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Label Polynomial Discriminant Galois group Class group
33.1.127648538450430124921412345101948252519681250837537.1 x33 - x - 1 \( 461\cdot 37057\cdot 7472134207648223752469291758363939923217381 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.130571541725091930757819714767380818558993115923489.1 x33 + 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 x33 + 2x - 1 \( 5\cdot 2510840719976680323086521337206272553373849285653050481261 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.33.27189028279553414235049966267283185807800188603627566700161.1 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 \( 67^{32} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.1.135046724818446388221933634434982517631405207927648667149753.1 x33 - 3 \( 3^{65}\cdot 11^{27} \) 33T11 Trivial (GRH)
33.33.277966181338944111003326058293667039541136678070715028736001.1 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 \( 7^{22}\cdot 23^{30} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.1.529414992820635861379153224073910531208073502358201920651264.1 x33 - 4x - 4 \( 2^{32}\cdot 677\cdot 4266637\cdot 48046836047629\cdot 888172284811267871458394629 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.541969196291409222906824802920325864040278213247129989677056.1 x33 - 2x - 2 \( 2^{32}\cdot 17881556731651\cdot 7056826131348151479446323473239686411 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.554523399760721082797165478848537512039766641116402126159872.1 x33 - x - 2 \( 2^{32}\cdot 31\cdot 491\cdot 35603\cdot 238248533303420450650042664615870752238639 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.554523399762182584434156099399820258409019549528626290491392.1 x33 - 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 x33 - 2 \( 2^{32}\cdot 3^{33}\cdot 11^{33} \) 33T11 Trivial (GRH)
33.1.567077603232955945962167960613156529704687635024986127728640.1 x33 + 2x - 2 \( 2^{32}\cdot 5\cdot 53\cdot 3229\cdot 6433737122028757573993\cdot 23983104676408544038373 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.579631806703729307489839539459571862536892345913914196754432.1 x33 + 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 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 \( 3^{44}\cdot 23^{30} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.1.174757860384289043464817628942563291244649385569927086025238153.1 x33 - x - 3 \( 32159\cdot 1547725797949519945333\cdot 3511075445128887057511203662401094299 \) $S_{33}$ (as 33T162) n/a
33.3.8124576120042424569795315330246821593959810515006765161304275935.1 x33 - 3x - 1 \( -\,3^{33}\cdot 5\cdot 40739\cdot 11781157\cdot 3137660461139\cdot 194099782564469344251877 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.8124576120042682789875490852302500826019679844077843835671036961.1 x33 + 3x - 1 \( 3^{34}\cdot 647\cdot 52009\cdot 14477556462738066936816722835108959527303 \) $S_{33}$ (as 33T162) n/a
33.1.8125130643442315862419837587656427951186617662466440556546359296.1 x33 + 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 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 \( 13^{22}\cdot 23^{30} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.1.231118934746049148285001568261997402707620096381970895925995917985.1 x33 - 3x - 3 \( 3^{33}\cdot 5\cdot 7\cdot 29264269\cdot 40590873456269216446987174322351841903133 \) $S_{33}$ (as 33T162) n/a
33.1.239243498311888231191475443681693217502277009356802311496414548641.1 x33 - 2x - 3 \( 131009\cdot 1826160785227642613801154452607784331628185921248176167258849 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.239243510866091703426338608684174982121294674277796220080416117409.1 x33 + x - 3 \( 7\cdot 17\cdot 59\cdot 34075418154976741692969464276338838074532783688619316348157829 \) $S_{33}$ (as 33T162) n/a
33.1.247368086986134255644672374444546725127599586741055504922971230881.1 x33 + 3x - 3 \( 3^{33}\cdot 251\cdot 6097463\cdot 19738007\cdot 1473045192123599817714547811290817 \) $S_{33}$ (as 33T162) Trivial (GRH)
33.1.23816598668578625811976939754461557199096269743150231273749084110848.1 x33 + 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 x33 - 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 x33 - 4x - 2 \( -\,2^{32}\cdot 131\cdot 1332938071\cdot 25239878589041\cdot 5697057818890456747980454141102531 \) $S_{33}$ (as 33T162) n/a
33.3.107839786668602559049558020260317494854932547755497754385077257616351.1 x33 - 4x - 1 \( -\,157\cdot 862680509293\cdot 8877052066229\cdot 395644289235529\cdot 226702188673068757097323811 \) $S_{33}$ (as 33T162) n/a
33.1.107839787223125958940850644782574904461289774562645214060472499699712.1 x33 + 4x - 2 \( 2^{32}\cdot 717559\cdot 45863269\cdot 561933804328655053279\cdot 1357723639278128039889733 \) $S_{33}$ (as 33T162) n/a
33.1.108079030179468650880632897319431794758466187531723803124838924571297.1 x33 + 4x - 3 \( 7\cdot 383\cdot 9151\cdot 4405305888814048278095373581053517274104732666158978723088087 \) $S_{33}$ (as 33T162) n/a
33.3.177045976545176595558715006380280550828546575237385553668953113362432.1 x33 - 5x - 2 \( -\,2^{32}\cdot 28938953909\cdot 1424437414184534000994590725571052163866999948163 \) $S_{33}$ (as 33T162) n/a
33.1.595414966708188543564036813097703140554199077162653426399263068258304.1 x33 - 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 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 \( 19^{22}\cdot 23^{30} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.1.1020845226788843432600084167631967987390906577760253363411159646994432.1 x33 + 5x - 4 \( 2^{64}\cdot 163\cdot 181\cdot 50551\cdot 28444257707\cdot 1304516704756865886343705176787 \) $S_{33}$ (as 33T162) n/a
33.1.2381659866845308377728382115555815043981415326315534699505636274601984.1 x33 + 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 x33 + 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 x33 - 5x - 1 \( -\,40857347\cdot 123238837\cdot 33790272568641220049426121100592716765978452363500500033 \) $S_{33}$ (as 33T162) n/a
33.1.170141183460469231731816413755971866755839616029934664535539337183380513.1 x33 + 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 x33 + 5x - 3 \( 1297\cdot 12431057\cdot 17435333\cdot 170510057517160450557111079\cdot 3549619313840451585263090411 \) $S_{33}$ (as 33T162) n/a
33.1.334008597967289686032440026411889237194831462070890289459890946473671897.1 x33 + 3x - 5 \( 3^{33}\cdot 37\cdot 643\cdot 390353972345549\cdot 2624049677604259\cdot 2465544740666077701019 \) $S_{33}$ (as 33T162) n/a
33.1.2835936190120561822517719254155715937750821948648267425596714019775390625.1 x33 - 5x - 5 \( 5^{32}\cdot 20333\cdot 35554829\cdot 26184343821271\cdot 6434496458277638628370639 \) $S_{33}$ (as 33T162) n/a
33.1.3006077365456454934206852878036196952204160738658522246054409521287734177.1 x33 - 3x - 5 \( 3^{33}\cdot 79\cdot 263\cdot 465137788789\cdot 55954405270679204355252370860858804532583 \) $S_{33}$ (as 33T162) n/a
33.1.3006077373581031054249406557871600043478821948648267425596714019775390625.1 x33 - 5 \( 3^{33}\cdot 5^{32}\cdot 11^{33} \) 33T11 n/a
33.1.3006077373581031054249408019373237374381740152333100141879733675707933601.1 x33 + x - 5 \( 17\cdot 947963\cdot 2718169\cdot 899817429526243\cdot 49025681184056655667\cdot 1555626574856691502779379 \) $S_{33}$ (as 33T162) n/a
33.1.3006077373581043608452877331233127715057668363981099630307602947844416417.1 x33 + 2x - 5 \( 347\cdot 21709529\cdot 399043534574726038672262189398446701674184314276727689712708459 \) $S_{33}$ (as 33T162) n/a
33.1.3176218557041500285981093861587484149206821948648267425596714019775390625.1 x33 + 5x - 5 \( 5^{32}\cdot 271\cdot 5918259675491\cdot 101848657603787\cdot 835125266081452453199 \) $S_{33}$ (as 33T162) n/a
33.33.23681050358190252966666038984115482490423545779778728084912954382239302601.1 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 \( 7^{22}\cdot 67^{30} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.33.36584611296554742180833097810429342639777502523008874222975105176339833601.1 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 \( 199^{32} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.33.45897850273808078905473711375352471596627685094598222212495078792349891889.1 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 \( 23^{30}\cdot 31^{22} \) $C_{33}$ (as 33T1) Trivial (GRH)
33.33.2250468870721257864915422491944078011918280366020799086767808384626842687481.1 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 \( 23^{30}\cdot 37^{22} \) $C_{33}$ (as 33T1) n/a
33.33.5964572044631662930869897974580631723402610311315668047983759159277483196969.1 x33 - 3x32 - 120x31 + 450x30 + 5757x29 - 26439x28 - 139216x27 + 813933x26 + 1676889x25 - 14588595x24 - 5289417x23 + 158067366x22 - 111316484x21 - 1026324261x20 + 1580724570x19 + 3707180205x18 - 9398785623x17 - 5392982019x16 + 29700176281x15 - 7076803698x14 - 50183067855x13 + 37619683596x12 + 40721934162x11 - 52500002157x10 - 9740363856x9 + 32585743542x8 - 5020929429x7 - 9149246964x6 + 3064214298x5 + 963373038x4 - 501812162x3 + 1428300x2 + 21340050x - 2255257 \( 3^{44}\cdot 67^{30} \) $C_{33}$ (as 33T1) Trivial (GRH)

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