Number field search results

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Results (1-50 of 71 matches)

 

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 - 3x^32 - 3x^31 + 28x^30 - 58x^29 + 22x^28 + 191x^27 - 526x^26 + 330x^25 + 728x^24 - 1012x^23 + 413x^22 - 2524x^21 + 3437x^20 + 6311x^19 - 13555x^18 - 573x^17 + 14501x^16 - 6805x^15 - 2479x^14 + 5007x^13 - 7594x^12 - 344x^11 + 8602x^10 - 626x^9 - 5041x^8 + 15x^7 + 1789x^6 + 121x^5 - 352x^4 - 33x^3 + 32x^2 + 2x - 1	$33$	[11,11]	$-\,23^{31}$	$$	$19.01949039124947$			not computed	$C_{11}\times S_3$ (as 33T2)	trivial	$2$	$21$	$255776199.8931762$
33.1.127...537.1	x^33 - x - 1	$33$	[1,16]	$461\cdot 37057\cdot 74\!\cdots\!81$	$$	$32.9886175927$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$477092908754.3794$
33.1.130...489.1	x^33 + x - 1	$33$	[1,16]	$17\cdot 43\cdot 1579\cdot 2609\cdot 13153817\cdot 216865282965193\cdot 15199633537674804809$	$$	$33.0112581443$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$794597544869.8735$
33.1.125...305.1	x^33 + 2x - 1	$33$	[1,16]	$5\cdot 25\!\cdots\!61$	$$	$57.6194845298$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$12254017574219786$
33.33.271...161.1	x^33 - x^32 - 32x^31 + 31x^30 + 465x^29 - 435x^28 - 4060x^27 + 3654x^26 + 23751x^25 - 20475x^24 - 98280x^23 + 80730x^22 + 296010x^21 - 230230x^20 - 657800x^19 + 480700x^18 + 1081575x^17 - 735471x^16 - 1307504x^15 + 817190x^14 + 1144066x^13 - 646646x^12 - 705432x^11 + 352716x^10 + 293930x^9 - 125970x^8 - 77520x^7 + 27132x^6 + 11628x^5 - 3060x^4 - 816x^3 + 136x^2 + 17x - 1	$33$	[33,0]	$67^{32}$	$$	$58.9846766001$		✓	✓	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$3985748844865106400$
33.1.135...753.1	x^33 - 3	$33$	[1,16]	$3^{65}\cdot 11^{27}$	$$	$61.9202712528$			not computed	$S_3\times F_{11}$ (as 33T11)	trivial	$2$	$16$	$62662652284763790$
33.33.277...001.1	x^33 - x^32 - 52x^31 + 47x^30 + 1159x^29 - 945x^28 - 14589x^27 + 10741x^26 + 115099x^25 - 76770x^24 - 597580x^23 + 362822x^22 + 2088771x^21 - 1160546x^20 - 4956062x^19 + 2531215x^18 + 7980244x^17 - 3753538x^16 - 8674935x^15 + 3750773x^14 + 6304834x^13 - 2497276x^12 - 3006793x^11 + 1087323x^10 + 908614x^9 - 298518x^8 - 163557x^7 + 48112x^6 + 15777x^5 - 3955x^4 - 691x^3 + 126x^2 + 12x - 1	$33$	[33,0]	$7^{22}\cdot 23^{30}$	$$	$63.2897076721$		✓	not computed	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$15716532070591353000$
33.1.529...264.1	x^33 - 4x - 4	$33$	[1,16]	$2^{32}\cdot 677\cdot 4266637\cdot 48046836047629\cdot 888172284811267871458394629$	$$	$64.5374805481$			not computed	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$80551974751644370$
33.1.541...056.1	x^33 - 2x - 2	$33$	[1,16]	$2^{32}\cdot 17881556731651\cdot 70\!\cdots\!11$	$$	$64.5833312616$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$88168911953428100$
33.1.554...872.1	x^33 - x - 2	$33$	[1,16]	$2^{32}\cdot 31\cdot 491\cdot 35603\cdot 23\!\cdots\!39$	$$	$64.6281634182$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$133008702440587730$
33.1.554...392.1	x^33 - 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	x^33 - 2	$33$	[1,16]	$2^{32}\cdot 3^{33}\cdot 11^{33}$	$$	$64.6281634182$			✓	$S_3\times F_{11}$ (as 33T11)	trivial	$2$	$16$	$95573511152749460$
33.1.567...640.1	x^33 + 2x - 2	$33$	[1,16]	$2^{32}\cdot 5\cdot 53\cdot 3229\cdot 6433737122028757573993\cdot 23983104676408544038373$	$$	$64.6720219514$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$96056886306925100$
33.1.579...432.1	x^33 + 4x - 4	$33$	[1,16]	$2^{32}\cdot 7\cdot 127\cdot 361279\cdot 459803\cdot 149099734067\cdot 6129135169246811499255607$	$$	$64.7149488714$			not computed	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$84037986779048380$
33.33.700...569.1	x^33 - 63x^31 - 4x^30 + 1710x^29 + 204x^28 - 26254x^27 - 4392x^26 + 251754x^25 + 52248x^24 - 1572192x^23 - 377544x^22 + 6479940x^21 + 1717920x^20 - 17548167x^19 - 4953616x^18 + 30725595x^17 + 8949468x^16 - 34072421x^15 - 9933084x^14 + 23552382x^13 + 6584132x^12 - 10086444x^11 - 2580438x^10 + 2636960x^9 + 587106x^8 - 404862x^7 - 74061x^6 + 33768x^5 + 4755x^4 - 1326x^3 - 135x^2 + 18x + 1	$33$	[33,0]	$3^{44}\cdot 23^{30}$	$$	$74.8335019768$		✓	not computed	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$176588774716401650000$
33.1.174...153.1	x^33 - 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	x^33 - 3x - 1	$33$	[3,15]	$-\,3^{33}\cdot 5\cdot 40739\cdot 11781157\cdot 3137660461139\cdot 194099782564469344251877$	$$	$86.4292267677$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$17$	$10925780584629996000$
33.1.812...961.1	x^33 + 3x - 1	$33$	[1,16]	$3^{34}\cdot 647\cdot 52009\cdot 14\!\cdots\!03$	$$	$86.4292267677$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.1.812...296.1	x^33 + 3x - 2	$33$	[1,16]	$2^{32}\cdot 3^{34}\cdot 5273\cdot 13873073\cdot 79403245997\cdot 19528960698348533$	$$	$86.4294055199$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$22262502678802630000$
33.33.228...681.1	x^33 - 8x^32 - 48x^31 + 488x^30 + 889x^29 - 13082x^28 - 6681x^27 + 203003x^26 - 17780x^25 - 2022483x^24 + 832653x^23 + 13572345x^22 - 8326527x^21 - 62657637x^20 + 47704277x^19 + 199663335x^18 - 178099102x^17 - 433344046x^16 + 447058648x^15 + 617907878x^14 - 750473359x^13 - 533823452x^12 + 817138243x^11 + 221279551x^10 - 544192951x^9 + 11597098x^8 + 199867737x^7 - 43176794x^6 - 33036600x^5 + 11713378x^4 + 1505253x^3 - 925381x^2 + 72350x + 1013	$33$	[33,0]	$13^{22}\cdot 23^{30}$	$$	$95.6232054578$		✓	not computed	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$22765796489209540000000$
33.1.231...985.1	x^33 - 3x - 3	$33$	[1,16]	$3^{33}\cdot 5\cdot 7\cdot 29264269\cdot 40\!\cdots\!33$	$$	$95.6582185472$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.1.239...641.1	x^33 - 2x - 3	$33$	[1,16]	$131009\cdot 18\!\cdots\!49$	$$	$95.7584205303$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$91796156039521290000$
33.1.239...409.1	x^33 + 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	x^33 + 3x - 3	$33$	[1,16]	$3^{33}\cdot 251\cdot 6097463\cdot 19738007\cdot 14\!\cdots\!17$	$$	$95.8553759516$			✓	$S_{33}$ (as 33T162)	trivial	$2$	$16$	$64586856090532960000$
33.1.238...848.1	x^33 + 2x - 4	$33$	[1,16]	$2^{62}\cdot 7\cdot 13\cdot 131\cdot 331\cdot 373\cdot 16487\cdot 339517\cdot 72016601\cdot 8704317240727202644261$	$$	$110.083854703$			not computed	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.1.486...440.1	x^33 - 3x - 4	$33$	[1,16]	$2^{64}\cdot 3^{33}\cdot 5\cdot 7\cdot 211\cdot 47701\cdot 56203340663\cdot 23939822997841$	$$	$112.489395024$			not computed	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.3.107...016.1	x^33 - 4x - 2	$33$	[3,15]	$-\,2^{32}\cdot 131\cdot 1332938071\cdot 25239878589041\cdot 56\!\cdots\!31$	$$	$115.238969006$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$17$	$$
33.3.107...351.1	x^33 - 4x - 1	$33$	[3,15]	$-\,157\cdot 862680509293\cdot 8877052066229\cdot 395644289235529\cdot 226702188673068757097323811$	$$	$115.238969024$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$17$	$$
33.1.107...712.1	x^33 + 4x - 2	$33$	[1,16]	$2^{32}\cdot 717559\cdot 45863269\cdot 561933804328655053279\cdot 1357723639278128039889733$	$$	$115.238969042$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.1.108...297.1	x^33 + 4x - 3	$33$	[1,16]	$7\cdot 383\cdot 9151\cdot 44\!\cdots\!87$	$$	$115.246707935$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.3.177...432.1	x^33 - 5x - 2	$33$	[3,15]	$-\,2^{32}\cdot 28938953909\cdot 14\!\cdots\!63$	$$	$116.983287009$			not computed	$S_{33}$ (as 33T162)	not computed	$2$	$17$	$$
33.1.595...304.1	x^33 - 2x - 4	$33$	[1,16]	$2^{62}\cdot 41\cdot 5227\cdot 495043\cdot 2489722643\cdot 103976867383\cdot 4701030158746705429$	$$	$121.362760665$			not computed	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.33.964...489.1	x^33 - 8x^32 - 70x^31 + 734x^30 + 1439x^29 - 27994x^28 + 11289x^27 + 571079x^26 - 1005928x^25 - 6614661x^24 + 19440415x^23 + 40980613x^22 - 194665653x^21 - 82258867x^20 + 1125872365x^19 - 536982871x^18 - 3781576926x^17 + 4155619240x^16 + 6998281772x^15 - 12201861484x^14 - 5994133153x^13 + 18812121252x^12 + 75160599x^11 - 16337602363x^10 + 3902636199x^9 + 8090155706x^8 - 3031301627x^7 - 2187750082x^6 + 1012187926x^5 + 277584302x^4 - 153651191x^3 - 8485173x^2 + 8057502x - 470213	$33$	[33,0]	$19^{22}\cdot 23^{30}$	$$	$123.150675121$		✓	not computed	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$859641744829651100000000$
33.1.102...432.1	x^33 + 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	x^33 + x - 4	$33$	[1,16]	$2^{64}\cdot 7\cdot 17\cdot 19\cdot 157\cdot 33211\cdot 277757\cdot 4264681\cdot 80479969\cdot 114878428009485623479$	$$	$126.569682025$			✓	$S_{33}$ (as 33T162)	not computed	$2$	$16$	$$
33.1.425...712.1	x^33 + 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	x^33 - 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	x^33 + 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	x^33 + 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	x^33 + 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	x^33 - 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	x^33 - 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	x^33 - 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	x^33 + 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	x^33 + 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	x^33 + 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	x^33 - 8x^32 - 86x^31 + 690x^30 + 3527x^29 - 25876x^28 - 92162x^27 + 549745x^26 + 1676544x^25 - 7221169x^24 - 21518451x^23 + 59984529x^22 + 192193744x^21 - 307177110x^20 - 1170053321x^19 + 864215343x^18 + 4741699040x^17 - 637264044x^16 - 12404482875x^15 - 3656463713x^14 + 19997642137x^13 + 12376322490x^12 - 18399788371x^11 - 16849661483x^10 + 8289542908x^9 + 11391691466x^8 - 842642325x^7 - 3707258605x^6 - 522452271x^5 + 463178377x^4 + 128777001x^3 - 2389174x^2 - 1929880x + 90889	$33$	[33,0]	$7^{22}\cdot 67^{30}$	$$	$167.288734484$		✓		$C_{33}$ (as 33T1)	trivial	$2$	$32$	$503657750536712100000000000$
33.33.365...601.1	x^33 - x^32 - 96x^31 + 217x^30 + 3795x^29 - 13403x^28 - 74197x^27 + 394231x^26 + 599821x^25 - 6350170x^24 + 2832807x^23 + 56803105x^22 - 104532088x^21 - 244229488x^20 + 932758015x^19 + 5618002x^18 - 3890173018x^17 + 4529747891x^16 + 6495127532x^15 - 18110944809x^14 + 4574986912x^13 + 26694143816x^12 - 29645825157x^11 - 6037403432x^10 + 30417132332x^9 - 15468969217x^8 - 6737165737x^7 + 8515927088x^6 - 1017730658x^5 - 1409177433x^4 + 395068072x^3 + 75602260x^2 - 21210003x - 2947097	$33$	[33,0]	$199^{32}$	$$	$169.508258478$		✓	not computed	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$194708110268326050000000000$
33.33.458...889.1	x^33 - 8x^32 - 114x^31 + 1061x^30 + 5059x^29 - 60653x^28 - 96801x^27 + 1959353x^26 - 29225x^25 - 39423204x^24 + 40518048x^23 + 513641811x^22 - 918583926x^21 - 4362858468x^20 + 10893040871x^19 + 23607826158x^18 - 79952364670x^17 - 75116228962x^16 + 381639679930x^15 + 98812353215x^14 - 1205788951741x^13 + 175885903114x^12 + 2530475990857x^11 - 987113141315x^10 - 3498652499635x^9 + 1841635007257x^8 + 3110258033850x^7 - 1787906886467x^6 - 1685908305594x^5 + 902138910730x^4 + 495599994390x^3 - 195854103442x^2 - 57250484608x + 8460460991	$33$	[33,0]	$23^{30}\cdot 31^{22}$	$$	$170.677206312$		✓	not computed	$C_{33}$ (as 33T1)	trivial	$2$	$32$	$478444878328119400000000000$
33.33.225...481.1	x^33 - 8x^32 - 136x^31 + 1010x^30 + 9089x^29 - 56260x^28 - 391707x^27 + 1778015x^26 + 11776892x^25 - 33684927x^24 - 250499393x^23 + 352249669x^22 + 3723230595x^21 - 869647969x^20 - 37516024451x^19 - 27213591295x^18 + 241140895308x^17 + 392273336476x^16 - 846902299600x^15 - 2477173011886x^14 + 614677458641x^13 + 7779541229922x^12 + 5903210349213x^11 - 9094078083973x^10 - 16773542913789x^9 - 4693562989906x^8 + 8584245508513x^7 + 7302900918860x^6 + 488836631314x^5 - 1567611092278x^4 - 601455629303x^3 - 17378174655x^2 + 24259321620x + 3109630591	$33$	[33,0]	$23^{30}\cdot 37^{22}$	$$	$192.044649724$		✓	not computed	$C_{33}$ (as 33T1)	not computed	$2$	$32$	$$