Global number field search results

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Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.18.2769192260679449143892527783203125.1	x^22 - x^21 - 19x^20 + 14x^19 + 121x^18 - 78x^17 - 261x^16 + 287x^15 - 160x^14 - 852x^13 + 1239x^12 + 1601x^11 - 1405x^10 - 1576x^9 + 348x^8 + 692x^7 + 274x^6 - 60x^5 - 159x^4 - 32x^3 + 22x^2 + 4x - 1	\( 5^{11}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T47	Trivial (GRH)
22.18.3674011011924955171910111767578125.1	x^22 - x^21 - 22x^20 + 5x^19 + 191x^18 + 88x^17 - 819x^16 - 753x^15 + 1905x^14 + 2178x^13 - 2680x^12 - 3041x^11 + 2570x^10 + 2301x^9 - 1770x^8 - 1001x^7 + 811x^6 + 259x^5 - 211x^4 - 38x^3 + 25x^2 + 2x - 1	\( 5^{11}\cdot 8674315276967^{2} \)	22T47	Trivial (GRH)
22.18.4098058278162967431271914143428729.1	x^22 - 3x^21 - 14x^20 + 42x^19 + 35x^18 - 82x^17 - 76x^16 - 508x^15 + 1938x^14 - 984x^13 - 5144x^12 + 9774x^11 + 1291x^10 - 17627x^9 + 8445x^8 + 12822x^7 - 10291x^6 - 3443x^5 + 4487x^4 - 121x^3 - 672x^2 + 130x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.18.7198079267989980836471065337135104.1	x^22 - 14x^20 + 64x^18 - 52x^16 - 451x^14 + 1535x^12 - 2054x^10 + 1332x^8 - 396x^6 + 30x^4 + 7x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.18.7198079267989980836471065337135104.2	x^22 - 10x^20 + 12x^18 + 145x^16 - 502x^14 + 434x^12 + 331x^10 - 775x^8 + 484x^6 - 139x^4 + 19x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.18.10184378952996122520694192412373661.1	x^22 - 11x^21 + 40x^20 - 15x^19 - 254x^18 + 519x^17 + 310x^16 - 1970x^15 + 1107x^14 + 2977x^13 - 3993x^12 - 1171x^11 + 5121x^10 - 1997x^9 - 2876x^8 + 2700x^7 + 340x^6 - 1207x^5 + 283x^4 + 173x^3 - 80x^2 + 3x + 1	\( 3363181\cdot 55029067682009^{2} \)	22T53	Trivial (GRH)
22.18.33833812608216375123231853716176896.1	x^22 - 16x^20 + 105x^18 - 363x^16 + 700x^14 - 709x^12 + 248x^10 + 146x^8 - 135x^6 + 20x^4 + 5x^2 - 1	\( 2^{22}\cdot 2053^{2}\cdot 43747835269^{2} \)	22T51	Trivial (GRH)
22.18.39034415726392643532837005585022976.1	x^22 - 15x^20 + 91x^18 - 279x^16 + 417x^14 - 130x^12 - 453x^10 + 544x^8 - 66x^6 - 185x^4 + 75x^2 - 1	\( 2^{22}\cdot 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2} \)	22T51	Trivial (GRH)
22.18.165555823163769559238834502754107392.1	x^22 - 23x^20 + 184x^18 - 598x^16 + 437x^14 + 1840x^12 - 4324x^10 + 2875x^8 + 253x^6 - 828x^4 + 253x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.18.1084207284535529251075925938636327901.1	x^22 - 11x^21 + 40x^20 - 15x^19 - 254x^18 + 519x^17 + 309x^16 - 1962x^15 + 1086x^14 + 2984x^13 - 3923x^12 - 1318x^11 + 5184x^10 - 1751x^9 - 3296x^8 + 2717x^7 + 803x^6 - 1525x^5 + 161x^4 + 436x^3 - 110x^2 - 75x - 1	\( 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}\cdot 116499629 \)	22T53	Trivial (GRH)
22.18.1549178202413742486505281033483865049.1	x^22 - 11x^21 + 39x^20 - 5x^19 - 289x^18 + 549x^17 + 438x^16 - 2382x^15 + 1432x^14 + 3832x^13 - 6324x^12 - 692x^11 + 9779x^10 - 5877x^9 - 7100x^8 + 8177x^7 + 1805x^6 - 4599x^5 + 512x^4 + 1102x^3 - 307x^2 - 80x + 29	\( 1297^{10}\cdot 115001 \)	22T32	Trivial (GRH)
22.18.2286755966908882115410998176681804581.1	x^22 - 11x^21 + 30x^20 + 85x^19 - 518x^18 + 45x^17 + 3394x^16 - 2978x^15 - 12837x^14 + 16021x^13 + 32642x^12 - 44805x^11 - 60933x^10 + 75322x^9 + 86609x^8 - 74536x^7 - 89913x^6 + 34489x^5 + 58999x^4 + 3076x^3 - 17033x^2 - 7149x - 883	\( 131\cdot 2297\cdot 71647\cdot 10298992926983^{2} \)	22T53	Trivial (GRH)
22.18.3731141344940612691471625994285238301.1	x^22 - 11x^21 + 30x^20 + 85x^19 - 516x^18 + 27x^17 + 3420x^16 - 2778x^15 - 13418x^14 + 15160x^13 + 36613x^12 - 43034x^11 - 75553x^10 + 73248x^9 + 119719x^8 - 70453x^7 - 136889x^6 + 22305x^5 + 97142x^4 + 21717x^3 - 29073x^2 - 17742x - 2953	\( 29\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}\cdot 1702694681 \)	22T53	Trivial (GRH)
22.18.56501459388151144478039723653407440896.1	x^22 - 16x^20 + 46x^18 + 155x^16 - 748x^14 + 688x^12 + 579x^10 - 1382x^8 + 904x^6 - 253x^4 + 28x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.18.56501459388151144478039723653407440896.2	x^22 - 19x^20 + 110x^18 - 228x^16 - 81x^14 + 1073x^12 - 1656x^10 + 934x^8 - 71x^6 - 67x^4 + 16x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.18.2009284128530624004997349500428572968553.1	x^22 - 5x^21 - 19x^20 + 138x^19 - 234x^18 - 576x^17 + 8567x^16 - 17893x^15 - 75853x^14 + 255414x^13 + 209204x^12 - 1338618x^11 + 411447x^10 + 2870120x^9 - 2750667x^8 - 1555277x^7 + 2988765x^6 - 574462x^5 - 751638x^4 + 329506x^3 + 6664x^2 - 14874x + 289	\( 1297^{11}\cdot 115001 \)	22T32	$[2]$ (GRH)
22.18.2855192247049898659094689096800227295232.1	x^22 - 22x^20 + 207x^18 - 2x^17 - 1092x^16 + 28x^15 + 3559x^14 - 156x^13 - 7445x^12 + 450x^11 + 10059x^10 - 736x^9 - 8611x^8 + 714x^7 + 4442x^6 - 426x^5 - 1238x^4 + 152x^3 + 140x^2 - 24x - 1	\( 2^{33}\cdot 79\cdot 3767\cdot 449833\cdot 2443537\cdot 1016137678657 \)	22T57	Trivial (GRH)
22.18.4299288794103243236127943577240214703609.1	x^22 - 5x^21 - 49x^20 + 149x^19 + 1117x^18 - 1000x^17 - 12006x^16 - 3533x^15 + 64273x^14 + 63958x^13 - 171145x^12 - 263217x^11 + 207316x^10 + 471355x^9 - 84325x^8 - 394692x^7 + 1221x^6 + 166543x^5 + 881x^4 - 34179x^3 + 1826x^2 + 2665x - 347	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.18.73282392826432034388017521578469450842112.1	x^22 - 48x^20 + 668x^18 - 3452x^16 + 1836x^14 + 41707x^12 - 117661x^10 + 18659x^8 + 239887x^6 - 220532x^4 + 55347x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.18.395038411464701473449113907238603048615936.1	x^22 - 33x^20 + 429x^18 - 2673x^16 + 6578x^14 + 12122x^12 - 121726x^10 + 319682x^8 - 379335x^6 + 172667x^4 + 11253x^2 - 20449	\( 2^{34}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.18.1580153645858805893796455628954412194463744.1	x^22 - 11x^20 - 319x^18 + 7183x^16 - 57794x^14 + 234762x^12 - 526174x^10 + 651002x^8 - 398827x^6 + 67529x^4 + 26565x^2 - 3721	\( 2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.18.2765268880252910314143797350670221340311552.1	x^22 - 22x^20 - 88x^18 + 3520x^16 - 4576x^14 - 99132x^12 + 468424x^10 - 870980x^8 + 806696x^6 - 380600x^4 + 81092x^2 - 4732	\( 2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.18.4345422526111716207940252979624633534775296.1	x^22 - 44x^20 + 660x^18 - 2640x^16 - 27456x^14 + 312576x^12 - 1046848x^10 + 991232x^8 + 892672x^6 - 1402368x^4 + 259072x^2 - 11264	\( 2^{34}\cdot 7^{10}\cdot 11^{23} \)	22T37	Trivial (GRH)
22.18.15646172003756569249283257910156250000000000.1	x^22 - 36x^20 + 45x^18 + 7290x^16 - 90045x^14 + 482778x^12 - 1333233x^10 + 1837620x^8 - 984150x^6 - 46170x^4 + 102141x^2 - 1296	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.18.17830448338954983961633748005017386674552832.1	x^22 - 88x^20 - 198x^19 + 2024x^18 + 6270x^17 - 19580x^16 - 78364x^15 + 78408x^14 + 496276x^13 + 7304x^12 - 1707542x^11 - 1055472x^10 + 3197810x^9 + 3138322x^8 - 3066712x^7 - 3678862x^6 + 1424742x^5 + 1891010x^4 - 280808x^3 - 376200x^2 + 13574x + 18010	\( 2^{22}\cdot 7^{15}\cdot 11^{23} \)	22T35	Trivial (GRH)
22.18.30417957682782013455581770857372434743427072.1	x^22 - 44x^20 + 660x^18 - 1408x^17 - 7304x^16 + 46200x^15 + 166496x^14 - 350240x^13 - 2140512x^12 - 1464576x^11 + 7791168x^10 + 16937536x^9 + 2342208x^8 - 31841920x^7 - 40416640x^6 - 4983616x^5 + 31308288x^4 + 32414976x^3 + 14386944x^2 + 2818816x + 144512	\( 2^{34}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.18.62584688015026276997133031640625000000000000.1	x^22 - 29x^20 - 35x^18 + 7965x^16 - 79140x^14 + 140187x^12 + 1374597x^10 - 6587220x^8 + 8430720x^6 - 2011840x^4 + 141056x^2 - 1024	\( 2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T33	Trivial (GRH)
22.18.78230860018782846246416289550781250000000000.1	x^22 - 30x^20 - 30x^18 + 7440x^16 - 53325x^14 - 224685x^12 + 3618405x^10 - 14109120x^8 + 24309270x^6 - 19294740x^4 + 6187365x^2 - 669780	\( 2^{10}\cdot 3^{20}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (GRH)
22.18.172107892041322261742115837011718750000000000.1	x^22 - 19x^20 - 35x^18 + 2820x^16 - 19335x^14 + 18417x^12 + 263922x^10 - 1087185x^8 + 1651980x^6 - 1077890x^4 + 270611x^2 - 11264	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.18.924610449303392395108565351166810367173677581.1	x^22 - 11x^21 + 44x^20 - 55x^19 - 149x^18 + 714x^17 - 1042x^16 - 742x^15 + 5168x^14 - 5630x^13 - 5248x^12 + 15888x^11 - 6710x^10 - 12738x^9 + 15541x^8 - 1265x^7 - 8234x^6 + 5083x^5 + 294x^4 - 1334x^3 + 492x^2 - 67x + 3	\( 74843^{8}\cdot 939181 \)	22T42	Trivial (GRH)
22.18.4129233136056857981979443884256982828952059904.1	x^22 - 62x^20 + 1332x^18 - 12445x^16 + 46846x^14 - 17000x^12 - 234649x^10 + 219644x^8 + 210856x^6 - 218489x^4 + 42680x^2 - 81	\( 2^{22}\cdot 74843^{8} \)	22T39	Trivial (GRH)
22.18.4129233136056857981979443884256982828952059904.2	x^22 - 50x^20 + 967x^18 - 9172x^16 + 44799x^14 - 106893x^12 + 101941x^10 - 12539x^8 - 4786x^6 + 708x^4 + 4x^2 - 1	\( 2^{22}\cdot 74843^{8} \)	22T39	Trivial (GRH)
22.18.6619266216731178498524686856912912840533726732.1	x^22 - 2x^21 - 22x^20 + 36x^19 + 205x^18 - 257x^17 - 1042x^16 + 939x^15 + 3122x^14 - 1916x^13 - 5652x^12 + 2249x^11 + 6166x^10 - 1525x^9 - 3959x^8 + 601x^7 + 1438x^6 - 143x^5 - 281x^4 + 19x^3 + 27x^2 - x - 1	\( 2^{2}\cdot 23\cdot 43\cdot 2083\cdot 1669897\cdot 13592816541193\cdot 35388744506094820229 \)	22T59	Trivial (GRH)
22.18.1068551434733836007957455525975439914646912978721.1	x^22 - 2x^21 - 22x^20 + 36x^19 + 205x^18 - 257x^17 - 1042x^16 + 939x^15 + 3122x^14 - 1916x^13 - 5652x^12 + 2249x^11 + 6168x^10 - 1525x^9 - 3960x^8 + 601x^7 + 1438x^6 - 143x^5 - 281x^4 + 19x^3 + 27x^2 - x - 1	\( 3^{4}\cdot 29\cdot 1051\cdot 7796988506731\cdot 55511479826982340639646618909 \)	22T59	Trivial (GRH)
22.18.309044195601903421945287518629445365867259019395072.1	x^22 - 152x^20 + 8733x^18 - 236350x^16 + 3051787x^14 - 17399125x^12 + 47374033x^10 - 62687488x^8 + 35737999x^6 - 4125223x^4 - 1571703x^2 - 74843	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.18.35968643551695332182677064543344800913941547158154336510998469613936975508099279042617383314590716452143104.1	x^22 - 257x^20 + 24474x^18 - 973488x^16 + 4911342x^14 + 833458818x^12 - 24773125392x^10 + 177479869188x^8 + 2609466379182x^6 - 46742377664590x^4 + 197759461441604x^2 - 49242609059256	\( 2^{73}\cdot 3^{20}\cdot 31\cdot 337^{8}\cdot 991\cdot 310501^{8}\cdot 2473607 \)	22T44	n/a
22.18.2300872385477501581227693106652852098399533470342000869126199943093917599041643904688100198470522867623396821870956126029973998089.1	x^22 - 11x^21 - 8375382071x^20 + 83753821095x^19 + 30239391842106235938x^18 - 272154528965940026844x^17 - 62299005944745132263794581393x^16 + 498392053726797058825990959294x^15 + 81735614144568549821065357941455889481x^14 - 572149307733840810557332053781243645619x^13 - 72054944016577680888382418513797041923435706453x^12 + 432329671537407108547063573092233206919075350347x^11 + 43757681734213856060620813669474737589565734087455676069x^10 - 218788412634091283032227790410382382555583750616259162451x^9 - 18383728547378112693986359299316156439853557115655196996194040079x^8 + 73534915502242931336119545678495670841428298811136294653478844046x^7 + 5255787908282428375256316952646409006236043296299117696458810525050810930x^6 - 15767363982219490302530548353167437085483306741165131698814519612745966636x^5 - 976871499505339856726687787443673148702119347232311492713368377627444025708264939x^4 + 1953743025289619769609927935965174424151875711944819663352020838970899069862489543x^3 + 106511320841640709718273593909091112261150331893177419007223913489960065681716929693177288x^2 - 106511321818512224990977488006456113342508309352392142460740805431636636438802684226477536x - 5171816474167505628125246930786194146064674226046415678576793740063088827110117886469640427968531	\( 131^{10}\cdot 2297^{10}\cdot 71647^{10}\cdot 10298992926983^{2} \)	22T51	n/a
22.18.6511104967027765891307644276629607242862811084151155627686835522699344960186990690054789097605243779917127958669178659213839357848449.1	x^22 - 11x^21 - 15789084607x^20 + 157890846455x^19 + 110746971971048806316x^18 - 996722752239328383006x^17 - 456686908335859663186856128341x^16 + 3653495289279259709985789751062x^15 + 1233340365680532560255064426238448307608x^14 - 8633382623699895563245834354737997399860x^13 - 2295306548915827818503229932405383312648591807203x^12 + 13771839405728941185352057872535434682817913093144x^11 + 3008235976397770175167222399027423306040909666725371574201x^10 - 15041180008230712300780359161086680732594538490261818878188x^9 - 2778656157484847280982897747877969488922506517585296579872733446640x^8 + 11114624720186469324806098611947733941638935381034067180114602303069x^7 + 1772974228559093358263195450183082391905157516634653024580978835244385317895x^6 - 5318922724578466658615185173429817814200518248972628117560517528924164100228x^5 - 744044115416507765021021196646690610169866572713152856848171728626532956098421434479x^4 + 1488088239697886750639882361285264147203086069826044503097773504915513387520157567545x^3 + 184729416370582242638251447645440388704667291009348175277482602807244002974054527942977543281x^2 - 184729417114626363373681945580896803659929128262623837964712319402315440375343750732884448014x - 20544135315942859966369326009302529501882658344474338458010659738621792061984845009538823872127218171	\( 29^{10}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}\cdot 1702694681^{10} \)	22T51	n/a