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

Results (1-50 of 70 matches)

 

Label	Polynomial	Discriminant	Galois group	Class group
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	\( -\,23^{31} \)	$C_{11}\times S_3$ (as 33T2)	trivial (GRH)
33.1.127...537.1	x^33 - x - 1	\( 461\cdot 37057\cdot 7472134207648223752469291758363939923217381 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.130...489.1	x^33 + x - 1	\( 17\cdot 43\cdot 1579\cdot 2609\cdot 13153817\cdot 216865282965193\cdot 15199633537674804809 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.125...305.1	x^33 + 2x - 1	\( 5\cdot 2510840719976680323086521337206272553373849285653050481261 \)	$S_{33}$ (as 33T162)	trivial (GRH)
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	\( 67^{32} \)	$C_{33}$ (as 33T1)	trivial (GRH)
33.1.135...753.1	x^33 - 3	\( 3^{65}\cdot 11^{27} \)	33T11	trivial (GRH)
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	\( 7^{22}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	trivial (GRH)
33.1.529...264.1	x^33 - 4x - 4	\( 2^{32}\cdot 677\cdot 4266637\cdot 48046836047629\cdot 888172284811267871458394629 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.541...056.1	x^33 - 2x - 2	\( 2^{32}\cdot 17881556731651\cdot 7056826131348151479446323473239686411 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.554...872.1	x^33 - x - 2	\( 2^{32}\cdot 31\cdot 491\cdot 35603\cdot 238248533303420450650042664615870752238639 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.554...392.1	x^33 - x - 4	\( 2^{32}\cdot 1621\cdot 3527\cdot 195457\cdot 11716761181\cdot 14330054499223\cdot 688121128326241 \)	$S_{33}$ (as 33T162)	n/a
33.1.554...848.1	x^33 - 2	\( 2^{32}\cdot 3^{33}\cdot 11^{33} \)	33T11	trivial (GRH)
33.1.567...640.1	x^33 + 2x - 2	\( 2^{32}\cdot 5\cdot 53\cdot 3229\cdot 6433737122028757573993\cdot 23983104676408544038373 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.579...432.1	x^33 + 4x - 4	\( 2^{32}\cdot 7\cdot 127\cdot 361279\cdot 459803\cdot 149099734067\cdot 6129135169246811499255607 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.33.700...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	\( 3^{44}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	trivial (GRH)
33.1.174...153.1	x^33 - x - 3	\( 32159\cdot 1547725797949519945333\cdot 3511075445128887057511203662401094299 \)	$S_{33}$ (as 33T162)	n/a
33.3.812...935.1	x^33 - 3x - 1	\( -\,3^{33}\cdot 5\cdot 40739\cdot 11781157\cdot 3137660461139\cdot 194099782564469344251877 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.812...961.1	x^33 + 3x - 1	\( 3^{34}\cdot 647\cdot 52009\cdot 14477556462738066936816722835108959527303 \)	$S_{33}$ (as 33T162)	n/a
33.1.812...296.1	x^33 + 3x - 2	\( 2^{32}\cdot 3^{34}\cdot 5273\cdot 13873073\cdot 79403245997\cdot 19528960698348533 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.33.228...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	\( 13^{22}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	trivial (GRH)
33.1.231...985.1	x^33 - 3x - 3	\( 3^{33}\cdot 5\cdot 7\cdot 29264269\cdot 40590873456269216446987174322351841903133 \)	$S_{33}$ (as 33T162)	n/a
33.1.239...641.1	x^33 - 2x - 3	\( 131009\cdot 1826160785227642613801154452607784331628185921248176167258849 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.239...409.1	x^33 + x - 3	\( 7\cdot 17\cdot 59\cdot 34075418154976741692969464276338838074532783688619316348157829 \)	$S_{33}$ (as 33T162)	n/a
33.1.247...881.1	x^33 + 3x - 3	\( 3^{33}\cdot 251\cdot 6097463\cdot 19738007\cdot 1473045192123599817714547811290817 \)	$S_{33}$ (as 33T162)	trivial (GRH)
33.1.238...848.1	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
33.1.486...440.1	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
33.3.107...016.1	x^33 - 4x - 2	\( -\,2^{32}\cdot 131\cdot 1332938071\cdot 25239878589041\cdot 5697057818890456747980454141102531 \)	$S_{33}$ (as 33T162)	n/a
33.3.107...351.1	x^33 - 4x - 1	\( -\,157\cdot 862680509293\cdot 8877052066229\cdot 395644289235529\cdot 226702188673068757097323811 \)	$S_{33}$ (as 33T162)	n/a
33.1.107...712.1	x^33 + 4x - 2	\( 2^{32}\cdot 717559\cdot 45863269\cdot 561933804328655053279\cdot 1357723639278128039889733 \)	$S_{33}$ (as 33T162)	n/a
33.1.108...297.1	x^33 + 4x - 3	\( 7\cdot 383\cdot 9151\cdot 4405305888814048278095373581053517274104732666158978723088087 \)	$S_{33}$ (as 33T162)	n/a
33.3.177...432.1	x^33 - 5x - 2	\( -\,2^{32}\cdot 28938953909\cdot 1424437414184534000994590725571052163866999948163 \)	$S_{33}$ (as 33T162)	n/a
33.1.595...304.1	x^33 - 2x - 4	\( 2^{62}\cdot 41\cdot 5227\cdot 495043\cdot 2489722643\cdot 103976867383\cdot 4701030158746705429 \)	$S_{33}$ (as 33T162)	n/a
33.33.964...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	\( 19^{22}\cdot 23^{30} \)	$C_{33}$ (as 33T1)	trivial (GRH)
33.1.102...432.1	x^33 + 5x - 4	\( 2^{64}\cdot 163\cdot 181\cdot 50551\cdot 28444257707\cdot 1304516704756865886343705176787 \)	$S_{33}$ (as 33T162)	n/a
33.1.238...984.1	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
33.1.425...712.1	x^33 + 5x - 2	\( 2^{30}\cdot 41\cdot 179\cdot 1579\cdot 2236133\cdot 39308148498265324319\cdot 38891111153367554795380843499 \)	$S_{33}$ (as 33T162)	n/a
33.3.170...487.1	x^33 - 5x - 1	\( -\,40857347\cdot 123238837\cdot 33790272568641220049426121100592716765978452363500500033 \)	$S_{33}$ (as 33T162)	n/a
33.1.170...513.1	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
33.1.170...433.1	x^33 + 5x - 3	\( 1297\cdot 12431057\cdot 17435333\cdot 170510057517160450557111079\cdot 3549619313840451585263090411 \)	$S_{33}$ (as 33T162)	n/a
33.1.334...897.1	x^33 + 3x - 5	\( 3^{33}\cdot 37\cdot 643\cdot 390353972345549\cdot 2624049677604259\cdot 2465544740666077701019 \)	$S_{33}$ (as 33T162)	n/a
33.1.283...625.1	x^33 - 5x - 5	\( 5^{32}\cdot 20333\cdot 35554829\cdot 26184343821271\cdot 6434496458277638628370639 \)	$S_{33}$ (as 33T162)	n/a
33.1.300...177.1	x^33 - 3x - 5	\( 3^{33}\cdot 79\cdot 263\cdot 465137788789\cdot 55954405270679204355252370860858804532583 \)	$S_{33}$ (as 33T162)	n/a
33.1.300...625.1	x^33 - 5	\( 3^{33}\cdot 5^{32}\cdot 11^{33} \)	33T11	n/a
33.1.300...601.1	x^33 + x - 5	\( 17\cdot 947963\cdot 2718169\cdot 899817429526243\cdot 49025681184056655667\cdot 1555626574856691502779379 \)	$S_{33}$ (as 33T162)	n/a
33.1.300...417.1	x^33 + 2x - 5	\( 347\cdot 21709529\cdot 399043534574726038672262189398446701674184314276727689712708459 \)	$S_{33}$ (as 33T162)	n/a
33.1.317...625.1	x^33 + 5x - 5	\( 5^{32}\cdot 271\cdot 5918259675491\cdot 101848657603787\cdot 835125266081452453199 \)	$S_{33}$ (as 33T162)	n/a
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	\( 7^{22}\cdot 67^{30} \)	$C_{33}$ (as 33T1)	trivial (GRH)
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	\( 199^{32} \)	$C_{33}$ (as 33T1)	trivial (GRH)
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	\( 23^{30}\cdot 31^{22} \)	$C_{33}$ (as 33T1)	trivial (GRH)
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	\( 23^{30}\cdot 37^{22} \)	$C_{33}$ (as 33T1)	n/a