Global number field search results

Degree	Signature	Galois group	Class number	Class group structure
Regulator	Number of ramified primes	Ram. primes	Unramified primes	CM field
Discriminant	Root discriminant	Intermediate field

Results (displaying matches 1-50 of 70)

Label	Polynomial	Discriminant	Galois group	Class group
33.1.127648538450430124921412345101948252519681250837537.1	x^33 - x - 1	\( 461\cdot 37057\cdot 7472134207648223752469291758363939923217381 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.130571541725091930757819714767380818558993115923489.1	x^33 + x - 1	\( 17\cdot 43\cdot 1579\cdot 2609\cdot 13153817\cdot 216865282965193\cdot 15199633537674804809 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.12554203599883401615432606686031362766869246428265252406305.1	x^33 + 2x - 1	\( 5\cdot 2510840719976680323086521337206272553373849285653050481261 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.33.27189028279553414235049966267283185807800188603627566700161.1	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	\( 67^{32} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.1.135046724818446388221933634434982517631405207927648667149753.1	x^33 - 3	\( 3^{65}\cdot 11^{27} \)	33T11	Trivial (GRH)
33.33.277966181338944111003326058293667039541136678070715028736001.1	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	\( 7^{22}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.1.529414992820635861379153224073910531208073502358201920651264.1	x^33 - 4x - 4	\( 2^{32}\cdot 677\cdot 4266637\cdot 48046836047629\cdot 888172284811267871458394629 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.541969196291409222906824802920325864040278213247129989677056.1	x^33 - 2x - 2	\( 2^{32}\cdot 17881556731651\cdot 7056826131348151479446323473239686411 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.554523399760721082797165478848537512039766641116402126159872.1	x^33 - x - 2	\( 2^{32}\cdot 31\cdot 491\cdot 35603\cdot 238248533303420450650042664615870752238639 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.554523399762182584434156099399820258409019549528626290491392.1	x^33 - x - 4	\( 2^{32}\cdot 1621\cdot 3527\cdot 195457\cdot 11716761181\cdot 14330054499223\cdot 688121128326241 \)	$S_{33}$ (as 33T162)	n/a
33.1.554523399762182584434496381766741196872482924136058058702848.1	x^33 - 2	\( 2^{32}\cdot 3^{33}\cdot 11^{33} \)	33T11	Trivial (GRH)
33.1.567077603232955945962167960613156529704687635024986127728640.1	x^33 + 2x - 2	\( 2^{32}\cdot 5\cdot 53\cdot 3229\cdot 6433737122028757573993\cdot 23983104676408544038373 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.579631806703729307489839539459571862536892345913914196754432.1	x^33 + 4x - 4	\( 2^{32}\cdot 7\cdot 127\cdot 361279\cdot 459803\cdot 149099734067\cdot 6129135169246811499255607 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.33.70011645999218458416472683122408534303895571350166174758601569.1	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	\( 3^{44}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.1.174757860384289043464817628942563291244649385569927086025238153.1	x^33 - x - 3	\( 32159\cdot 1547725797949519945333\cdot 3511075445128887057511203662401094299 \)	$S_{33}$ (as 33T162)	n/a
33.3.8124576120042424569795315330246821593959810515006765161304275935.1	x^33 - 3x - 1	\( -\,3^{33}\cdot 5\cdot 40739\cdot 11781157\cdot 3137660461139\cdot 194099782564469344251877 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.8124576120042682789875490852302500826019679844077843835671036961.1	x^33 + 3x - 1	\( 3^{34}\cdot 647\cdot 52009\cdot 14477556462738066936816722835108959527303 \)	$S_{33}$ (as 33T162)	n/a
33.1.8125130643442315862419837587656427951186617662466440556546359296.1	x^33 + 3x - 2	\( 2^{32}\cdot 3^{34}\cdot 5273\cdot 13873073\cdot 79403245997\cdot 19528960698348533 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.33.228343593450302703244344174036290254973199912242460469577320120681.1	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	\( 13^{22}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.1.231118934746049148285001568261997402707620096381970895925995917985.1	x^33 - 3x - 3	\( 3^{33}\cdot 5\cdot 7\cdot 29264269\cdot 40590873456269216446987174322351841903133 \)	$S_{33}$ (as 33T162)	n/a
33.1.239243498311888231191475443681693217502277009356802311496414548641.1	x^33 - 2x - 3	\( 131009\cdot 1826160785227642613801154452607784331628185921248176167258849 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.239243510866091703426338608684174982121294674277796220080416117409.1	x^33 + x - 3	\( 7\cdot 17\cdot 59\cdot 34075418154976741692969464276338838074532783688619316348157829 \)	$S_{33}$ (as 33T162)	n/a
33.1.247368086986134255644672374444546725127599586741055504922971230881.1	x^33 + 3x - 3	\( 3^{33}\cdot 251\cdot 6097463\cdot 19738007\cdot 1473045192123599817714547811290817 \)	$S_{33}$ (as 33T162)	Trivial (GRH)
33.1.23816598668578625811976939754461557199096269743150231273749084110848.1	x^33 + 2x - 4	\( 2^{62}\cdot 7\cdot 13\cdot 131\cdot 331\cdot 373\cdot 16487\cdot 339517\cdot 72016601\cdot 8704317240727202644261 \)	$S_{33}$ (as 33T162)	n/a
33.1.48605137597330374187208995479905976865346972484441609677173099069440.1	x^33 - 3x - 4	\( 2^{64}\cdot 3^{33}\cdot 5\cdot 7\cdot 211\cdot 47701\cdot 56203340663\cdot 23939822997841 \)	$S_{33}$ (as 33T162)	n/a
33.3.107839786114079159416485475913582140927807380817679365788356382294016.1	x^33 - 4x - 2	\( -\,2^{32}\cdot 131\cdot 1332938071\cdot 25239878589041\cdot 5697057818890456747980454141102531 \)	$S_{33}$ (as 33T162)	n/a
33.3.107839786668602559049558020260317494854932547755497754385077257616351.1	x^33 - 4x - 1	\( -\,157\cdot 862680509293\cdot 8877052066229\cdot 395644289235529\cdot 226702188673068757097323811 \)	$S_{33}$ (as 33T162)	n/a
33.1.107839787223125958940850644782574904461289774562645214060472499699712.1	x^33 + 4x - 2	\( 2^{32}\cdot 717559\cdot 45863269\cdot 561933804328655053279\cdot 1357723639278128039889733 \)	$S_{33}$ (as 33T162)	n/a
33.1.108079030179468650880632897319431794758466187531723803124838924571297.1	x^33 + 4x - 3	\( 7\cdot 383\cdot 9151\cdot 4405305888814048278095373581053517274104732666158978723088087 \)	$S_{33}$ (as 33T162)	n/a
33.3.177045976545176595558715006380280550828546575237385553668953113362432.1	x^33 - 5x - 2	\( -\,2^{32}\cdot 28938953909\cdot 1424437414184534000994590725571052163866999948163 \)	$S_{33}$ (as 33T162)	n/a
33.1.595414966708188543564036813097703140554199077162653426399263068258304.1	x^33 - 2x - 4	\( 2^{62}\cdot 41\cdot 5227\cdot 495043\cdot 2489722643\cdot 103976867383\cdot 4701030158746705429 \)	$S_{33}$ (as 33T162)	n/a
33.33.964748920938762847635574420140466077720720339834593232479190796888489.1	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	\( 19^{22}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.1.1020845226788843432600084167631967987390906577760253363411159646994432.1	x^33 + 5x - 4	\( 2^{64}\cdot 163\cdot 181\cdot 50551\cdot 28444257707\cdot 1304516704756865886343705176787 \)	$S_{33}$ (as 33T162)	n/a
33.1.2381659866845308377728382115555815043981415326315534699505636274601984.1	x^33 + x - 4	\( 2^{64}\cdot 7\cdot 17\cdot 19\cdot 157\cdot 33211\cdot 277757\cdot 4264681\cdot 80479969\cdot 114878428009485623479 \)	$S_{33}$ (as 33T162)	n/a
33.1.42535295865255938782862371575079650527441685299218120731034014514675712.1	x^33 + 5x - 2	\( 2^{30}\cdot 41\cdot 179\cdot 1579\cdot 2236133\cdot 39308148498265324319\cdot 38891111153367554795380843499 \)	$S_{33}$ (as 33T162)	n/a
33.3.170141183460469231731558193675796344700160383970065335464460662816619487.1	x^33 - 5x - 1	\( -\,40857347\cdot 123238837\cdot 33790272568641220049426121100592716765978452363500500033 \)	$S_{33}$ (as 33T162)	n/a
33.1.170141183460469231731816413755971866755839616029934664535539337183380513.1	x^33 + 5x - 1	\( 59\cdot 107\cdot 113\cdot 167\cdot 9170594383\cdot 510233763264227\cdot 1295992890923813\cdot 235510051675084013415407 \)	$S_{33}$ (as 33T162)	n/a
33.1.170141422703980097823389268552855459000063917609841561513200424483574433.1	x^33 + 5x - 3	\( 1297\cdot 12431057\cdot 17435333\cdot 170510057517160450557111079\cdot 3549619313840451585263090411 \)	$S_{33}$ (as 33T162)	n/a
33.1.334008597967289686032440026411889237194831462070890289459890946473671897.1	x^33 + 3x - 5	\( 3^{33}\cdot 37\cdot 643\cdot 390353972345549\cdot 2624049677604259\cdot 2465544740666077701019 \)	$S_{33}$ (as 33T162)	n/a
33.1.2835936190120561822517719254155715937750821948648267425596714019775390625.1	x^33 - 5x - 5	\( 5^{32}\cdot 20333\cdot 35554829\cdot 26184343821271\cdot 6434496458277638628370639 \)	$S_{33}$ (as 33T162)	n/a
33.1.3006077365456454934206852878036196952204160738658522246054409521287734177.1	x^33 - 3x - 5	\( 3^{33}\cdot 79\cdot 263\cdot 465137788789\cdot 55954405270679204355252370860858804532583 \)	$S_{33}$ (as 33T162)	n/a
33.1.3006077373581031054249406557871600043478821948648267425596714019775390625.1	x^33 - 5	\( 3^{33}\cdot 5^{32}\cdot 11^{33} \)	33T11	n/a
33.1.3006077373581031054249408019373237374381740152333100141879733675707933601.1	x^33 + x - 5	\( 17\cdot 947963\cdot 2718169\cdot 899817429526243\cdot 49025681184056655667\cdot 1555626574856691502779379 \)	$S_{33}$ (as 33T162)	n/a
33.1.3006077373581043608452877331233127715057668363981099630307602947844416417.1	x^33 + 2x - 5	\( 347\cdot 21709529\cdot 399043534574726038672262189398446701674184314276727689712708459 \)	$S_{33}$ (as 33T162)	n/a
33.1.3176218557041500285981093861587484149206821948648267425596714019775390625.1	x^33 + 5x - 5	\( 5^{32}\cdot 271\cdot 5918259675491\cdot 101848657603787\cdot 835125266081452453199 \)	$S_{33}$ (as 33T162)	n/a
33.33.23681050358190252966666038984115482490423545779778728084912954382239302601.1	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	\( 7^{22}\cdot 67^{30} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.33.36584611296554742180833097810429342639777502523008874222975105176339833601.1	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	\( 199^{32} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.33.45897850273808078905473711375352471596627685094598222212495078792349891889.1	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	\( 23^{30}\cdot 31^{22} \)	$C_{33}$ (as 33T1)	Trivial (GRH)
33.33.2250468870721257864915422491944078011918280366020799086767808384626842687481.1	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	\( 23^{30}\cdot 37^{22} \)	$C_{33}$ (as 33T1)	n/a
33.33.5964572044631662930869897974580631723402610311315668047983759159277483196969.1	x^33 - 3x^32 - 120x^31 + 450x^30 + 5757x^29 - 26439x^28 - 139216x^27 + 813933x^26 + 1676889x^25 - 14588595x^24 - 5289417x^23 + 158067366x^22 - 111316484x^21 - 1026324261x^20 + 1580724570x^19 + 3707180205x^18 - 9398785623x^17 - 5392982019x^16 + 29700176281x^15 - 7076803698x^14 - 50183067855x^13 + 37619683596x^12 + 40721934162x^11 - 52500002157x^10 - 9740363856x^9 + 32585743542x^8 - 5020929429x^7 - 9149246964x^6 + 3064214298x^5 + 963373038x^4 - 501812162x^3 + 1428300x^2 + 21340050x - 2255257	\( 3^{44}\cdot 67^{30} \)	$C_{33}$ (as 33T1)	Trivial (GRH)