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 62)

Label	Polynomial	Discriminant	Galois group	Class group
22.2.10787252710010591209601111089.1	x^22 - x^21 + x^20 - 11x^19 - 5x^18 + 22x^17 + 22x^16 + 62x^15 - 83x^14 - 148x^13 + 44x^12 + 72x^11 + 52x^10 + 25x^9 + 50x^8 - 75x^7 - 65x^6 + 60x^5 - 17x^3 + 17x^2 - 7x + 1	\( 167^{10}\cdot 639361 \)	22T32	Trivial (GRH)
22.0.70765994783241803539463274496.2	x^22 + 3x^20 + 4x^18 + 4x^16 + 11x^14 + 10x^12 + 4x^10 + 12x^8 + 7x^6 + 6x^4 + 4x^2 + 1	\( -\,2^{22}\cdot 167^{10} \)	22T32	Trivial (GRH)
22.0.70765994783241803539463274496.3	x^22 + x^20 - 7x^18 - 6x^16 + 23x^14 + x^12 - 24x^10 + 21x^8 - 17x^6 + 9x^4 - 2x^2 + 1	\( -\,2^{22}\cdot 167^{10} \)	22T32	Trivial (GRH)
22.2.1627617880014561481407655313408.1	x^22 - 10x^20 + 45x^18 - 125x^16 + 250x^14 - 392x^12 + 498x^10 - 516x^8 + 428x^6 - 264x^4 + 107x^2 - 23	\( 2^{22}\cdot 23\cdot 167^{10} \)	22T32	Trivial (GRH)
22.4.1539829330034588067972966835892211043.1	x^22 - 11x^21 + 72x^20 - 335x^19 + 1211x^18 - 3546x^17 + 8610x^16 - 17574x^15 + 30322x^14 - 44228x^13 + 54150x^12 - 54734x^11 + 44075x^10 - 25887x^9 + 7693x^8 + 4031x^7 - 7645x^6 + 6006x^5 - 3064x^4 + 1060x^3 - 235x^2 + 28x - 1	\( -\,151\cdot 757\cdot 1297^{10} \)	22T32	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)
22.12.56501459388151144478039723653407440896.1	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)
22.16.56501459388151144478039723653407440896.1	x^22 - 17x^20 + 76x^18 + 4x^16 - 654x^14 + 958x^12 + 990x^10 - 2740x^8 + 855x^6 + 1065x^4 - 556x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.20.56501459388151144478039723653407440896.1	x^22 - 25x^20 + 250x^18 - 1243x^16 + 2879x^14 - 334x^12 - 14126x^10 + 33691x^8 - 35857x^6 + 18585x^4 - 4105x^2 + 289	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.4.56501459388151144478039723653407440896.1	x^22 + 14x^20 + 48x^18 - 43x^16 - 492x^14 - 675x^12 + 603x^10 + 2355x^8 + 2294x^6 + 937x^4 + 136x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.1	x^22 + 16x^20 + 62x^18 - 216x^16 - 1948x^14 - 3000x^12 + 4363x^10 + 9892x^8 - 2285x^6 - 747x^4 + 4x^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)
22.16.56501459388151144478039723653407440896.2	x^22 - 17x^20 + 74x^18 + 62x^16 - 919x^14 + 1316x^12 + 196x^10 - 1389x^8 + 887x^6 - 194x^4 + 7x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.20.56501459388151144478039723653407440896.2	x^22 - 28x^20 + 296x^18 - 1503x^16 + 3716x^14 - 3348x^12 - 2647x^10 + 7446x^8 - 5457x^6 + 1686x^4 - 192x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.2	x^22 + 16x^20 + 46x^18 - 346x^16 - 2536x^14 - 5981x^12 - 4843x^10 + 1475x^8 + 2688x^6 - 302x^4 - 144x^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)
22.16.56501459388151144478039723653407440896.3	x^22 - 17x^20 + 56x^18 + 103x^16 - 578x^14 + 31x^12 + 1647x^10 - 963x^8 - 1208x^6 + 1034x^4 - 112x^2 + 1	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.3	x^22 + 9x^20 - 34x^18 - 335x^16 + 207x^14 + 3414x^12 + 981x^10 - 8064x^8 + 51x^6 + 3070x^4 + 710x^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)
22.16.56501459388151144478039723653407440896.4	x^22 - 14x^20 + 39x^18 + 167x^16 - 805x^14 - 22x^12 + 3282x^10 - 2173x^8 - 3246x^6 + 3447x^4 - 852x^2 + 25	\( -\,2^{22}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.8.56501459388151144478039723653407440896.4	x^22 + 9x^20 - 9x^18 - 259x^16 - 351x^14 + 1960x^12 + 4198x^10 - 1414x^8 - 4092x^6 - 774x^4 + 197x^2 + 25	\( -\,2^{22}\cdot 1297^{10} \)	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)
22.8.56501459388151144478039723653407440896.5	x^22 - 7x^20 - 72x^18 - 36x^16 + 711x^14 + 1469x^12 - 353x^10 - 3136x^8 - 2011x^6 + 858x^4 + 1172x^2 + 289	\( -\,2^{22}\cdot 1297^{10} \)	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)
22.8.56501459388151144478039723653407440896.6	x^22 + 6x^20 - 87x^18 - 904x^16 - 2836x^14 - 3349x^12 - 591x^10 + 1601x^8 + 959x^6 + 43x^4 - 47x^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)
22.8.56501459388151144478039723653407440896.7	x^22 + x^20 - 89x^18 + 172x^16 + 1434x^14 - 3373x^12 - 5614x^10 + 7890x^8 + 12675x^6 + 3940x^4 + 219x^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)
22.8.56501459388151144478039723653407440896.8	x^22 + 4x^20 - 67x^18 - 65x^16 + 801x^14 + 697x^12 - 3324x^10 - 3913x^8 + 3601x^6 + 7419x^4 + 3784x^2 + 625	\( -\,2^{22}\cdot 1297^{10} \)	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)
22.14.282507296940755722390198618267037204480.1	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)
22.6.1638542322256383189863151985948815785984.1	x^22 + 16x^20 + 101x^18 + 300x^16 + 301x^14 - 580x^12 - 1949x^10 - 1883x^8 - 328x^6 + 387x^4 + 80x^2 - 29	\( 2^{22}\cdot 29\cdot 1297^{10} \)	22T32	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)
22.10.7062682423518893059754965456675930112000.1	x^22 - x^20 - 143x^18 + 101x^16 + 5979x^14 - 2898x^12 - 68016x^10 + 70946x^8 + 77468x^6 + 10420x^4 - 775x^2 - 125	\( 2^{22}\cdot 5^{3}\cdot 1297^{10} \)	22T32	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)
22.10.7062682423518893059754965456675930112000.2	x^22 - x^20 - 95x^18 - 245x^16 + 1309x^14 + 5175x^12 - 515x^10 - 17702x^8 - 12109x^6 + 5200x^4 + 250x^2 - 125	\( 2^{22}\cdot 5^{3}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.10.7062682423518893059754965456675930112000.3	x^22 - 3x^20 - 75x^18 + 197x^16 + 1892x^14 - 3669x^12 - 19581x^10 + 18944x^8 + 69583x^6 + 8985x^4 - 1300x^2 - 125	\( 2^{22}\cdot 5^{3}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.10.7062682423518893059754965456675930112000.4	x^22 + 7x^20 - 33x^18 - 240x^16 + 448x^14 + 2512x^12 - 3317x^10 - 6568x^8 + 6624x^6 + 2235x^4 - 675x^2 - 125	\( 2^{22}\cdot 5^{3}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.2.26386181534266584471244550946141274898432.1	x^22 + 28x^20 + 341x^18 + 2376x^16 + 10477x^14 + 30512x^12 + 59347x^10 + 75927x^8 + 60744x^6 + 26813x^4 + 4280x^2 - 467	\( 2^{22}\cdot 467\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.10.176567060587972326493874136416898252800000.1	x^22 + 22x^20 - 125x^18 - 3424x^16 - 15641x^14 - 11801x^12 + 53721x^10 + 67470x^8 - 67150x^6 - 62500x^4 + 49375x^2 - 3125	\( 2^{22}\cdot 5^{5}\cdot 1297^{10} \)	22T32	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)
22.6.176567060587972326493874136416898252800000.1	x^22 + 40x^20 + 510x^18 + 878x^16 - 29393x^14 - 208069x^12 - 262302x^10 + 1411560x^8 + 3529300x^6 - 1343500x^4 - 7430625x^2 - 3003125	\( 2^{22}\cdot 5^{5}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.10.176567060587972326493874136416898252800000.2	x^22 - 19x^20 - 147x^18 + 2747x^16 + 11007x^14 - 95394x^12 - 336467x^10 + 923410x^8 + 2888250x^6 - 1883125x^4 - 2819375x^2 - 378125	\( 2^{22}\cdot 5^{5}\cdot 1297^{10} \)	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)
22.10.1378014093017618262674910820182954076012544.1	x^22 + 52x^20 + 780x^18 + 1155x^16 - 30984x^14 + 41420x^12 + 107934x^10 - 185407x^8 - 82238x^6 + 204914x^4 - 34481x^2 - 24389	\( 2^{22}\cdot 29^{3}\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.22.3102551636462767494433639265532255987040256.1	x^22 - 38x^20 + 641x^18 - 6318x^16 + 40285x^14 - 173650x^12 + 512983x^10 - 1028619x^8 + 1350984x^6 - 1075867x^4 + 438092x^2 - 54911	\( 2^{22}\cdot 43\cdot 1277\cdot 1297^{10} \)	22T32	Trivial (GRH)
22.10.4414176514699308162346853410422456320000000.1	x^22 + 27x^20 - 135x^18 - 6202x^16 - 11519x^14 + 276940x^12 + 499375x^10 - 3850750x^8 - 4878750x^6 + 13925000x^4 + 6890625x^2 - 1953125	\( 2^{22}\cdot 5^{7}\cdot 1297^{10} \)	22T32	Trivial (GRH)