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 91)

Label	Polynomial	Discriminant	Galois group	Class group
22.14.1855164453672687836700730712281.1	x^22 - 3x^21 - 14x^20 + 42x^19 + 81x^18 - 220x^17 - 283x^16 + 596x^15 + 627x^14 - 1145x^13 - 429x^12 + 1655x^11 - 1009x^10 - 1021x^9 + 1683x^8 - 196x^7 - 608x^6 + 283x^5 - 44x^4 - 6x^3 + 18x^2 - 8x + 1	\( 23^{21}\cdot 47 \)	22T28	Trivial (GRH)
22.14.3790988231418101231518884499009.1	x^22 - x^21 - 16x^20 + 27x^19 + 68x^18 - 193x^17 + 15x^16 + 436x^15 - 469x^14 - 26x^13 + 234x^12 - 345x^11 + 554x^10 - 110x^9 - 487x^8 + 401x^7 + 17x^6 - 196x^5 + 76x^4 + 32x^3 - 18x^2 - 2x + 1	\( 23^{20}\cdot 47^{2} \)	22T23	Trivial (GRH)
22.14.3790988231418101231518884499009.2	x^22 - 3x^21 - 10x^20 + 29x^19 + 22x^18 - 50x^17 - 4x^16 - 40x^15 - 36x^14 + 30x^13 + 27x^12 + 115x^11 + 27x^10 + 30x^9 - 36x^8 - 40x^7 - 4x^6 - 50x^5 + 22x^4 + 29x^3 - 10x^2 - 3x + 1	\( 23^{20}\cdot 47^{2} \)	22T23	Trivial (GRH)
22.14.13471519681654627790892423970816.1	x^22 - 12x^20 + 64x^18 - 200x^16 + 403x^14 - 544x^12 + 510x^10 - 358x^8 + 197x^6 - 73x^4 + 14x^2 - 1	\( 2^{22}\cdot 1792166448977^{2} \)	22T51	Trivial (GRH)
22.14.18194557110085700393779736328125.1	x^22 - x^21 - 13x^20 + 54x^18 + 93x^17 - 138x^16 - 339x^15 + 439x^14 + 258x^13 - 887x^12 + 343x^11 + 764x^10 - 601x^9 - 162x^8 + 341x^7 - 73x^6 - 118x^5 + 5x^4 + 25x^3 + 10x^2 - x - 1	\( 5^{11}\cdot 610429790897^{2} \)	22T47	Trivial (GRH)
22.14.31919563459480622441144580078125.1	x^22 - 2x^21 - 7x^20 + 14x^19 + 18x^18 - 67x^17 - 101x^16 + 234x^15 + 497x^14 - 273x^13 - 893x^12 + 23x^11 + 753x^10 + 147x^9 - 418x^8 - 88x^7 + 226x^6 + 6x^5 - 90x^4 + 7x^3 + 16x^2 - x - 1	\( 5^{11}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2} \)	22T47	Trivial (GRH)
22.14.191266300800812904024665746296529.1	x^22 - 11x^21 + 43x^20 - 45x^19 - 146x^18 + 402x^17 + 46x^16 - 1082x^15 + 512x^14 + 1700x^13 - 1234x^12 - 1826x^11 + 1419x^10 + 1403x^9 - 797x^8 - 807x^7 + 55x^6 + 331x^5 + 160x^4 - 51x^3 - 59x^2 - 14x - 1	\( 7\cdot 251\cdot 33893\cdot 1792166448977^{2} \)	22T53	Trivial (GRH)
22.14.315595142827230969392399757869056.1	x^22 - 12x^20 + 58x^18 - 144x^16 + 193x^14 - 130x^12 + 21x^10 + 40x^8 - 45x^6 + 18x^4 - 1	\( 2^{22}\cdot 8674315276967^{2} \)	22T51	Trivial (GRH)
22.14.316932538277153190033818958954496.1	x^22 - 14x^20 + 84x^18 - 285x^16 + 607x^14 - 843x^12 + 745x^10 - 363x^8 + 45x^6 + 29x^4 - 6x^2 - 1	\( 2^{22}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2} \)	22T51	Trivial (GRH)
22.14.1252214624578349298453638315804341.1	x^22 - 11x^21 + 34x^20 + 45x^19 - 419x^18 + 294x^17 + 2039x^16 - 2950x^15 - 5716x^14 + 11278x^13 + 10840x^12 - 25208x^11 - 15904x^10 + 35866x^9 + 19724x^8 - 31917x^7 - 19447x^6 + 15438x^5 + 12389x^4 - 1977x^3 - 3512x^2 - 887x - 59	\( 113\cdot 29739173\cdot 610429790897^{2} \)	22T53	Trivial (GRH)
22.14.4098058278162967431271914143428729.1	x^22 - 4x^21 - 7x^20 + 51x^19 - 43x^18 - 173x^17 + 600x^16 - 652x^15 - 2636x^14 + 6381x^13 + 6768x^12 - 16676x^11 - 7057x^10 + 24180x^9 + 2364x^8 - 20611x^7 - 494x^6 + 7657x^5 - 659x^4 - 998x^3 + 289x^2 - 29x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.14.4098058278162967431271914143428729.2	x^22 - 3x^21 - 14x^20 + 65x^19 - 57x^18 - 197x^17 + 729x^16 - 508x^15 - 1121x^14 + 1546x^13 - 935x^12 + 160x^11 + 1889x^10 - 975x^9 + 579x^8 + 80x^7 - 700x^6 + 99x^5 - 159x^4 - 75x^3 + 41x^2 + 15x + 1	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.14.7198079267989980836471065337135104.1	x^22 - 7x^20 - 7x^18 + 74x^16 + 2x^14 - 223x^12 + 52x^10 + 221x^8 - 86x^6 - 41x^4 + 14x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.14.7198079267989980836471065337135104.2	x^22 - 14x^20 + 64x^18 - 75x^16 - 198x^14 + 523x^12 - 122x^10 - 531x^8 + 386x^6 - 16x^4 - 16x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.14.7198079267989980836471065337135104.3	x^22 - 5x^20 - 20x^18 + 90x^16 + 144x^14 - 445x^12 - 333x^10 + 572x^8 - 107x^6 - 50x^4 + 15x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.14.7198079267989980836471065337135104.4	x^22 - 7x^20 - 7x^18 + 97x^16 - 21x^14 - 269x^12 + 29x^10 + 198x^8 - 40x^6 - 41x^4 + 14x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.14.7198079267989980836471065337135104.5	x^22 - 14x^20 + 64x^18 - 75x^16 - 175x^14 + 339x^12 + 200x^10 - 370x^8 - 166x^6 + 53x^4 + 7x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.14.7198079267989980836471065337135104.6	x^22 - 7x^20 - 7x^18 + 97x^16 - 67x^14 - 338x^12 + 512x^10 + 14x^8 - 362x^6 + 166x^4 - 9x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.14.13844017509319141075535476685799424.1	x^22 - 11x^20 + 43x^18 - 62x^16 - 16x^14 + 116x^12 - 53x^10 - 56x^8 + 32x^6 + 10x^4 - 4x^2 - 1	\( 2^{22}\cdot 233^{2}\cdot 246572816873^{2} \)	22T51	Trivial (GRH)
22.14.17471883970840462300304775614373553.1	x^22 - 8x^21 + 12x^20 + 43x^19 - 133x^18 + 143x^17 - 51x^16 - 1197x^15 + 2298x^14 + 2198x^13 - 4854x^12 - 1488x^11 + 3269x^10 - 955x^9 - 610x^8 + 2045x^7 + 101x^6 - 1059x^5 - 151x^4 + 211x^3 + 62x^2 - x - 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.14.17471883970840462300304775614373553.2	x^22 - x^21 - 14x^20 + 62x^18 + 129x^17 - 52x^16 - 983x^15 + 160x^14 + 2384x^13 - 603x^12 - 2192x^11 - 1350x^10 + 4200x^9 + 91x^8 - 3234x^7 + 1064x^6 + 775x^5 - 416x^4 - 33x^3 + 39x^2 - x - 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.14.17471883970840462300304775614373553.3	x^22 - x^21 - 26x^20 + 49x^19 + 237x^18 - 701x^17 - 634x^16 + 4156x^15 - 2565x^14 - 9376x^13 + 16978x^12 - 1217x^11 - 24957x^10 + 25854x^9 + 3793x^8 - 25081x^7 + 13524x^6 + 5616x^5 - 7257x^4 + 961x^3 + 908x^2 - 278x + 11	\( 1297^{11} \)	22T29	Trivial (GRH)
22.14.117878729824697053517614720214892544.1	x^22 - 8x^20 + 16x^18 + 21x^16 - 100x^14 + 69x^12 + 67x^10 - 76x^8 - 4x^6 + 17x^4 - x^2 - 1	\( 2^{22}\cdot 233^{2}\cdot 937^{2}\cdot 5279^{2}\cdot 145459^{2} \)	22T51	Trivial (GRH)
22.14.165555823163769559238834502754107392.1	x^22 - 69x^18 + 115x^16 + 1265x^14 - 3680x^12 - 1426x^10 + 9752x^8 - 4646x^6 - 2369x^4 + 943x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.14.165555823163769559238834502754107392.2	x^22 - 69x^18 + 207x^16 + 368x^14 - 1863x^12 + 920x^10 + 3036x^8 - 4186x^6 + 1794x^4 - 184x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.14.165555823163769559238834502754107392.3	x^22 - 46x^18 - 23x^16 + 552x^14 + 115x^12 - 2093x^10 + 759x^8 + 2070x^6 - 1633x^4 + 368x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.14.165555823163769559238834502754107392.4	x^22 - 69x^18 + 138x^16 + 897x^14 - 2553x^12 - 575x^10 + 5934x^8 - 4002x^6 + 368x^4 + 161x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.14.165555823163769559238834502754107392.5	x^22 - 92x^18 + 345x^16 + 690x^14 - 4301x^12 + 1012x^10 + 13156x^8 - 11523x^6 - 322x^4 + 414x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.14.22661033510180079603495293971842498241.3	x^22 - 7x^21 - 9x^20 + 171x^19 - 276x^18 - 1022x^17 + 3668x^16 - 1134x^15 - 10988x^14 + 19765x^13 - 17789x^12 + 6x^11 + 111532x^10 - 268518x^9 - 21573x^8 + 707388x^7 - 501170x^6 - 789327x^5 + 795886x^4 + 400629x^3 - 428800x^2 - 69431x + 68279	\( 1297^{12} \)	22T30	Trivial (GRH)
22.14.56501459388151144478039723653407440896.1	x^22 - 6x^20 - 8x^18 + 116x^16 - 174x^14 - 339x^12 + 1060x^10 - 606x^8 - 386x^6 + 335x^4 + 7x^2 - 25	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.14.56501459388151144478039723653407440896.2	x^22 - 15x^20 + 49x^18 + 116x^16 - 777x^14 + 894x^12 + 527x^10 - 1202x^8 + 244x^6 + 212x^4 - 65x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.14.56501459388151144478039723653407440896.3	x^22 - 5x^20 - 49x^18 + 168x^16 + 746x^14 - 1298x^12 - 2537x^10 + 4881x^8 + 681x^6 - 5264x^4 + 3300x^2 - 625	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.14.56501459388151144478039723653407440896.4	x^22 - x^20 - 23x^18 + 27x^16 + 145x^14 - 193x^12 - 240x^10 + 421x^8 - 162x^6 + 9x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.14.282507296940755722390198618267037204480.1	x^22 - 5x^20 - 4x^18 + 54x^16 - 53x^14 - 127x^12 + 208x^10 + 69x^8 - 222x^6 + 29x^4 + 56x^2 - 5	\( 2^{22}\cdot 5\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.14.385779698695997532665150300037698289664.1	x^22 - 220x^18 - 572x^16 + 6468x^14 - 880x^12 - 27676x^10 + 33396x^8 - 15136x^6 + 2904x^4 - 176x^2 - 4	\( 2^{24}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.1543118794783990130660601200150793158656.1	x^22 - 33x^20 + 143x^18 - 22x^17 + 385x^16 - 2222x^15 - 902x^14 + 14586x^13 - 3234x^12 + 94x^11 - 39512x^10 - 28006x^9 + 136862x^8 - 99286x^7 - 30151x^6 + 136136x^5 - 99561x^4 - 13794x^3 + 44385x^2 - 17182x + 2039	\( 2^{26}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.4299288794103243236127943577240214703609.1	x^22 - 9x^21 - 5x^20 + 230x^19 - 343x^18 - 2094x^17 + 5295x^16 + 8119x^15 - 33602x^14 - 6253x^13 + 119287x^12 - 91272x^11 - 182743x^10 + 403919x^9 - 287584x^8 - 116709x^7 + 557374x^6 - 666253x^5 + 340515x^4 + 15415x^3 - 98010x^2 + 39788x - 5047	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.14.4299288794103243236127943577240214703609.2	x^22 - 6x^21 - 17x^20 + 128x^19 + 36x^18 - 939x^17 + 1324x^16 + 1351x^15 - 14113x^14 + 19961x^13 + 63677x^12 - 139022x^11 - 153919x^10 + 426871x^9 + 228955x^8 - 682443x^7 - 246758x^6 + 494621x^5 + 166486x^4 - 90530x^3 - 15247x^2 + 1575x + 49	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.14.6172475179135960522642404800603172634624.1	x^22 - 33x^20 - 44x^19 + 253x^18 + 660x^17 + 1177x^16 + 2992x^15 - 2266x^14 - 27214x^13 - 75812x^12 - 258772x^11 - 808192x^10 - 1679018x^9 - 2491038x^8 - 3007114x^7 - 3012009x^6 - 2244528x^5 - 1081113x^4 - 281710x^3 - 22011x^2 + 4268x + 561	\( 2^{28}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.7062682423518893059754965456675930112000.1	x^22 - 12x^20 - 29x^18 + 759x^16 - 1847x^14 - 5157x^12 + 22844x^10 - 17301x^8 - 12609x^6 + 12000x^4 - 1775x^2 - 125	\( 2^{22}\cdot 5^{3}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.14.11415669953671419566832206870342147244032.1	x^22 - 6x^21 - 5x^20 + 90x^19 - 75x^18 - 502x^17 + 754x^16 + 1304x^15 - 2700x^14 - 1626x^13 + 4915x^12 + 730x^11 - 4996x^10 + 344x^9 + 2915x^8 - 496x^7 - 983x^6 + 192x^5 + 193x^4 - 32x^3 - 21x^2 + 2x + 1	\( 2^{33}\cdot 7\cdot 5926651993\cdot 32033476985376969871 \)	22T57	Trivial (GRH)
22.14.24689900716543842090569619202412690538496.1	x^22 - 11x^20 - 55x^18 - 154x^17 + 517x^16 + 1628x^15 + 3058x^14 + 2332x^13 - 6160x^12 - 33934x^11 - 105996x^10 - 79684x^9 + 136972x^8 + 243364x^7 + 221111x^6 + 106920x^5 - 143297x^4 - 191466x^3 - 62843x^2 - 5258x + 245	\( 2^{30}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.24689900716543842090569619202412690538496.2	x^22 - 44x^20 - 22x^19 + 660x^18 + 704x^17 - 4048x^16 - 8448x^15 + 10516x^14 + 48312x^13 - 15180x^12 - 118720x^11 + 17776x^10 + 67408x^9 + 84392x^8 + 3696x^7 - 151976x^6 - 9328x^5 + 131648x^4 + 71104x^3 + 8976x^2 - 704x - 48	\( 2^{30}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.24689900716543842090569619202412690538496.3	x^22 - 11x^20 - 44x^19 - 33x^18 + 748x^17 + 869x^16 - 3630x^15 - 6578x^14 + 7018x^13 + 25894x^12 - 17722x^11 - 24992x^10 - 3784x^9 + 25476x^8 + 25014x^7 - 29799x^6 - 9218x^5 + 10329x^4 + 1870x^3 - 1133x^2 - 264x - 13	\( 2^{30}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.24689900716543842090569619202412690538496.4	x^22 - 22x^20 - 22x^19 - 44x^18 - 374x^17 + 2970x^16 + 15444x^15 + 2442x^14 - 88748x^13 - 127732x^12 + 115336x^11 + 383570x^10 + 156442x^9 - 287386x^8 - 325028x^7 - 118162x^6 + 23628x^5 + 120978x^4 + 79508x^3 - 17270x^2 - 9416x + 1554	\( 2^{30}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.14.95495132016543203413964761918289025880897.1	x^22 - 3x^21 - 29x^20 + 26x^19 + 420x^18 + 885x^17 - 3122x^16 - 19486x^15 - 3640x^14 + 188637x^13 + 243555x^12 - 1052571x^11 - 1941345x^10 + 3343356x^9 + 7877194x^8 - 4368623x^7 - 16343655x^6 - 3154416x^5 + 10462530x^4 + 4628676x^3 - 1677053x^2 - 994739x - 67717	\( 97\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.14.101482802839751113302452158783383633133568.1	x^22 - 2x^21 - 21x^20 + 32x^19 + 193x^18 - 192x^17 - 983x^16 + 496x^15 + 2915x^14 - 344x^13 - 4994x^12 - 730x^11 + 4915x^10 + 1626x^9 - 2700x^8 - 1304x^7 + 754x^6 + 502x^5 - 77x^4 - 90x^3 - 5x^2 + 6x + 1	\( 2^{33}\cdot 1721\cdot 9473\cdot 146628265753\cdot 4942156467121 \)	22T57	Trivial (GRH)
22.14.176567060587972326493874136416898252800000.1	x^22 - 43x^20 + 447x^18 + 746x^16 - 22193x^14 + 39852x^12 + 120052x^10 - 99825x^8 - 76100x^6 + 38750x^4 + 10625x^2 - 3125	\( 2^{22}\cdot 5^{5}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.14.176567060587972326493874136416898252800000.2	x^22 - 17x^20 - 190x^18 + 2055x^16 + 1860x^14 - 40912x^12 + 25031x^10 + 170900x^8 - 29700x^6 - 113125x^4 + 38125x^2 - 3125	\( 2^{22}\cdot 5^{5}\cdot 1297^{10} \)	22T32	Trivial (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)