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 188)

Label	Polynomial	Discriminant	Galois group	Class group
22.2.41217344982318472393444237.1	x^22 - 7x^20 - 3x^19 + 17x^18 + 12x^17 - 15x^16 - 16x^15 - x^14 - x^13 - 28x^12 - 42x^11 + 3x^10 + 25x^9 - 16x^8 - 47x^7 - 35x^6 + 7x^5 + 16x^4 - 7x^3 - 5x^2 + 2x + 1	\( 1070197\cdot 6205948139^{2} \)	22T53	Trivial (GRH)
22.2.147982356498821950109384704.1	x^22 - 2x^20 + 6x^18 - 14x^16 + 22x^14 - 31x^12 + 38x^10 - 34x^8 + 27x^6 - 17x^4 + 6x^2 - 1	\( 2^{22}\cdot 12917^{2}\cdot 459847^{2} \)	22T51	Trivial (GRH)
22.2.147982356498821950109384704.2	x^22 + x^18 - 2x^16 - 2x^14 - x^12 + 3x^8 + x^6 + x^4 - 1	\( 2^{22}\cdot 12917^{2}\cdot 459847^{2} \)	22T51	Trivial (GRH)
22.2.178901193768541138691065033.1	x^22 - 11x^21 + 65x^20 - 265x^19 + 825x^18 - 2067x^17 + 4301x^16 - 7582x^15 + 11469x^14 - 15003x^13 + 17039x^12 - 16811x^11 + 14374x^10 - 10594x^9 + 6680x^8 - 3576x^7 + 1630x^6 - 656x^5 + 261x^4 - 113x^3 + 48x^2 - 15x + 1	\( 149\cdot 33797\cdot 64661^{2}\cdot 92179^{2} \)	22T53	Trivial (GRH)
22.2.289863980721044983135295513.1	x^22 - x^21 + x^20 - 3x^19 + 3x^18 + x^17 + 5x^16 - 4x^15 - 18x^14 + 11x^13 + 16x^12 + 32x^11 - 45x^10 - 81x^9 + 100x^8 + 75x^7 - 101x^6 - 41x^5 + 53x^4 + 15x^3 - 15x^2 - 4x + 1	\( 359753\cdot 28385393161^{2} \)	22T53	Trivial (GRH)
22.2.635524829577904360423933313.1	x^22 - x^21 + 5x^20 - 8x^19 + 16x^18 - 27x^17 + 41x^16 - 61x^15 + 80x^14 - 104x^13 + 121x^12 - 138x^11 + 143x^10 - 142x^9 + 131x^8 - 112x^7 + 89x^6 - 64x^5 + 43x^4 - 24x^3 + 12x^2 - 4x + 1	\( 60821\cdot 1487459\cdot 7024799976319967 \)	22T59	Trivial (GRH)
22.2.716463968651672990739595264.1	x^22 + 4x^20 + x^18 - 20x^16 - 7x^14 + 93x^12 + 46x^10 - 121x^8 - 80x^6 - 34x^4 - 9x^2 - 1	\( 2^{22}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T49	Trivial (GRH)
22.2.890830078698256823295734989.1	x^22 - 2x^21 + 6x^20 - 10x^19 + 17x^18 - 21x^17 + 22x^16 - 15x^15 - 5x^14 + 38x^13 - 83x^12 + 135x^11 - 185x^10 + 221x^9 - 234x^8 + 222x^7 - 187x^6 + 138x^5 - 88x^4 + 47x^3 - 20x^2 + 6x - 1	\( 34092855421\cdot 26129523845912209 \)	22T59	Trivial (GRH)
22.2.1722741365651855595751953125.1	x^22 + 3x^20 - 8x^19 - 13x^18 - 13x^17 - 10x^16 + 79x^15 + 45x^14 + 111x^13 + 59x^12 - 172x^11 + 31x^10 - 94x^9 - 96x^8 + 55x^7 - 26x^6 + x^5 + 20x^4 - 4x^3 + 3x^2 - 1	\( 5^{11}\cdot 12917^{2}\cdot 459847^{2} \)	22T47	Trivial (GRH)
22.2.1734677982017693835986328125.1	x^22 - x^21 + 2x^20 + x^19 - 13x^18 + 3x^17 - 35x^16 - 18x^15 + 37x^14 + 27x^13 + 152x^12 + 277x^11 + 160x^10 + 72x^9 - 42x^8 - 69x^7 - 31x^6 - 22x^5 + 3x^4 + 4x^3 + x^2 + x - 1	\( 5^{11}\cdot 64661^{2}\cdot 92179^{2} \)	22T47	Trivial (GRH)
22.2.1767712543554828434373148672.1	x^22 - 5x^21 + 17x^20 - 40x^19 + 70x^18 - 93x^17 + 99x^16 - 86x^15 + 53x^14 + 37x^13 - 283x^12 + 778x^11 - 1493x^10 + 2198x^9 - 2575x^8 + 2425x^7 - 1840x^6 + 1108x^5 - 512x^4 + 173x^3 - 33x^2 + x + 1	\( 2^{16}\cdot 37^{5}\cdot 4441^{4} \)	22T52	Trivial (GRH)
22.2.2865855874606691962958381056.1	x^22 - 5x^20 + 9x^18 - 6x^16 - 12x^14 + 37x^12 - 45x^10 + 75x^8 - 54x^6 - 17x^4 + 44x^2 - 16	\( 2^{24}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T49	Trivial (GRH)
22.2.3029890053010200585803137024.1	x^22 + 3x^20 - 11x^16 - 24x^14 - 24x^12 + x^10 + 11x^8 - 9x^6 - 5x^4 + 5x^2 - 1	\( 2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2} \)	22T51	Trivial (GRH)
22.2.3115164990344181117349789696.1	x^22 + 2x^16 - x^14 - x^12 + x^10 + x^8 - 2x^6 - x^4 + 2x^2 - 1	\( 2^{22}\cdot 1559^{2}\cdot 17480927^{2} \)	22T51	Trivial (GRH)
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)
22.2.31524414620673611592542191616.1	x^22 - 2x^21 + x^20 - x^19 - 7x^17 + 5x^16 + 45x^15 + 31x^14 - 38x^13 - 205x^12 - 278x^11 - 123x^10 + 249x^9 + 532x^8 + 371x^7 + 205x^6 + 153x^5 + 236x^4 + 94x^3 + 34x^2 + 5x + 25	\( 2^{24}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.2.70765994783241803539463274496.1	x^22 - 3x^20 + x^18 + x^16 + 6x^14 - 8x^12 + 5x^6 - x^2 - 1	\( 2^{22}\cdot 167^{10} \)	22T30	Trivial (GRH)
22.2.70765994783241803539463274496.2	x^22 - 6x^20 + 15x^18 - 27x^16 + 57x^14 - 109x^12 + 140x^10 - 129x^8 + 89x^6 - 41x^4 + 10x^2 - 1	\( 2^{22}\cdot 167^{10} \)	22T30	Trivial (GRH)
22.2.104070916689387515610916716544.1	x^22 + 2x^20 - x^18 + 2x^16 - 18x^12 - 24x^10 + 3x^8 + 36x^6 + 27x^4 + 4x^2 - 1	\( 2^{22}\cdot 19457^{2}\cdot 8095783^{2} \)	22T51	Trivial (GRH)
22.2.126778690041778214971308507136.1	x^22 - 4x^21 + 14x^20 - 38x^19 + 89x^18 - 184x^17 + 341x^16 - 572x^15 + 876x^14 - 1228x^13 + 1579x^12 - 1862x^11 + 2008x^10 - 1978x^9 + 1765x^8 - 1416x^7 + 1009x^6 - 628x^5 + 333x^4 - 144x^3 + 47x^2 - 10x + 1	\( 2^{33}\cdot 11^{2}\cdot 121975057867858073 \)	22T57	Trivial (GRH)
22.2.168783011453769015346390368256.1	x^22 + x^20 - 12x^14 - 14x^12 + 16x^10 + 28x^8 + x^6 - 14x^4 - 7x^2 - 1	\( 2^{22}\cdot 200601609583^{2} \)	22T51	Trivial (GRH)
22.2.347270464382605539918027848005.1	x^22 - x - 1	\( 5\cdot 69454092876521107983605569601 \)	22T59	Trivial (GRH)
22.2.499131506491608208145638755501.1	x^22 - 2x^21 + 5x^20 - 4x^19 + 4x^18 - 14x^17 + 63x^16 - 228x^15 + 497x^14 - 686x^13 + 792x^12 - 793x^11 + 1821x^10 - 3315x^9 + 78x^8 + 1215x^7 + 1528x^6 + 168x^5 - 351x^4 - 826x^3 - 4x^2 + 39x - 5	\( 3^{11}\cdot 167^{11} \)	$D_{22}$ (as 22T3)	Trivial (GRH)
22.2.639745687664639805566853620073.1	x^22 - x^21 + 14x^19 - 11x^18 - 42x^17 + 99x^16 + 27x^15 - 297x^14 + 205x^13 + 473x^12 - 780x^11 - 121x^10 + 1273x^9 - 891x^8 - 915x^7 + 1485x^6 - 27x^5 - 1166x^4 + 1016x^3 - 429x^2 + 98x - 8	\( 3^{21}\cdot 11^{19} \)	$C_2\times F_{11}$ (as 22T6)	Trivial (GRH)
22.2.823824605709428474533642578125.1	x^22 - x^21 + 14x^20 - 11x^19 + 83x^18 - 46x^17 + 290x^16 - 162x^15 + 710x^14 - 312x^13 + 966x^12 - 47x^11 + 930x^10 + 311x^9 + 628x^8 + 309x^7 + 259x^6 + 141x^5 + 87x^4 + 44x^3 + 16x^2 + 2x - 1	\( 5^{11}\cdot 167^{10} \)	$D_{22}$ (as 22T3)	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)
22.2.3974743622404285210611376953125.1	x^22 - x^11 - 1	\( 5^{11}\cdot 11^{22} \)	$C_2\times F_{11}$ (as 22T6)	Trivial (GRH)
22.2.10994531599582075769676214829056.1	x^22 + 12x^20 + 64x^18 + 200x^16 + 406x^14 + 557x^12 + 507x^10 + 271x^8 + 51x^6 - 18x^4 - 9x^2 - 1	\( 2^{22}\cdot 1619043113033^{2} \)	22T51	Trivial (GRH)
22.2.10994531599582075769676214829056.2	x^22 + 10x^20 + 44x^18 + 112x^16 + 182x^14 + 199x^12 + 151x^10 + 67x^8 - 13x^6 - 36x^4 - 13x^2 - 1	\( 2^{22}\cdot 1619043113033^{2} \)	22T51	Trivial (GRH)
22.2.12816596924190768698410425412337.1	x^22 - 11x^21 + 75x^20 - 365x^19 + 1409x^18 - 4473x^17 + 12052x^16 - 27974x^15 + 56686x^14 - 100938x^13 + 158847x^12 - 221312x^11 + 273270x^10 - 298381x^9 + 287150x^8 - 241819x^7 + 176511x^6 - 109912x^5 + 57096x^4 - 23845x^3 + 7532x^2 - 1599x + 163	\( 31\cdot 43^{2}\cdot 547^{2}\cdot 632447\cdot 34374601^{2} \)	22T53	Trivial (GRH)
22.2.52963188445448362085110426970892.1	x^22 - 4x^21 + 8x^20 - 17x^19 + 25x^18 + 9x^17 - 75x^16 + 78x^15 - 51x^14 - 5x^13 + 143x^12 - 112x^11 + 22x^10 + 109x^9 + 123x^8 + 246x^7 + 108x^6 - 39x^5 - 82x^4 - 107x^3 - 65x^2 - 4x + 8	\( 2^{2}\cdot 3^{20}\cdot 11^{18}\cdot 683 \)	22T37	Trivial (GRH)
22.2.58315043828929313782568927100928.1	x^22 - 8x^21 + 32x^20 - 90x^19 + 202x^18 - 378x^17 + 607x^16 - 856x^15 + 1073x^14 - 1210x^13 + 1241x^12 - 1164x^11 + 1007x^10 - 806x^9 + 595x^8 - 406x^7 + 253x^6 - 144x^5 + 73x^4 - 34x^3 + 14x^2 - 4x + 1	\( 2^{33}\cdot 223\cdot 94616983\cdot 321748692401 \)	22T57	Trivial (GRH)
22.2.102653502644738770935211181640625.1	x^22 - x^21 - 11x^20 + 5x^19 + 71x^18 + 39x^17 - 241x^16 - 440x^15 + 36x^14 + 974x^13 + 1084x^12 - 1095x^11 - 6129x^10 - 12496x^9 - 16556x^8 - 15445x^7 - 9954x^6 - 3936x^5 - 451x^4 + 325x^3 + 155x^2 - 10x - 5	\( 5^{16}\cdot 11^{20} \)	$C_{11}:D_{11}.C_2$ (as 22T8)	Trivial (GRH)
22.2.145648768224982995734053674169953.1	x^22 - 4x^21 + x^20 + 6x^19 + 21x^18 - 27x^17 - 24x^16 - 255x^15 + 291x^14 + 226x^13 + 1112x^12 + 1378x^11 + 1776x^10 + 2229x^9 + 2715x^8 + 2358x^7 + 1791x^6 + 360x^5 - 828x^4 - 9x^3 + 405x^2 + 117x - 72	\( 3^{20}\cdot 11^{19}\cdot 683 \)	22T37	Trivial (GRH)
22.2.499858877615201668877221298700288.1	x^22 - 8x^21 + 23x^20 - 8x^19 - 123x^18 + 364x^17 - 662x^16 + 1316x^15 - 2070x^14 + 1360x^13 - 62x^12 + 2204x^11 - 5167x^10 + 2080x^9 + 795x^8 + 8072x^7 - 22483x^6 + 26464x^5 - 17824x^4 + 7236x^3 - 1720x^2 + 224x - 8	\( 2^{22}\cdot 3^{11}\cdot 11^{20} \)	$D_{11}^2$ (as 22T9)	Trivial (GRH)
22.2.529866739430089519756710630129664.1	x^22 + 5x^20 - 11x^18 - 34x^16 + 29x^14 + 127x^12 - 268x^10 + 239x^8 - 119x^6 + 29x^4 - 1	\( 2^{22}\cdot 1831^{8} \)	22T39	Trivial (GRH)
22.2.529866739430089519756710630129664.2	x^22 - 3x^20 - 5x^18 + 58x^16 - 141x^14 + 140x^12 - 16x^10 - 89x^8 + 13x^6 + 49x^4 + 21x^2 - 1	\( 2^{22}\cdot 1831^{8} \)	22T39	Trivial (GRH)
22.2.1249711388122384634961076169998336.1	x^22 + 11x^20 + 55x^18 + 154x^16 + 253x^14 + 253x^12 + 209x^10 + 187x^8 + 77x^6 + 33x^2 - 4	\( 2^{20}\cdot 11^{26} \)	22T34	Trivial (GRH)
22.2.1249711388122384634961076169998336.2	x^22 - 44x^16 - 11x^14 - 88x^12 + 264x^10 - 275x^8 + 154x^6 - 55x^4 + 11x^2 - 1	\( 2^{20}\cdot 11^{26} \)	22T34	Trivial (GRH)
22.2.1288033148279983900699565800554496.1	x^22 + 14x^20 + 84x^18 + 284x^16 + 596x^14 + 794x^12 + 632x^10 + 220x^8 - 53x^6 - 65x^4 - 15x^2 - 1	\( 2^{22}\cdot 17524013040643^{2} \)	22T51	$[2]$ (GRH)
22.2.1589600218290268559270131890388992.1	x^22 + 9x^20 + 36x^18 + 79x^16 + 99x^14 + 68x^12 + 24x^10 + 3x^8 - 9x^6 - 15x^4 - 11x^2 - 3	\( 2^{22}\cdot 3\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.2.1589600218290268559270131890388992.2	x^22 + 13x^20 + 78x^18 + 280x^16 + 657x^14 + 1027x^12 + 1021x^10 + 513x^8 - 88x^6 - 299x^4 - 163x^2 - 27	\( 2^{22}\cdot 3\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.2.7198079267989980836471065337135104.1	x^22 + 24x^20 + 220x^18 + 980x^16 + 2267x^14 + 2696x^12 + 1324x^10 - 265x^8 - 563x^6 - 215x^4 - 29x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.2.13079147944053004756241817943013989.1	x^22 - 11x^21 + 78x^20 - 395x^19 + 1595x^18 - 5292x^17 + 14883x^16 - 35934x^15 + 75375x^14 - 138055x^13 + 221616x^12 - 311835x^11 + 383985x^10 - 411930x^9 + 382260x^8 - 303600x^7 + 203205x^6 - 112125x^5 + 49335x^4 - 16445x^3 + 3795x^2 - 506x + 23	\( 23^{20}\cdot 7621189 \)	22T28	$[3]$ (GRH)
22.2.24505586101645802782745775444611305.1	x^22 - 4x - 1	\( 5\cdot 549569\cdot 7345029585473\cdot 1214169483036053 \)	22T59	Trivial (GRH)
22.2.24505927529441764252916332330221568.1	x^22 - 2x - 1	\( 2^{23}\cdot 19\cdot 37\cdot 68639\cdot 132989\cdot 10028509\cdot 45394463 \)	22T59	Trivial (GRH)
22.2.34444799740547072471091200000000000.1	x^22 - 22x^11 - 4	\( 2^{20}\cdot 5^{11}\cdot 11^{20} \)	22T15	Trivial (GRH)
22.2.69983356443819950699150910123147264.1	x^22 + 16x^20 + 103x^18 + 331x^16 + 485x^14 - 75x^12 - 1440x^10 - 2340x^8 - 1825x^6 - 744x^4 - 144x^2 - 9	\( 2^{22}\cdot 3^{6}\cdot 4784137656827^{2} \)	22T51	Trivial (GRH)
22.2.165555823163769559238834502754107392.1	x^22 + 23x^20 + 207x^18 + 897x^16 + 1679x^14 - 483x^12 - 7636x^10 - 13041x^8 - 9660x^6 - 3312x^4 - 483x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.2.243935263341322672277116036916969472.1	x^22 - 3	\( 2^{22}\cdot 3^{21}\cdot 11^{18} \)	$C_2\times F_{11}$ (as 22T6)	Trivial (GRH)