1 |
x33 - x - 2 |
$33$ |
[1,16] |
$2^{32}\cdot 31\cdot 491\cdot 35603\cdot 23\!\cdots\!39$ |
$$ |
$64.6281634182$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$133008702440587730$ |
33.1.554...392.1 |
x33 - x - 4 |
$33$ |
[1,16] |
$2^{32}\cdot 1621\cdot 3527\cdot 195457\cdot 11716761181\cdot 14330054499223\cdot 688121128326241$ |
$$ |
$64.6281634182$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.554...848.1 |
x33 - 2 |
$33$ |
[1,16] |
$2^{32}\cdot 3^{33}\cdot 11^{33}$ |
$$ |
$64.6281634182$ |
|
|
✓ |
$S_3\times F_{11}$ (as 33T11) |
trivial |
$2$ |
$16$ |
$95573511152749460$ |
33.1.567...640.1 |
x33 + 2x - 2 |
$33$ |
[1,16] |
$2^{32}\cdot 5\cdot 53\cdot 3229\cdot 6433737122028757573993\cdot 23983104676408544038373$ |
$$ |
$64.6720219514$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$96056886306925100$ |
33.1.579...432.1 |
x33 + 4x - 4 |
$33$ |
[1,16] |
$2^{32}\cdot 7\cdot 127\cdot 361279\cdot 459803\cdot 149099734067\cdot 6129135169246811499255607$ |
$$ |
$64.7149488714$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$84037986779048380$ |
33.33.700...569.1 |
x33 - 63x31 - 4x30 + 1710x29 + 204x28 - 26254x27 - 4392x26 + 251754x25 + 52248x24 - 1572192x23 - 377544x22 + 6479940x21 + 1717920x20 - 17548167x19 - 4953616x18 + 30725595x17 + 8949468x16 - 34072421x15 - 9933084x14 + 23552382x13 + 6584132x12 - 10086444x11 - 2580438x10 + 2636960x9 + 587106x8 - 404862x7 - 74061x6 + 33768x5 + 4755x4 - 1326x3 - 135x2 + 18x + 1 |
$33$ |
[33,0] |
$3^{44}\cdot 23^{30}$ |
$$ |
$74.8335019768$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$176588774716401650000$ |
33.1.174...153.1 |
x33 - x - 3 |
$33$ |
[1,16] |
$32159\cdot 1547725797949519945333\cdot 35\!\cdots\!99$ |
$$ |
$76.9368579483$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.3.812...935.1 |
x33 - 3x - 1 |
$33$ |
[3,15] |
$-\,3^{33}\cdot 5\cdot 40739\cdot 11781157\cdot 3137660461139\cdot 194099782564469344251877$ |
$$ |
$86.4292267677$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$17$ |
$10925780584629996000$ |
33.1.812...961.1 |
x33 + 3x - 1 |
$33$ |
[1,16] |
$3^{34}\cdot 647\cdot 52009\cdot 14\!\cdots\!03$ |
$$ |
$86.4292267677$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.812...296.1 |
x33 + 3x - 2 |
$33$ |
[1,16] |
$2^{32}\cdot 3^{34}\cdot 5273\cdot 13873073\cdot 79403245997\cdot 19528960698348533$ |
$$ |
$86.4294055199$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$22262502678802630000$ |
33.33.228...681.1 |
x33 - 8x32 - 48x31 + 488x30 + 889x29 - 13082x28 - 6681x27 + 203003x26 - 17780x25 - 2022483x24 + 832653x23 + 13572345x22 - 8326527x21 - 62657637x20 + 47704277x19 + 199663335x18 - 178099102x17 - 433344046x16 + 447058648x15 + 617907878x14 - 750473359x13 - 533823452x12 + 817138243x11 + 221279551x10 - 544192951x9 + 11597098x8 + 199867737x7 - 43176794x6 - 33036600x5 + 11713378x4 + 1505253x3 - 925381x2 + 72350x + 1013 |
$33$ |
[33,0] |
$13^{22}\cdot 23^{30}$ |
$$ |
$95.6232054578$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$22765796489209540000000$ |
33.1.231...985.1 |
x33 - 3x - 3 |
$33$ |
[1,16] |
$3^{33}\cdot 5\cdot 7\cdot 29264269\cdot 40\!\cdots\!33$ |
$$ |
$95.6582185472$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.239...641.1 |
x33 - 2x - 3 |
$33$ |
[1,16] |
$131009\cdot 18\!\cdots\!49$ |
$$ |
$95.7584205303$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$91796156039521290000$ |
33.1.239...409.1 |
x33 + x - 3 |
$33$ |
[1,16] |
$7\cdot 17\cdot 59\cdot 34\!\cdots\!29$ |
$$ |
$95.7584206826$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.247...881.1 |
x33 + 3x - 3 |
$33$ |
[1,16] |
$3^{33}\cdot 251\cdot 6097463\cdot 19738007\cdot 14\!\cdots\!17$ |
$$ |
$95.8553759516$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
trivial |
$2$ |
$16$ |
$64586856090532960000$ |
33.1.238...848.1 |
x33 + 2x - 4 |
$33$ |
[1,16] |
$2^{62}\cdot 7\cdot 13\cdot 131\cdot 331\cdot 373\cdot 16487\cdot 339517\cdot 72016601\cdot 8704317240727202644261$ |
$$ |
$110.083854703$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.486...440.1 |
x33 - 3x - 4 |
$33$ |
[1,16] |
$2^{64}\cdot 3^{33}\cdot 5\cdot 7\cdot 211\cdot 47701\cdot 56203340663\cdot 23939822997841$ |
$$ |
$112.489395024$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.3.107...016.1 |
x33 - 4x - 2 |
$33$ |
[3,15] |
$-\,2^{32}\cdot 131\cdot 1332938071\cdot 25239878589041\cdot 56\!\cdots\!31$ |
$$ |
$115.238969006$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
33.3.107...351.1 |
x33 - 4x - 1 |
$33$ |
[3,15] |
$-\,157\cdot 862680509293\cdot 8877052066229\cdot 395644289235529\cdot 226702188673068757097323811$ |
$$ |
$115.238969024$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
33.1.107...712.1 |
x33 + 4x - 2 |
$33$ |
[1,16] |
$2^{32}\cdot 717559\cdot 45863269\cdot 561933804328655053279\cdot 1357723639278128039889733$ |
$$ |
$115.238969042$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.108...297.1 |
x33 + 4x - 3 |
$33$ |
[1,16] |
$7\cdot 383\cdot 9151\cdot 44\!\cdots\!87$ |
$$ |
$115.246707935$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.3.177...432.1 |
x33 - 5x - 2 |
$33$ |
[3,15] |
$-\,2^{32}\cdot 28938953909\cdot 14\!\cdots\!63$ |
$$ |
$116.983287009$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
33.1.595...304.1 |
x33 - 2x - 4 |
$33$ |
[1,16] |
$2^{62}\cdot 41\cdot 5227\cdot 495043\cdot 2489722643\cdot 103976867383\cdot 4701030158746705429$ |
$$ |
$121.362760665$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.33.964...489.1 |
x33 - 8x32 - 70x31 + 734x30 + 1439x29 - 27994x28 + 11289x27 + 571079x26 - 1005928x25 - 6614661x24 + 19440415x23 + 40980613x22 - 194665653x21 - 82258867x20 + 1125872365x19 - 536982871x18 - 3781576926x17 + 4155619240x16 + 6998281772x15 - 12201861484x14 - 5994133153x13 + 18812121252x12 + 75160599x11 - 16337602363x10 + 3902636199x9 + 8090155706x8 - 3031301627x7 - 2187750082x6 + 1012187926x5 + 277584302x4 - 153651191x3 - 8485173x2 + 8057502x - 470213 |
$33$ |
[33,0] |
$19^{22}\cdot 23^{30}$ |
$$ |
$123.150675121$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$859641744829651100000000$ |
33.1.102...432.1 |
x33 + 5x - 4 |
$33$ |
[1,16] |
$2^{64}\cdot 163\cdot 181\cdot 50551\cdot 28444257707\cdot 13\!\cdots\!87$ |
$$ |
$123.361773147$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.238...984.1 |
x33 + x - 4 |
$33$ |
[1,16] |
$2^{64}\cdot 7\cdot 17\cdot 19\cdot 157\cdot 33211\cdot 277757\cdot 4264681\cdot 80479969\cdot 114878428009485623479$ |
$$ |
$126.569682025$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.425...712.1 |
x33 + 5x - 2 |
$33$ |
[1,16] |
$2^{30}\cdot 41\cdot 179\cdot 1579\cdot 2236133\cdot 39308148498265324319\cdot 38891111153367554795380843499$ |
$$ |
$138.122724111$ |
|
|
|
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.3.170...487.1 |
x33 - 5x - 1 |
$33$ |
[3,15] |
$-\,40857347\cdot 123238837\cdot 33\!\cdots\!33$ |
$$ |
$144.04871128$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$17$ |
$$ |
33.1.170...513.1 |
x33 + 5x - 1 |
$33$ |
[1,16] |
$59\cdot 107\cdot 113\cdot 167\cdot 9170594383\cdot 510233763264227\cdot 1295992890923813\cdot 235510051675084013415407$ |
$$ |
$144.04871128$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.170...433.1 |
x33 + 5x - 3 |
$33$ |
[1,16] |
$1297\cdot 12431057\cdot 17435333\cdot 170510057517160450557111079\cdot 3549619313840451585263090411$ |
$$ |
$144.048717417$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.334...897.1 |
x33 + 3x - 5 |
$33$ |
[1,16] |
$3^{33}\cdot 37\cdot 643\cdot 390353972345549\cdot 2624049677604259\cdot 2465544740666077701019$ |
$$ |
$147.023445198$ |
|
|
not computed |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.283...625.1 |
x33 - 5x - 5 |
$33$ |
[1,16] |
$5^{32}\cdot 20333\cdot 35554829\cdot 26184343821271\cdot 6434496458277638628370639$ |
$$ |
$156.86868509$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.300...177.1 |
x33 - 3x - 5 |
$33$ |
[1,16] |
$3^{33}\cdot 79\cdot 263\cdot 465137788789\cdot 55\!\cdots\!83$ |
$$ |
$157.145892898$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.300...625.1 |
x33 - 5 |
$33$ |
[1,16] |
$3^{33}\cdot 5^{32}\cdot 11^{33}$ |
$$ |
$157.145892911$ |
|
|
✓ |
$S_3\times F_{11}$ (as 33T11) |
not computed |
$2$ |
$16$ |
$$ |
33.1.300...601.1 |
x33 + x - 5 |
$33$ |
[1,16] |
$17\cdot 947963\cdot 2718169\cdot 899817429526243\cdot 49025681184056655667\cdot 1555626574856691502779379$ |
$$ |
$157.145892911$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.300...417.1 |
x33 + 2x - 5 |
$33$ |
[1,16] |
$347\cdot 21709529\cdot 39\!\cdots\!59$ |
$$ |
$157.145892911$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.1.317...625.1 |
x33 + 5x - 5 |
$33$ |
[1,16] |
$5^{32}\cdot 271\cdot 5918259675491\cdot 101848657603787\cdot 835125266081452453199$ |
$$ |
$157.408285012$ |
|
|
✓ |
$S_{33}$ (as 33T162) |
not computed |
$2$ |
$16$ |
$$ |
33.33.236...601.1 |
x33 - 8x32 - 86x31 + 690x30 + 3527x29 - 25876x28 - 92162x27 + 549745x26 + 1676544x25 - 7221169x24 - 21518451x23 + 59984529x22 + 192193744x21 - 307177110x20 - 1170053321x19 + 864215343x18 + 4741699040x17 - 637264044x16 - 12404482875x15 - 3656463713x14 + 19997642137x13 + 12376322490x12 - 18399788371x11 - 16849661483x10 + 8289542908x9 + 11391691466x8 - 842642325x7 - 3707258605x6 - 522452271x5 + 463178377x4 + 128777001x3 - 2389174x2 - 1929880x + 90889 |
$33$ |
[33,0] |
$7^{22}\cdot 67^{30}$ |
$$ |
$167.288734484$ |
|
✓ |
|
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$503657750536712100000000000$ |
33.33.365...601.1 |
x33 - x32 - 96x31 + 217x30 + 3795x29 - 13403x28 - 74197x27 + 394231x26 + 599821x25 - 6350170x24 + 2832807x23 + 56803105x22 - 104532088x21 - 244229488x20 + 932758015x19 + 5618002x18 - 3890173018x17 + 4529747891x16 + 6495127532x15 - 18110944809x14 + 4574986912x13 + 26694143816x12 - 29645825157x11 - 6037403432x10 + 30417132332x9 - 15468969217x8 - 6737165737x7 + 8515927088x6 - 1017730658x5 - 1409177433x4 + 395068072x3 + 75602260x2 - 21210003x - 2947097 |
$33$ |
[33,0] |
$199^{32}$ |
$$ |
$169.508258478$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$194708110268326050000000000$ |
33.33.458...889.1 |
x33 - 8x32 - 114x31 + 1061x30 + 5059x29 - 60653x28 - 96801x27 + 1959353x26 - 29225x25 - 39423204x24 + 40518048x23 + 513641811x22 - 918583926x21 - 4362858468x20 + 10893040871x19 + 23607826158x18 - 79952364670x17 - 75116228962x16 + 381639679930x15 + 98812353215x14 - 1205788951741x13 + 175885903114x12 + 2530475990857x11 - 987113141315x10 - 3498652499635x9 + 1841635007257x8 + 3110258033850x7 - 1787906886467x6 - 1685908305594x5 + 902138910730x4 + 495599994390x3 - 195854103442x2 - 57250484608x + 8460460991 |
$33$ |
[33,0] |
$23^{30}\cdot 31^{22}$ |
$$ |
$170.677206312$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
trivial |
$2$ |
$32$ |
$478444878328119400000000000$ |
33.33.225...481.1 |
x33 - 8x32 - 136x31 + 1010x30 + 9089x29 - 56260x28 - 391707x27 + 1778015x26 + 11776892x25 - 33684927x24 - 250499393x23 + 352249669x22 + 3723230595x21 - 869647969x20 - 37516024451x19 - 27213591295x18 + 241140895308x17 + 392273336476x16 - 846902299600x15 - 2477173011886x14 + 614677458641x13 + 7779541229922x12 + 5903210349213x11 - 9094078083973x10 - 16773542913789x9 - 4693562989906x8 + 8584245508513x7 + 7302900918860x6 + 488836631314x5 - 1567611092278x4 - 601455629303x3 - 17378174655x2 + 24259321620x + 3109630591 |
$33$ |
[33,0] |
$23^{30}\cdot 37^{22}$ |
$$ |
$192.044649724$ |
|
✓ |
not computed |
$C_{33}$ (as 33T1) |
not computed |
$2$ |
$32$ |
$$ |