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 245)

Label	Polynomial	Discriminant	Galois group	Class group
20.14.2854696149767119301830443008.1	x^20 - 5x^19 + 5x^18 + 14x^17 - 55x^16 + 81x^15 + 28x^14 - 281x^13 + 368x^12 + x^11 - 699x^10 + 872x^9 + 242x^8 - 1190x^7 + 324x^6 + 650x^5 - 277x^4 - 157x^3 + 67x^2 + 14x - 4	\( -\,2^{16}\cdot 83^{4}\cdot 983^{5} \)	20T992	Trivial (GRH)
20.14.2854696149767119301830443008.2	x^20 - 5x^19 + 3x^18 + 20x^17 - 34x^16 + 16x^15 + 11x^14 - 155x^13 + 216x^12 + 203x^11 - 282x^10 - 69x^9 - 236x^8 + 87x^7 + 636x^6 - 241x^5 - 374x^4 + 179x^3 + 55x^2 - 36x + 4	\( -\,2^{16}\cdot 83^{4}\cdot 983^{5} \)	20T992	Trivial (GRH)
20.14.3698056327053752876991753216.1	x^20 - 11x^18 + 22x^16 + 88x^14 - 264x^12 + 22x^10 + 374x^8 - 253x^6 - 22x^4 + 55x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.14.3698056327053752876991753216.2	x^20 - 33x^16 + 33x^14 + 253x^12 - 616x^10 + 363x^8 + 231x^6 - 341x^4 + 121x^2 - 11	\( -\,2^{10}\cdot 3^{10}\cdot 11^{19} \)	20T409	Trivial (GRH)
20.14.5278844430406469058634448896.1	x^20 - 12x^18 + 57x^16 - 136x^14 + 168x^12 - 90x^10 - 14x^8 + 51x^6 - 35x^4 + 10x^2 - 1	\( -\,2^{20}\cdot 11^{16}\cdot 331^{2} \)	20T846	Trivial (GRH)
20.14.7711305966949474347885177419.1	x^20 - 10x^19 + 30x^18 + 15x^17 - 243x^16 + 312x^15 + 496x^14 - 1282x^13 - 141x^12 + 2094x^11 - 590x^10 - 1841x^9 + 678x^8 + 1032x^7 - 268x^6 - 398x^5 + 34x^4 + 84x^3 + 4x^2 - 7x - 1	\( -\,31\cdot 47\cdot 67\cdot 211^{2}\cdot 36497^{4} \)	20T1015	Trivial (GRH)
20.14.7753892385981245440000000000.1	x^20 - 11x^18 + 44x^16 - 71x^14 + 11x^12 + 92x^10 - 84x^8 + 16x^6 - 2x^4 + 4x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 27517559^{2} \)	20T1045	Trivial (GRH)
20.14.9297543283501805026208859136.1	x^20 - 10x^18 + 15x^16 + 109x^14 - 292x^12 - 215x^10 + 954x^8 - 377x^6 - 357x^4 + 196x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T846	Trivial (GRH)
20.14.9297543283501805026208859136.2	x^20 - 9x^18 + 5x^16 + 113x^14 - 305x^12 + 204x^10 + 127x^8 - 153x^6 + 7x^4 + 10x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T846	Trivial (GRH)
20.14.9297543283501805026208859136.3	x^20 - 5x^18 - 5x^16 + 50x^14 - 17x^12 - 145x^10 + 106x^8 + 109x^6 - 129x^4 + 35x^2 - 1	\( -\,2^{10}\cdot 11^{16}\cdot 14057^{2} \)	20T846	Trivial (GRH)
20.14.9428099289122298266741899264.1	x^20 - 11x^18 + 50x^16 - 121x^14 + 161x^12 - 85x^10 - 75x^8 + 158x^6 - 97x^4 + 19x^2 - 1	\( -\,2^{20}\cdot 111847^{2}\cdot 847789^{2} \)	20T1110	Trivial (GRH)
20.14.10058060015112571274939858944.1	x^20 - 8x^18 + 14x^16 + 28x^14 - 109x^12 + 91x^10 + 9x^8 - 12x^6 - 26x^4 + 12x^2 - 1	\( -\,2^{20}\cdot 61^{4}\cdot 167^{2}\cdot 397^{4} \)	20T1015	Trivial (GRH)
20.14.13757744271328447008064363083.1	x^20 - 8x^19 + 20x^18 - 5x^17 - 64x^16 + 169x^15 - 274x^14 + 192x^13 + 204x^12 - 680x^11 + 1106x^10 - 1042x^9 + 322x^8 + 210x^7 - 582x^6 + 543x^5 + 90x^4 - 201x^3 - 9x^2 + 10x + 1	\( -\,3^{7}\cdot 97^{2}\cdot 401^{8} \)	20T845	Trivial (GRH)
20.14.15624230405892634824090320896.1	x^20 - 12x^18 + 59x^16 - 153x^14 + 218x^12 - 136x^10 - 60x^8 + 168x^6 - 106x^4 + 21x^2 - 1	\( -\,2^{24}\cdot 30516826559^{2} \)	20T1110	Trivial (GRH)
20.14.18079489015266793067734899712.1	x^20 - 6x^19 - 3x^18 + 63x^17 - 9x^16 - 282x^15 - 34x^14 + 628x^13 + 532x^12 - 500x^11 - 1656x^10 - 422x^9 + 2972x^8 + 1787x^7 - 3354x^6 - 3144x^5 + 1146x^4 + 2077x^3 + 548x^2 - 102x - 43	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.14.18079489015266793067734899712.2	x^20 - 8x^19 + 14x^18 + 40x^17 - 164x^16 + 152x^15 + 112x^14 - 599x^13 + 1522x^12 - 1809x^11 - 838x^10 + 4742x^9 - 4663x^8 + 499x^7 + 2314x^6 - 1661x^5 + 226x^4 + 183x^3 - 64x^2 + x + 1	\( -\,2^{10}\cdot 11^{16}\cdot 727^{3} \)	20T747	Trivial (GRH)
20.14.18993732228844275002500000000.1	x^20 - 18x^18 + 116x^16 - 292x^14 + 78x^12 + 601x^10 - 298x^8 - 180x^6 + 94x^4 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.14.18993732228844275002500000000.2	x^20 - 7x^18 - 12x^16 + 171x^14 - 318x^12 - 12x^10 + 371x^8 - 140x^6 - 55x^4 + 18x^2 - 1	\( -\,2^{8}\cdot 5^{10}\cdot 52501^{4} \)	20T876	Trivial (GRH)
20.14.22476272209051426554096123904.1	x^20 - 12x^18 + 48x^16 - 76x^14 + 27x^12 + 72x^10 - 135x^8 + 124x^6 - 60x^4 + 13x^2 - 1	\( -\,2^{20}\cdot 11^{16}\cdot 683^{2} \)	20T846	Trivial (GRH)
20.14.49036818365441822963250257479.1	x^20 - 10x^19 + 37x^18 - 48x^17 - 59x^16 + 268x^15 - 263x^14 - 197x^13 + 698x^12 - 483x^11 - 389x^10 + 828x^9 - 300x^8 - 365x^7 + 388x^6 - 38x^5 - 119x^4 + 53x^3 + 5x^2 - 7x + 1	\( -\,53\cdot 61^{4}\cdot 397^{4}\cdot 1373^{2}\cdot 1427 \)	20T1015	Trivial (GRH)
20.14.64346596468266980521002844679.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 168x^16 + 324x^15 + 102x^14 - 876x^13 + 620x^12 + 752x^11 - 1254x^10 + 148x^9 + 841x^8 - 550x^7 - 137x^6 + 260x^5 - 53x^4 - 38x^3 + 16x^2 + x - 1	\( -\,17^{4}\cdot 157^{2}\cdot 4153^{4}\cdot 105071 \)	20T1015	Trivial (GRH)
20.14.72735891382281174868544921875.1	x^20 - 6x^19 - 6x^18 + 104x^17 - 119x^16 - 601x^15 + 1425x^14 + 922x^13 - 5543x^12 + 2934x^11 + 7806x^10 - 10328x^9 - 227x^8 + 7303x^7 - 4163x^6 + 143x^5 + 484x^4 - 188x^3 + 68x^2 - 7x - 1	\( -\,5^{10}\cdot 19^{7}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.14.72735891382281174868544921875.2	x^20 - x^19 - 22x^18 + 12x^17 + 158x^16 - 61x^15 - 475x^14 + 121x^13 + 691x^12 + 24x^11 - 877x^10 + 24x^9 + 691x^8 + 121x^7 - 475x^6 - 61x^5 + 158x^4 + 12x^3 - 22x^2 - x + 1	\( -\,5^{10}\cdot 19^{7}\cdot 1699^{4} \)	20T876	Trivial (GRH)
20.14.75744139454672614891787109375.1	x^20 - 10x^19 + 35x^18 - 30x^17 - 120x^16 + 348x^15 - 218x^14 - 484x^13 + 1049x^12 - 522x^11 - 762x^10 + 1263x^9 - 440x^8 - 478x^7 + 515x^6 - 87x^5 - 115x^4 + 62x^3 - 7x + 1	\( -\,3^{4}\cdot 5^{10}\cdot 439\cdot 21611^{4} \)	20T887	Trivial (GRH)
20.14.110088938158843764415696897024.1	x^20 - 16x^18 - 5x^17 + 89x^16 + 111x^15 - 299x^14 - 527x^13 + 427x^12 + 1313x^11 + 119x^10 - 2063x^9 - 704x^8 + 1326x^7 + 1326x^6 - 781x^5 - 683x^4 + 303x^3 + 105x^2 - 42x - 1	\( -\,2^{10}\cdot 401^{10} \)	20T423	Trivial (GRH)
20.14.163956765044529790397060546875.1	x^20 - 10x^19 + 34x^18 - 21x^17 - 142x^16 + 320x^15 - 13x^14 - 715x^13 + 751x^12 + 343x^11 - 1189x^10 + 593x^9 + 561x^8 - 775x^7 + 150x^6 + 275x^5 - 192x^4 + 4x^3 + 38x^2 - 13x + 1	\( -\,5^{10}\cdot 13^{4}\cdot 166099\cdot 1881241^{2} \)	20T1045	Trivial (GRH)
20.14.203483763895883268631630859375.1	x^20 - 2x^19 - 3x^18 + 10x^17 - 39x^16 + 21x^15 + 122x^14 - 94x^13 + 25x^12 + 32x^11 - 238x^10 + 142x^9 + 36x^8 - 70x^7 + 170x^6 - 104x^5 - 63x^4 + 69x^3 - 11x^2 - 4x + 1	\( -\,5^{10}\cdot 27517559^{3} \)	20T540	Trivial (GRH)
20.14.206548481879697235603429344256.1	x^20 - 16x^18 + 69x^16 - 19x^14 - 264x^12 + 95x^10 + 332x^8 - 7x^6 - 67x^4 + 16x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T808	Trivial (GRH)
20.14.206548481879697235603429344256.2	x^20 - 17x^18 + 76x^16 - 24x^14 - 471x^12 + 659x^10 + 489x^8 - 1266x^6 + 675x^4 - 108x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T808	Trivial (GRH)
20.14.206548481879697235603429344256.3	x^20 - 4x^19 - 12x^18 + 54x^17 + 52x^16 - 266x^15 - 212x^14 + 826x^13 + 698x^12 - 1923x^11 - 1232x^10 + 2994x^9 + 1066x^8 - 2717x^7 - 451x^6 + 1303x^5 + 116x^4 - 291x^3 - 19x^2 + 19x - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T808	Trivial (GRH)
20.14.206548481879697235603429344256.4	x^20 - 11x^18 + 20x^16 + 106x^14 - 302x^12 - 30x^10 + 220x^8 - 39x^6 - 38x^4 + 13x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T808	Trivial (GRH)
20.14.206548481879697235603429344256.5	x^20 - 14x^18 + 40x^16 + 145x^14 - 629x^12 + 316x^10 + 572x^8 - 498x^6 + 74x^4 + 11x^2 - 1	\( -\,2^{10}\cdot 61^{6}\cdot 397^{6} \)	20T808	Trivial (GRH)
20.14.212741473756985846817177734375.1	x^20 - 10x^19 + 33x^18 - 12x^17 - 169x^16 + 332x^15 + 88x^14 - 918x^13 + 782x^12 + 690x^11 - 1620x^10 + 592x^9 + 1001x^8 - 1104x^7 + 95x^6 + 428x^5 - 236x^4 + 4x^3 + 26x^2 - 3x - 1	\( -\,5^{10}\cdot 79\cdot 359^{2}\cdot 1361\cdot 1253831^{2} \)	20T1045	Trivial (GRH)
20.14.222885303081664970605068359375.1	x^20 - x^19 - 24x^18 + 27x^17 + 193x^16 - 196x^15 - 751x^14 + 655x^13 + 1588x^12 - 1241x^11 - 1939x^10 + 1425x^9 + 1378x^8 - 973x^7 - 555x^6 + 368x^5 + 125x^4 - 69x^3 - 16x^2 + 5x + 1	\( -\,5^{10}\cdot 3169^{3}\cdot 8951^{3} \)	20T540	Trivial (GRH)
20.14.240370663965418608640000000000.1	x^20 - 18x^18 + 143x^16 - 656x^14 + 1903x^12 - 3584x^10 + 4315x^8 - 3116x^6 + 1139x^4 - 95x^2 - 31	\( -\,2^{20}\cdot 5^{10}\cdot 31\cdot 27517559^{2} \)	20T1045	Trivial (GRH)
20.14.470525233802978928640000000000.1	x^20 - 13x^18 + 56x^16 - 56x^14 - 213x^12 + 524x^10 - 150x^8 - 309x^6 + 43x^4 + 9x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.2	x^20 - 11x^18 + 35x^16 - 170x^12 + 198x^10 + 119x^8 - 253x^6 + 81x^4 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.3	x^20 - 4x^18 - 18x^16 + 91x^14 + 13x^12 - 480x^10 + 652x^8 - 238x^6 - 47x^4 + 32x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.4	x^20 - 8x^18 - 6x^16 + 123x^14 - 78x^12 - 488x^10 + 500x^8 + 314x^6 - 306x^4 + 38x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.5	x^20 - 4x^18 - 21x^16 + 127x^14 - 148x^12 - 176x^10 + 419x^8 - 174x^6 - 25x^4 + 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.470525233802978928640000000000.6	x^20 - 8x^18 + 5x^16 + 101x^14 - 276x^12 + 106x^10 + 401x^8 - 544x^6 + 255x^4 - 39x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T409	Trivial (GRH)
20.14.511072393702926193004148424704.1	x^20 - 18x^18 + 132x^16 - 514x^14 + 1157x^12 - 1529x^10 + 1146x^8 - 444x^6 + 72x^4 + x^2 - 1	\( -\,2^{20}\cdot 3^{6}\cdot 401^{8} \)	20T905	Trivial (GRH)
20.14.730802214340382541268593410048.1	x^20 - 17x^18 + 78x^16 + 169x^14 - 2308x^12 + 5257x^10 + 2272x^8 - 19123x^6 + 14566x^4 + 1571x^2 - 983	\( -\,2^{24}\cdot 83^{4}\cdot 983^{5} \)	20T992	Trivial (GRH)
20.14.730802214340382541268593410048.2	x^20 - 6x^19 + 2x^18 + 38x^17 - 27x^16 - 28x^15 - 480x^14 + 984x^13 + 1252x^12 - 4122x^11 + 2152x^10 - 986x^9 + 4021x^8 + 22x^7 - 7550x^6 + 5192x^5 + 868x^4 - 1938x^3 + 658x^2 - 68x - 1	\( -\,2^{24}\cdot 83^{4}\cdot 983^{5} \)	20T992	Trivial (GRH)
20.14.1533846811270295971840000000000.1	x^20 - 14x^18 + 81x^16 - 253x^14 + 468x^12 - 523x^10 + 325x^8 - 64x^6 - 34x^4 + 13x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 29^{2}\cdot 13345751^{2} \)	20T1045	Trivial (GRH)
20.14.1588027319649927224354711535616.1	x^20 - 9x^18 + 2x^16 + 95x^14 - 136x^12 - 189x^10 + 430x^8 - 58x^6 - 241x^4 + 107x^2 - 1	\( -\,2^{20}\cdot 11^{16}\cdot 5741^{2} \)	20T846	Trivial (GRH)
20.14.2419299596509789882588349379584.1	x^20 - 21x^18 + 188x^16 - 928x^14 + 2709x^12 - 4555x^10 + 3515x^8 + 1004x^6 - 4185x^4 + 2970x^2 - 701	\( -\,2^{10}\cdot 71^{2}\cdot 401^{8}\cdot 701 \)	20T905	Trivial (GRH)
20.14.2533781141191348418560000000000.1	x^20 - 14x^18 + 81x^16 - 251x^14 + 450x^12 - 459x^10 + 200x^8 + 103x^6 - 198x^4 + 105x^2 - 19	\( -\,2^{20}\cdot 5^{10}\cdot 19\cdot 149^{2}\cdot 765899^{2} \)	20T1045	Trivial (GRH)
20.14.3370778611471959737030176850944.1	x^20 - 10x^18 + 30x^16 - 147x^12 + 199x^10 + 75x^8 - 290x^6 + 146x^4 - 4x^2 - 1	\( -\,2^{10}\cdot 38569^{6} \)	20T808	Trivial (GRH)
20.14.3521934896736480471040000000000.1	x^20 - 10x^18 + 30x^16 - 4x^14 - 136x^12 + 244x^10 - 136x^8 - 13x^6 + 26x^4 - 2x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 61^{4}\cdot 397^{4} \)	20T887	Trivial (GRH)