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 matches 1-50 of 55)

Label	Polynomial	Discriminant	Galois group	Class group
22.12.61117859389674098630012726211547851562500.1	x^22 - x^21 - 30x^20 + 35x^19 + 265x^18 - 687x^17 + 357x^16 + 7305x^15 - 18675x^14 - 35840x^13 + 103856x^12 + 58224x^11 - 211240x^10 + 163795x^9 - 64050x^8 - 651165x^7 + 823710x^6 + 466155x^5 - 852830x^4 + 161150x^3 + 139095x^2 - 61765x + 6985	\( -\,2^{2}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.16.168074113321603771232534997081756591796875.1	x^22 - 7x^21 - 35x^20 + 270x^19 + 645x^18 - 4209x^17 - 9252x^16 + 31050x^15 + 96990x^14 - 65105x^13 - 614131x^12 - 561998x^11 + 1988085x^10 + 4067340x^9 - 2442075x^8 - 9864030x^7 - 410850x^6 + 10078335x^5 + 2192040x^4 - 3755745x^3 - 571725x^2 + 123390x - 4545	\( -\,3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.8.168074113321603771232534997081756591796875.1	x^22 + 49x^20 + 685x^18 + 1815x^16 - 17505x^14 - 55752x^12 + 164457x^10 + 203115x^8 - 250965x^6 - 61270x^4 + 1001x^2 + 44	\( -\,3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.10.183353578169022295890038178634643554687500.1	x^22 + 12x^20 - 180x^18 - 2655x^16 + 3060x^14 + 136809x^12 + 319203x^10 - 1133820x^8 - 2847825x^6 + 2709045x^4 + 747009x^2 - 415152	\( 2^{2}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.12.305589296948370493150063631057739257812500.1	x^22 - 50x^20 + 655x^18 - 570x^16 - 26565x^14 + 17640x^12 + 429960x^10 + 832590x^8 + 466125x^6 - 52030x^4 - 64735x^2 + 9680	\( -\,2^{2}\cdot 3^{20}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (GRH)
22.14.504222339964811313697604991245269775390625.1	x^22 - 3x^21 - 42x^20 + 90x^19 + 795x^18 - 951x^17 - 8547x^16 + 3882x^15 + 51570x^14 - 10425x^13 - 130425x^12 + 228675x^11 - 297975x^10 - 2683875x^9 + 3047535x^8 + 15171897x^7 - 9772041x^6 - 46458354x^5 + 22671390x^4 + 68608965x^3 - 35739546x^2 - 28301877x + 11611317	\( 3^{21}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.6.504222339964811313697604991245269775390625.1	x^22 - 11x^21 + 57x^20 - 185x^19 + 100x^18 + 2178x^17 - 13698x^16 + 50526x^15 - 125595x^14 + 212645x^13 - 151135x^12 - 372585x^11 + 1599575x^10 - 3294265x^9 + 3873360x^8 - 1752654x^7 - 4272321x^6 + 11175117x^5 - 14948990x^4 + 12783910x^3 - 6636471x^2 + 1870441x - 218792	\( 3^{21}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.14.504222339964811313697604991245269775390625.2	x^22 - x^21 - 36x^20 + 50x^19 + 490x^18 - 882x^17 - 3318x^16 + 7872x^15 + 13095x^14 - 42815x^13 - 35956x^12 + 163086x^11 + 52061x^10 - 435095x^9 + 120585x^8 + 633792x^7 - 557172x^6 - 237747x^5 + 494230x^4 - 200200x^3 + 26136x^2 - 7216x + 2464	\( 3^{21}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.10.672296453286415084930139988327026367187500.1	x^22 + 21x^20 - 165x^18 - 5445x^16 - 19470x^14 + 113817x^12 + 465597x^10 - 762300x^8 - 2270565x^6 + 419265x^4 + 1665081x^2 - 191664	\( 2^{2}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.6.672296453286415084930139988327026367187500.1	x^22 - 24x^20 - 495x^18 + 1650x^16 + 36795x^14 + 82962x^12 - 186318x^10 - 833085x^8 - 1007325x^6 - 539055x^4 - 131769x^2 - 11979	\( 2^{2}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	$[2]$ (GRH)
22.6.672296453286415084930139988327026367187500.2	x^22 + 24x^20 - 45x^18 - 2640x^16 - 5550x^14 + 77898x^12 + 299952x^10 - 235125x^8 - 1820835x^6 - 1506915x^4 - 228744x^2 - 4851	\( 2^{2}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.16.840370566608018856162674985408782958984375.1	x^22 - 25x^20 + 130x^18 + 975x^16 - 8280x^14 - 5580x^12 + 129810x^10 - 86460x^8 - 586080x^6 + 671935x^4 - 203995x^2 + 10780	\( -\,3^{20}\cdot 5^{21}\cdot 11^{17} \)	22T36	$[2]$ (GRH)
22.10.916767890845111479450190893173217773437500.1	x^22 - 10x^21 + 30x^20 - 25x^19 + 325x^18 - 3180x^17 + 11340x^16 - 9885x^15 - 62595x^14 + 261085x^13 - 416755x^12 - 26220x^11 + 1674680x^10 - 3966065x^9 + 2285520x^8 + 10714185x^7 - 18884505x^6 - 17519370x^5 + 28233430x^4 + 23392400x^3 - 5493645x^2 - 6705550x - 1073090	\( 2^{2}\cdot 3^{21}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (GRH)
22.12.2016889359859245254790419964981079101562500.1	x^22 - x^21 - 21x^20 + 20x^19 + 40x^18 - 672x^17 + 2292x^16 + 8442x^15 - 18060x^14 - 2615x^13 + 37889x^12 - 279954x^11 + 1556x^10 + 243895x^9 - 1841640x^8 - 428373x^7 + 1338348x^6 - 3568377x^5 - 1615535x^4 + 2039225x^3 - 424269x^2 + 24314x - 281	\( -\,2^{2}\cdot 3^{21}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.10.3361482266432075424650699941635131835937500.1	x^22 - 11x^21 + 34x^20 + 45x^19 - 615x^18 + 1113x^17 + 3927x^16 - 16488x^15 - 21855x^14 + 323585x^13 - 735736x^12 - 995059x^11 + 7829136x^10 - 12148350x^9 - 7463010x^8 + 46944717x^7 - 57659157x^6 + 23519613x^5 + 1558365x^4 - 6085635x^3 + 3842001x^2 + 255054x - 388581	\( 2^{2}\cdot 3^{20}\cdot 5^{21}\cdot 11^{17} \)	22T36	$[2]$ (GRH)
22.6.3361482266432075424650699941635131835937500.1	x^22 - 4x^21 - 26x^20 + 225x^19 - 195x^18 - 3183x^17 + 11967x^16 - 4032x^15 - 86025x^14 + 282910x^13 - 368011x^12 - 99386x^11 + 1108671x^10 - 1443225x^9 - 334350x^8 + 1018083x^7 + 6585843x^6 - 19265868x^5 + 22882725x^4 - 14084505x^3 + 3667101x^2 + 526311x - 381201	\( 2^{2}\cdot 3^{20}\cdot 5^{21}\cdot 11^{17} \)	22T36	$[2, 2]$ (GRH)
22.12.7395260986150565934231539871597290039062500.1	x^22 - 10x^21 + 20x^20 + 295x^19 - 1895x^18 + 1995x^17 + 22770x^16 - 99795x^15 + 84840x^14 + 441805x^13 - 1764685x^12 + 2660015x^11 + 1421125x^10 - 12108650x^9 + 18753225x^8 - 11528325x^7 - 2371350x^6 + 9223500x^5 - 6317350x^4 + 1656550x^3 + 182800x^2 - 138400x - 11575	\( -\,2^{2}\cdot 3^{20}\cdot 5^{20}\cdot 11^{18} \)	22T36	Trivial (GRH)
22.12.15646172003756569249283257910156250000000000.1	x^22 - 9x^20 - 360x^18 + 555x^16 + 26760x^14 + 15147x^12 - 403938x^10 - 194490x^8 + 1591830x^6 - 498555x^4 - 689454x^2 + 114921	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.20.15646172003756569249283257910156250000000000.1	x^22 - 61x^20 + 1150x^18 - 7485x^16 - 13755x^14 + 419313x^12 - 2209803x^10 + 5513775x^8 - 7283940x^6 + 4978855x^4 - 1483189x^2 + 85264	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.1	x^22 + 26x^20 - 110x^18 - 3315x^16 - 14415x^14 - 13548x^12 + 20277x^10 + 30555x^8 + 10620x^6 + 670x^4 - 94x^2 + 1	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.12.15646172003756569249283257910156250000000000.2	x^22 - 34x^20 - 135x^19 + 730x^18 + 2955x^17 - 5775x^16 - 27900x^15 + 10515x^14 + 131175x^13 + 47157x^12 - 367890x^11 - 324513x^10 + 592530x^9 + 850740x^8 - 437700x^7 - 1134615x^6 + 9675x^5 + 736120x^4 + 120945x^3 - 184954x^2 - 20295x + 15796	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.2	x^22 - 19x^20 - 170x^18 + 3015x^16 + 10980x^14 - 127398x^12 - 271758x^10 + 1040880x^8 + 1659690x^6 + 598255x^4 + 77051x^2 + 3136	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.12.15646172003756569249283257910156250000000000.3	x^22 - 16x^20 - 290x^18 + 4545x^16 - 2895x^14 - 58122x^12 + 68337x^10 + 195240x^8 - 204240x^6 - 152000x^4 + 10496x^2 + 1024	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.3	x^22 + 26x^20 - 20x^18 - 3330x^16 - 12255x^14 + 78192x^12 + 447987x^10 + 277980x^8 - 1318755x^6 - 2129930x^4 - 884209x^2 + 8836	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.12.15646172003756569249283257910156250000000000.4	x^22 + 14x^20 - 170x^18 - 1155x^16 + 8595x^14 + 24138x^12 - 119763x^10 - 182985x^8 + 375495x^6 + 78010x^4 - 213289x^2 + 34969	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.4	x^22 - 19x^20 - 395x^18 + 615x^16 + 20850x^14 + 16842x^12 - 223773x^10 - 144525x^8 + 284565x^6 + 250165x^4 + 38861x^2 + 1	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.15646172003756569249283257910156250000000000.5	x^22 + 44x^20 + 415x^18 - 2265x^16 - 52410x^14 - 232827x^12 + 61662x^10 + 2529105x^8 + 4141035x^6 - 550070x^4 + 15791x^2 + 64	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.8.22085756220567549162579756126980406366726963.1	x^22 - 33x^20 - 66x^19 - 165x^17 - 1584x^16 - 5379x^15 + 11517x^14 + 66462x^13 + 1452x^12 - 124158x^11 + 531795x^10 + 1346697x^9 - 72006x^8 - 136224x^7 + 4245747x^6 + 2948682x^5 - 3930531x^4 - 687159x^3 + 4962870x^2 + 314622x - 2099481	\( -\,3^{21}\cdot 11^{32} \)	22T36	Trivial (GRH)
22.12.46938516011269707747849773730468750000000000.1	x^22 - 27x^20 - 240x^18 + 7635x^16 - 38835x^14 - 12339x^12 + 285228x^10 + 89055x^8 - 150795x^6 - 22680x^4 + 17874x^2 + 27	\( -\,2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.4.46938516011269707747849773730468750000000000.1	x^22 + 48x^20 + 915x^18 + 8805x^16 + 44865x^14 + 113886x^12 + 96498x^10 - 129690x^8 - 305910x^6 - 179685x^4 - 26136x^2 + 3267	\( -\,2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.12.46938516011269707747849773730468750000000000.2	x^22 - 63x^20 + 405x^18 + 11820x^16 + 46320x^14 + 12519x^12 - 90537x^10 + 35880x^8 + 5520x^6 - 3510x^4 + 234x^2 + 3	\( -\,2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.12.46938516011269707747849773730468750000000000.3	x^22 + 3x^20 - 660x^18 - 3030x^16 + 54675x^14 + 25956x^12 - 596682x^10 - 780705x^8 + 214110x^6 + 207900x^4 - 27891x^2 + 27	\( -\,2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.10.46938516011269707747849773730468750000000000.1	x^22 + 3x^20 - 735x^18 + 2220x^16 + 37035x^14 - 35379x^12 - 392202x^10 - 80955x^8 + 1213110x^6 + 1401030x^4 + 428679x^2 - 108	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.14.46938516011269707747849773730468750000000000.1	x^22 - 15x^20 - 690x^18 + 180x^16 + 66870x^14 + 123210x^12 - 1524600x^10 - 1076175x^8 + 13072050x^6 - 13078125x^4 + 537975x^2 - 2700	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.2.46938516011269707747849773730468750000000000.1	x^22 + 72x^20 + 1935x^18 + 24510x^16 + 155250x^14 + 516744x^12 + 877113x^10 + 552870x^8 - 344925x^6 - 643680x^4 - 251991x^2 - 22707	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.10.46938516011269707747849773730468750000000000.2	x^22 + 3x^20 - 345x^18 - 975x^16 + 37710x^14 + 117291x^12 - 1264617x^10 - 5552430x^8 - 1316775x^6 + 13294755x^4 + 9076419x^2 - 2572428	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.14.46938516011269707747849773730468750000000000.2	x^22 + 12x^20 - 525x^18 + 2835x^16 + 10560x^14 - 94551x^12 + 106398x^10 + 265455x^8 - 376965x^6 - 171240x^4 + 254259x^2 - 8112	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.10.46938516011269707747849773730468750000000000.3	x^22 + 27x^20 - 15x^18 - 5925x^16 - 51585x^14 - 78831x^12 + 295833x^10 + 101415x^8 - 348870x^6 + 134850x^4 - 9141x^2 - 147	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.14.46938516011269707747849773730468750000000000.3	x^22 - 42x^20 + 480x^18 + 330x^16 - 26370x^14 + 37161x^12 + 346203x^10 - 454530x^8 - 1472070x^6 + 1147725x^4 + 643299x^2 - 98283	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.10.46938516011269707747849773730468750000000000.4	x^22 + 18x^20 - 120x^18 - 2610x^16 + 3375x^14 + 87291x^12 - 106542x^10 - 269325x^8 + 41715x^6 + 128790x^4 + 9234x^2 - 243	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.14.46938516011269707747849773730468750000000000.4	x^22 - 9x^21 - 9x^20 + 360x^19 - 1395x^18 + 267x^17 + 12357x^16 - 35418x^15 + 25365x^14 + 69285x^13 - 205122x^12 + 200823x^11 + 133848x^10 - 600885x^9 + 522135x^8 + 432342x^7 - 1004868x^6 - 20988x^5 + 735885x^4 - 20385x^3 - 232074x^2 - 26469x + 12591	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.14.46938516011269707747849773730468750000000000.5	x^22 + 18x^20 - 30x^18 - 1440x^16 - 1095x^14 + 19971x^12 - 36792x^10 + 22935x^8 + 1155x^6 - 7260x^4 + 2904x^2 - 363	\( 2^{10}\cdot 3^{21}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.4.62584688015026276997133031640625000000000000.1	x^22 + 35x^20 + 145x^18 - 6780x^16 - 104715x^14 - 644565x^12 - 2013750x^10 - 3324525x^8 - 2834100x^6 - 1163300x^4 - 180475x^2 + 400	\( -\,2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16} \)	22T36	Trivial (GRH)
22.20.78230860018782846246416289550781250000000000.1	x^22 - 80x^20 + 2125x^18 - 21360x^16 + 24165x^14 + 745935x^12 - 3014745x^10 + 3905820x^8 - 1835760x^6 + 250235x^4 - 8065x^2 + 20	\( -\,2^{10}\cdot 3^{20}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (GRH)
22.10.78230860018782846246416289550781250000000000.1	x^22 + 35x^20 - 35x^18 - 6735x^16 + 12900x^14 + 77100x^12 + 8175x^10 - 122925x^8 - 68625x^6 + 12625x^4 + 7625x^2 - 125	\( 2^{10}\cdot 3^{20}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (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)
22.10.78230860018782846246416289550781250000000000.2	x^22 + 60x^20 + 885x^18 - 4020x^16 - 91905x^14 + 414090x^12 + 521280x^10 - 3046275x^8 + 1375875x^6 + 62145x^4 - 25875x^2 - 45	\( 2^{10}\cdot 3^{20}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (GRH)
22.12.172107892041322261742115837011718750000000000.1	x^22 + 39x^20 - 75x^18 - 5610x^16 + 23175x^14 + 98193x^12 - 475848x^10 - 131175x^8 + 1204695x^6 - 6975x^4 - 611379x^2 + 66924	\( -\,2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (GRH)
22.14.172107892041322261742115837011718750000000000.1	x^22 - 21x^20 - 450x^18 + 8055x^16 + 16740x^14 - 655047x^12 + 2337012x^10 + 2067120x^8 - 15770700x^6 + 4664385x^4 + 15107796x^2 - 392931	\( 2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	Trivial (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)