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 69)

Label	Polynomial	Discriminant	Galois group	Class group
22.12.10994531599582075769676214829056.1	x^22 - 10x^20 + 44x^18 - 112x^16 + 182x^14 - 199x^12 + 151x^10 - 67x^8 - 13x^6 + 36x^4 - 13x^2 + 1	\( -\,2^{22}\cdot 1619043113033^{2} \)	22T53	Trivial (GRH)
22.12.10994531599582075769676214829056.2	x^22 - 12x^20 + 64x^18 - 200x^16 + 406x^14 - 557x^12 + 507x^10 - 271x^8 + 51x^6 + 18x^4 - 9x^2 + 1	\( -\,2^{22}\cdot 1619043113033^{2} \)	22T53	Trivial (GRH)
22.12.87192729322616328324934343477207.1	x^22 - 4x^21 - 7x^20 + 74x^19 - 135x^18 - 196x^17 + 1152x^16 - 1457x^15 - 1072x^14 + 5185x^13 - 5192x^12 - 461x^11 + 5455x^10 - 5559x^9 + 2042x^8 + 1469x^7 + 196x^6 - 5039x^5 + 4907x^4 - 446x^3 - 1666x^2 + 891x - 137	\( -\,23^{21}\cdot 47^{2} \)	22T28	Trivial (GRH)
22.12.87192729322616328324934343477207.2	x^22 - 3x^21 - 14x^20 + 65x^19 + 12x^18 - 404x^17 + 384x^16 + 1079x^15 - 1857x^14 - 1536x^13 + 4746x^12 + 574x^11 - 8668x^10 + 4752x^9 + 8353x^8 - 11765x^7 + 174x^6 + 9989x^5 - 6254x^4 - 2191x^3 + 3353x^2 - 560x - 229	\( -\,23^{21}\cdot 47^{2} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.1	x^22 - x^21 + 8x^20 + x^19 - 10x^18 + 79x^17 - 234x^16 + 293x^15 - 293x^14 - 441x^13 + 1283x^12 - 1700x^11 + 1629x^10 + 2222x^9 - 4511x^8 - 315x^7 + 2661x^6 - 55x^5 - 669x^4 - 21x^3 + 68x^2 + 7x - 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.2	x^22 - 9x^21 + 23x^20 + 32x^19 - 251x^18 + 219x^17 + 915x^16 - 1739x^15 - 1820x^14 + 6548x^13 + 969x^12 - 16878x^11 + 9906x^10 + 22070x^9 - 29522x^8 - 3288x^7 + 25694x^6 - 12946x^5 - 3524x^4 + 4687x^3 - 1081x^2 - 6x + 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.3	x^22 - 8x^21 + 12x^20 + 46x^19 - 109x^18 - 114x^17 + 165x^16 + 756x^15 + 9x^14 - 3299x^13 - 666x^12 + 8067x^11 + 4331x^10 - 16061x^9 - 4342x^8 + 13658x^7 + 3196x^6 - 4458x^5 - 1074x^4 + 552x^3 + 42x^2 - 12x - 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.4	x^22 - 5x^21 - 10x^20 + 78x^19 + 30x^18 - 586x^17 + 91x^16 + 3136x^15 - 3117x^14 - 7084x^13 + 12319x^12 + 6022x^11 - 23809x^10 + 9384x^9 + 15063x^8 - 18488x^7 + 10061x^6 - 2016x^5 - 5851x^4 + 8564x^3 - 4987x^2 + 1340x - 137	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.5	x^22 - 7x^21 + 10x^20 + 16x^19 - 10x^18 - 184x^17 + 468x^16 - 58x^15 - 1272x^14 + 816x^13 + 2227x^12 - 2216x^11 - 2463x^10 + 2895x^9 + 2624x^8 - 1329x^7 - 2547x^6 - 368x^5 + 990x^4 + 174x^3 - 144x^2 + 9x + 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.6	x^22 - 10x^21 + 42x^20 - 88x^19 + 26x^18 + 460x^17 - 1667x^16 + 3076x^15 - 2650x^14 - 1948x^13 + 9671x^12 - 13923x^11 + 7597x^10 + 7283x^9 - 18181x^8 + 15029x^7 - 2411x^6 - 6693x^5 + 6866x^4 - 3122x^3 + 705x^2 - 65x + 1	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.178176446876650757881387571453423.7	x^22 - 7x^21 + 8x^20 + 58x^19 - 243x^18 + 346x^17 + 333x^16 - 2299x^15 + 3786x^14 - 920x^13 - 7580x^12 + 14118x^11 - 5659x^10 - 17342x^9 + 33608x^8 - 19265x^7 - 19737x^6 + 44371x^5 - 35838x^4 + 14864x^3 - 2259x^2 - 482x + 139	\( -\,23^{20}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.12.237871803919090816246272099352576.1	x^22 - 12x^20 + 59x^18 - 151x^16 + 204x^14 - 106x^12 - 64x^10 + 101x^8 - 19x^6 - 16x^4 + 3x^2 + 1	\( -\,2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T53	Trivial (GRH)
22.12.1288033148279983900699565800554496.1	x^22 - 8x^20 + 24x^18 - 28x^16 - 12x^14 + 66x^12 - 48x^10 - 28x^8 + 43x^6 - 3x^4 - 7x^2 + 1	\( -\,2^{22}\cdot 17524013040643^{2} \)	22T53	Trivial (GRH)
22.12.7198079267989980836471065337135104.1	x^22 - 2x^20 - 17x^18 + 26x^16 + 93x^14 - 91x^12 - 180x^10 + 87x^8 + 59x^6 - 21x^4 - 3x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.12.7198079267989980836471065337135104.2	x^22 - x^20 - 33x^18 + 55x^16 + 243x^14 - 373x^12 - 608x^10 + 633x^8 + 334x^6 - 222x^4 + 17x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.12.7198079267989980836471065337135104.3	x^22 + 7x^20 - 7x^18 - 97x^16 + 48x^14 + 476x^12 - 454x^10 - 704x^8 + 1317x^6 - 718x^4 + 129x^2 + 1	\( -\,2^{22}\cdot 23^{20} \)	22T28	Trivial (GRH)
22.12.12701184200335173359101913935642624.1	x^22 - 7x^20 + 11x^18 + 20x^16 - 54x^14 - 17x^12 + 80x^10 + 11x^8 - 43x^6 - 9x^4 + 5x^2 + 1	\( -\,2^{22}\cdot 55029067682009^{2} \)	22T53	Trivial (GRH)
22.12.12701184200335173359101913935642624.2	x^22 - 4x^20 - 4x^18 + 31x^16 - 8x^14 - 81x^12 + 48x^10 + 88x^8 - 60x^6 - 35x^4 + 22x^2 + 1	\( -\,2^{22}\cdot 55029067682009^{2} \)	22T53	Trivial (GRH)
22.12.548480837855418232714401433337724928.1	x^22 - 2x^21 - 15x^20 + 28x^19 + 98x^18 - 162x^17 - 370x^16 + 496x^15 + 903x^14 - 844x^13 - 1496x^12 + 726x^11 + 1679x^10 - 122x^9 - 1197x^8 - 302x^7 + 462x^6 + 244x^5 - 62x^4 - 68x^3 - 5x^2 + 6x + 1	\( -\,2^{33}\cdot 7\cdot 113\cdot 66841\cdot 1207680851138975089 \)	22T57	Trivial (GRH)
22.12.640136435131832537454172869677734375.1	x^22 - 22x^20 + 209x^18 - 1122x^16 + 3740x^14 - 8008x^12 - 3x^11 + 11011x^10 + 33x^9 - 9438x^8 - 132x^7 + 4719x^6 + 231x^5 - 1210x^4 - 165x^3 + 121x^2 + 33x + 1	\( -\,5^{11}\cdot 11^{27} \)	22T20	Trivial (GRH)
22.12.954120607243639301569748987902164992.1	x^22 - 2x^21 - 21x^20 + 32x^19 + 193x^18 - 192x^17 - 983x^16 + 496x^15 + 2915x^14 - 344x^13 - 4994x^12 - 730x^11 + 4913x^10 + 1626x^9 - 2700x^8 - 1304x^7 + 754x^6 + 502x^5 - 75x^4 - 90x^3 - 5x^2 + 6x + 1	\( -\,2^{33}\cdot 71979199\cdot 1543143840124960849 \)	22T57	Trivial (GRH)
22.12.9841858708691628205709619862255859375.1	x^22 - 22x^20 + 209x^18 - 1122x^16 + 3740x^14 - 8008x^12 - 5x^11 + 11011x^10 + 55x^9 - 9438x^8 - 220x^7 + 4719x^6 + 385x^5 - 1210x^4 - 275x^3 + 121x^2 + 55x + 5	\( -\,5^{11}\cdot 11^{22}\cdot 19^{5} \)	22T20	Trivial (GRH)
22.12.56501459388151144478039723653407440896.1	x^22 - 5x^20 - 34x^18 + 42x^16 + 227x^14 - 96x^12 - 468x^10 + 59x^8 + 226x^6 - 53x^4 - 9x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.2	x^22 + 12x^20 - 9x^18 - 292x^16 + 315x^14 + 1323x^12 - 1408x^10 - 1431x^8 + 1122x^6 - 19x^4 - 30x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.3	x^22 + 9x^20 - 15x^18 - 204x^16 + 41x^14 + 1197x^12 + 373x^10 - 1423x^8 - 275x^6 + 468x^4 - 52x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.4	x^22 + x^20 - 41x^18 + 29x^16 + 336x^14 - 382x^12 - 647x^10 + 1003x^8 - 70x^6 - 340x^4 + 108x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.5	x^22 - 9x^20 + 12x^18 + 72x^16 - 184x^14 - 61x^12 + 443x^10 - 126x^8 - 340x^6 + 120x^4 + 76x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.6	x^22 + 2x^20 - 56x^18 - 245x^16 + 126x^14 + 1903x^12 + 1997x^10 - 1141x^8 - 1026x^6 + 464x^4 - 41x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.7	x^22 - 17x^20 + 86x^18 - 77x^16 - 371x^14 + 333x^12 + 807x^10 + 186x^8 - 158x^6 - 64x^4 - 2x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.8	x^22 - 16x^20 + 66x^18 + 76x^16 - 768x^14 + 416x^12 + 1381x^10 - 644x^8 - 483x^6 - 19x^4 + 14x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.9	x^22 - 2x^20 - 73x^18 + 332x^16 - 46x^14 - 1522x^12 + 1480x^10 + 1528x^8 - 1814x^6 - 620x^4 + 584x^2 + 121	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.10	x^22 - 6x^20 - 17x^18 + 153x^16 - 125x^14 - 483x^12 + 423x^10 + 426x^8 - 132x^6 - 53x^4 + 9x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.11	x^22 - 7x^20 - 6x^18 + 95x^16 - 21x^14 - 397x^12 + 82x^10 + 581x^8 + 43x^6 - 160x^4 - 27x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.56501459388151144478039723653407440896.12	x^22 - 19x^20 + 30x^18 + 427x^16 - 1235x^14 - 833x^12 + 3553x^10 + 222x^8 - 2608x^6 + 298x^4 + 42x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.12.43207326253951723658496833604222208442368.1	x^22 - 33x^20 + 451x^18 - 3575x^16 + 19338x^14 - 74074x^12 - 2852x^11 + 200662x^10 + 23496x^9 - 379214x^8 - 35640x^7 + 458469x^6 - 29568x^5 - 295317x^4 + 77132x^3 + 71159x^2 - 32472x + 2545	\( -\,2^{28}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
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)
22.12.67897226970495565749066452806634898980864.1	x^22 - 22x^20 + 220x^18 - 1584x^16 + 8448x^14 - 32032x^12 - 2852x^11 + 97152x^10 + 18084x^9 - 192896x^8 + 65120x^7 + 281600x^6 - 205568x^5 - 197120x^4 + 162272x^3 + 33792x^2 - 40128x + 6044	\( -\,2^{28}\cdot 7^{10}\cdot 11^{23} \)	22T37	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)
22.12.395038411464701473449113907238603048615936.1	x^22 + 22x^20 - 1672x^16 + 308x^14 + 24904x^12 - 42020x^10 - 12672x^8 + 47916x^6 - 18128x^4 - 484x^2 + 324	\( -\,2^{34}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.395038411464701473449113907238603048615936.2	x^22 - 132x^18 + 5104x^14 + 704x^12 - 72512x^10 - 22528x^8 + 301312x^6 + 129536x^4 - 202752x^2 + 25600	\( -\,2^{34}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.1580153645858805893796455628954412194463744.1	x^22 - 22x^20 - 44x^18 + 1892x^16 - 3740x^14 - 33968x^12 + 112464x^10 + 18480x^8 - 226336x^6 + 9152x^4 + 10032x^2 + 16	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.1580153645858805893796455628954412194463744.2	x^22 - 11x^20 - 275x^18 + 1529x^16 + 22814x^14 - 2178x^12 - 137698x^10 + 20262x^8 + 180081x^6 - 29315x^4 + 517x^2 + 1	\( -\,2^{36}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (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)
22.12.2765268880252910314143797350670221340311552.1	x^22 - 33x^20 + 33x^18 + 3751x^16 + 16654x^14 + 4818x^12 - 68354x^10 - 35706x^8 + 96261x^6 + 1683x^4 - 13079x^2 + 1183	\( -\,2^{34}\cdot 7^{11}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.6320614583435223575185822515817648777854976.1	x^22 - 220x^18 - 506x^16 + 6380x^14 + 14916x^12 - 26136x^10 - 44396x^8 + 40700x^6 + 30140x^4 - 24728x^2 + 2500	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (GRH)
22.12.6320614583435223575185822515817648777854976.2	x^22 - 132x^18 - 66x^16 + 4840x^14 + 4312x^12 - 43648x^10 - 24156x^8 + 144188x^6 + 10736x^4 - 162668x^2 + 66564	\( -\,2^{38}\cdot 7^{10}\cdot 11^{22} \)	22T37	Trivial (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)
22.12.15646172003756569249283257910156250000000000.2	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)
22.12.15646172003756569249283257910156250000000000.3	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)