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 117)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.39471584120695485887249589623.1	x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( -\,23^{21} \)	$C_{22}$ (as 22T1)	$[3]$
22.0.10046547996724887091059294601443.1	x^22 - x^21 + 7x^20 - 4x^19 + 31x^18 - 18x^17 + 77x^16 - 41x^15 + 140x^14 - 96x^13 + 153x^12 - 129x^11 + 145x^10 - 148x^9 + 84x^8 - 72x^7 + 94x^6 - 20x^5 + 39x^4 + 12x^3 + 18x^2 + 4x + 1	\( -\,3^{11}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T47	$[2]$ (GRH)
22.0.155979617226877172002898926703507.1	x^22 - 11x^21 + 76x^20 - 375x^19 + 1474x^18 - 4773x^17 + 13158x^16 - 31314x^15 + 65238x^14 - 119692x^13 + 194559x^12 - 280546x^11 + 359279x^10 - 407518x^9 + 408092x^8 - 358073x^7 + 272834x^6 - 177710x^5 + 97035x^4 - 42912x^3 + 14655x^2 - 3477x + 467	\( -\,23\cdot 2879\cdot 3371\cdot 56509^{2}\cdot 14792861^{2} \)	22T53	$[2]$ (GRH)
22.0.158889565336345086255331280912676.1	x^22 - 11x^21 + 66x^20 - 275x^19 + 880x^18 - 2277x^17 + 4917x^16 - 9042x^15 + 14355x^14 - 19855x^13 + 24068x^12 - 25650x^11 + 24035x^10 - 19723x^9 + 14058x^8 - 8646x^7 + 4653x^6 - 2343x^5 + 1210x^4 - 605x^3 + 231x^2 - 44x + 10	\( -\,2^{2}\cdot 3^{21}\cdot 11^{18}\cdot 683 \)	22T37	$[2]$ (GRH)
22.0.436946304674948987202161022509859.1	x^22 - 7x^21 + 27x^20 - 73x^19 + 238x^18 - 681x^17 + 1593x^16 - 3279x^15 + 6450x^14 - 11717x^13 + 18830x^12 - 25953x^11 + 31166x^10 - 32372x^9 + 28878x^8 - 22278x^7 + 14793x^6 - 8202x^5 + 3676x^4 - 1240x^3 + 279x^2 - 40x + 4	\( -\,3^{21}\cdot 11^{19}\cdot 683 \)	22T37	$[2]$ (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)
22.6.2009643344565206347646133417459817.1	x^22 - 11x^21 + 63x^20 - 245x^19 + 714x^18 - 1638x^17 + 3034x^16 - 4586x^15 + 5635x^14 - 5481x^13 + 3863x^12 - 1247x^11 - 1359x^10 + 2985x^9 - 3236x^8 + 2436x^7 - 1301x^6 + 435x^5 - 37x^4 - 42x^3 + 18x^2 - x - 1	\( 37\cdot 131\cdot 431\cdot 31015897276291^{2} \)	22T53	$[2]$ (GRH)
22.6.4098058278162967431271914143428729.2	x^22 - 5x^21 + 2x^20 + 36x^19 - 111x^18 + 141x^17 - 107x^16 + 558x^15 - 1962x^14 + 3577x^13 - 3027x^12 - 2023x^11 + 17912x^10 - 42755x^9 + 54822x^8 - 37877x^7 + 18311x^6 - 12826x^5 + 673x^4 + 3420x^3 + 4336x^2 - 3280x + 47	\( 23^{21}\cdot 47^{3} \)	22T28	$[2]$ (GRH)
22.6.12701184200335173359101913935642624.1	x^22 + 15x^20 + 91x^18 + 278x^16 + 410x^14 + 123x^12 - 404x^10 - 417x^8 - 19x^6 + 77x^4 - 3x^2 - 1	\( 2^{22}\cdot 55029067682009^{2} \)	22T51	$[2]$ (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)
22.0.13746825269346230984571837869981696.1	x^22 + 11x^18 - 132x^16 + 165x^14 + 187x^12 - 88x^10 + 121x^8 + 44x^6 + 11	\( -\,2^{20}\cdot 11^{27} \)	22T35	$[2]$ (GRH)
22.0.13746825269346230984571837869981696.2	x^22 + 11x^16 + 33x^14 + 121x^12 + 275x^10 + 286x^8 + 154x^6 + 121x^4 + 121x^2 + 44	\( -\,2^{20}\cdot 11^{27} \)	22T35	$[2]$ (GRH)
22.14.22661033510180079603495293971842498241.1	x^22 - 2x^21 - 39x^20 + 64x^19 + 637x^18 - 838x^17 - 5728x^16 + 5845x^15 + 31533x^14 - 23266x^13 - 111308x^12 + 50752x^11 + 255873x^10 - 41357x^9 - 384169x^8 - 55415x^7 + 364754x^6 + 157543x^5 - 189895x^4 - 128323x^3 + 35550x^2 + 35218x + 3037	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.6.22661033510180079603495293971842498241.1	x^22 - 10x^21 + 29x^20 + 3x^19 - 188x^18 + 381x^17 + 73x^16 - 825x^15 - 72x^14 + 1868x^13 - 351x^12 + 2371x^11 + 18854x^10 + 14453x^9 + 97552x^8 + 172564x^7 + 165961x^6 + 92915x^5 + 32329x^4 + 6644x^3 + 718x^2 + 72x + 5	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.10.22661033510180079603495293971842498241.2	x^22 - x^21 - 15x^20 + 49x^19 + 44x^18 - 485x^17 + 631x^16 + 1475x^15 - 5443x^14 + 3138x^13 + 10542x^12 - 20731x^11 + 9385x^10 - 1329x^9 + 26060x^8 - 12671x^7 - 46031x^6 + 81808x^5 - 90460x^4 + 26591x^3 + 21718x^2 - 4276x - 289	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.14.22661033510180079603495293971842498241.2	x^22 - 3x^21 - 24x^20 + 59x^19 + 273x^18 - 436x^17 - 1924x^16 + 1356x^15 + 5010x^14 + 14999x^13 - 9512x^12 - 114771x^11 + 18405x^10 + 290616x^9 + 69522x^8 - 375325x^7 - 259853x^6 + 293924x^5 + 260945x^4 - 133418x^3 - 93266x^2 + 21174x + 11623	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.14.22661033510180079603495293971842498241.4	x^22 - 4x^21 - 15x^20 + 64x^19 + 79x^18 - 540x^17 + 528x^16 + 1865x^15 - 4894x^14 - 1811x^13 + 8981x^12 + 4163x^11 - 6857x^10 - 8000x^9 + 2421x^8 + 4419x^7 - 158x^6 - 547x^5 - 172x^4 - 39x^3 + 52x^2 - 2x - 1	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.10.22661033510180079603495293971842498241.6	x^22 - 5x^21 + x^20 + 45x^19 - 310x^18 + 927x^17 - 1531x^16 + 1204x^15 + 2550x^14 - 9408x^13 + 18565x^12 - 24332x^11 + 23469x^10 + 9560x^9 - 46190x^8 + 69717x^7 - 91965x^6 + 67098x^5 - 36153x^4 + 9787x^3 + 1002x^2 - 474x - 25	\( 1297^{12} \)	22T30	$[2]$ (GRH)
22.2.56501459388151144478039723653407440896.2	x^22 + 25x^20 + 250x^18 + 1243x^16 + 2879x^14 + 334x^12 - 14126x^10 - 33691x^8 - 35857x^6 - 18585x^4 - 4105x^2 - 289	\( 2^{22}\cdot 1297^{10} \)	22T30	$[3]$ (GRH)
22.10.1856564799974488125951035818931423019008.1	x^22 - 11x^21 + 44x^20 - 11x^19 - 572x^18 + 2057x^17 - 1199x^16 - 10714x^15 + 29843x^14 - 10395x^13 - 81246x^12 + 129491x^11 + 33000x^10 - 193941x^9 - 23001x^8 + 208758x^7 - 19723x^6 - 296241x^5 + 63338x^4 + 196317x^3 + 17182x^2 + 1155x - 63	\( 2^{20}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (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)
22.0.3388109619085565148335762714038503428163.1	x^22 - 3x + 3	\( -\,3^{21}\cdot 19\cdot 17047374542582189991184386859 \)	22T59	$[2]$ (GRH)
22.6.29391360462703563245733396281479720218577.1	x^22 - 2x^21 - 6x^20 - 12x^19 - 51x^18 - 1294x^17 - 4139x^16 + 11844x^15 + 45982x^14 + 14721x^13 + 173096x^12 + 635309x^11 - 626140x^10 - 2954875x^9 + 1702700x^8 + 10537521x^7 + 4899648x^6 - 12306030x^5 - 9650007x^4 + 20971742x^3 + 32748639x^2 + 9514395x - 381517	\( 1297^{13} \)	22T29	$[2, 2]$ (GRH)
22.10.29391360462703563245733396281479720218577.2	x^22 - 4x^21 - 25x^20 + 187x^19 - 427x^18 - 1387x^17 + 11048x^16 - 19578x^15 - 51688x^14 + 291735x^13 - 208406x^12 - 1486531x^11 + 3652116x^10 + 922479x^9 - 15631207x^8 + 22761255x^7 - 1886833x^6 - 28646815x^5 + 31917632x^4 - 11208552x^3 - 2785752x^2 + 2849336x - 485809	\( 1297^{13} \)	22T29	$[2]$ (GRH)
22.14.29705036799591810015216573102902768304128.1	x^22 - 33x^20 - 44x^19 + 385x^18 + 990x^17 - 1815x^16 - 7436x^15 + 902x^14 + 23584x^13 + 14058x^12 - 48740x^11 - 23034x^10 + 158444x^9 + 133782x^8 - 268796x^7 - 608399x^6 - 263560x^5 + 354255x^4 + 374352x^3 + 107129x^2 + 9086x - 63	\( 2^{24}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.10.73282392826432034388017521578469450842112.1	x^22 + 17x^20 - 16x^18 - 1089x^16 - 1819x^14 + 10241x^12 + 27179x^10 - 263x^8 - 38576x^6 - 10325x^4 + 12922x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.14.73282392826432034388017521578469450842112.1	x^22 + 6x^20 - 128x^18 - 67x^16 + 5045x^14 - 14909x^12 - 18753x^10 + 142110x^8 - 181519x^6 - 9369x^4 + 98505x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.18.73282392826432034388017521578469450842112.1	x^22 - 48x^20 + 668x^18 - 3452x^16 + 1836x^14 + 41707x^12 - 117661x^10 + 18659x^8 + 239887x^6 - 220532x^4 + 55347x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.2.73282392826432034388017521578469450842112.1	x^22 + 42x^20 + 682x^18 + 5751x^16 + 27661x^14 + 76030x^12 + 104221x^10 + 9257x^8 - 183787x^6 - 260704x^4 - 150852x^2 - 32425	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.10.73282392826432034388017521578469450842112.2	x^22 - 201x^18 + 110x^16 + 3992x^14 - 857x^12 - 16194x^10 - 624x^8 + 15461x^6 + 3758x^4 - 3752x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.14.73282392826432034388017521578469450842112.2	x^22 - x^20 - 353x^18 - 1722x^16 + 5661x^14 + 15526x^12 - 37578x^10 - 11324x^8 + 62186x^6 - 45444x^4 + 12972x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.2.73282392826432034388017521578469450842112.2	x^22 + 63x^20 + 1659x^18 + 23877x^16 + 206080x^14 + 1097796x^12 + 3551233x^10 + 6433703x^8 + 4872652x^6 - 1515055x^4 - 3671807x^2 - 1090777	\( 2^{22}\cdot 1297^{11} \)	22T29	$[3]$ (GRH)
22.10.73282392826432034388017521578469450842112.3	x^22 - 11x^20 - 82x^18 + 1254x^16 - 1266x^14 - 19635x^12 + 12421x^10 + 127961x^8 + 135714x^6 + 24994x^4 - 12375x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.14.73282392826432034388017521578469450842112.3	x^22 - 31x^20 + 150x^18 + 1799x^16 - 7047x^14 - 30271x^12 + 46860x^10 + 53483x^8 - 89614x^6 + 29753x^4 + 1393x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.10.73282392826432034388017521578469450842112.4	x^22 + 19x^20 - 204x^18 - 1314x^16 + 11139x^14 + 10593x^12 - 133681x^10 + 103014x^8 + 141613x^6 - 2116x^4 - 12142x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.10.73282392826432034388017521578469450842112.5	x^22 + 11x^20 - 283x^18 - 955x^16 + 16593x^14 + 43210x^12 - 272219x^10 - 862533x^8 - 376478x^6 + 667131x^4 + 455494x^2 - 1297	\( 2^{22}\cdot 1297^{11} \)	22T29	$[2]$ (GRH)
22.10.118820147198367240060866292411611073216512.1	x^22 - 11x^20 - 165x^18 + 803x^16 + 5874x^14 - 18722x^12 - 80146x^10 + 172370x^8 + 448525x^6 - 530387x^4 - 836825x^2 - 27797	\( 2^{26}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.14.118820147198367240060866292411611073216512.1	x^22 - 44x^20 - 88x^19 + 308x^18 + 1188x^17 + 616x^16 - 8052x^15 - 12188x^14 + 41448x^13 + 24640x^12 - 126200x^11 + 70840x^10 + 100672x^9 - 139040x^8 + 236368x^7 - 144144x^6 - 281600x^5 + 293568x^4 - 36608x^3 - 25344x^2 + 5984x - 160	\( 2^{26}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.10.118820147198367240060866292411611073216512.2	x^22 + 11x^20 - 22x^19 - 143x^18 - 682x^17 - 2563x^16 + 396x^15 + 17490x^14 + 77352x^13 + 194766x^12 + 246656x^11 - 220990x^10 - 2045912x^9 - 6045534x^8 - 12294788x^7 - 18335339x^6 - 20263760x^5 - 15664121x^4 - 7715994x^3 - 2197811x^2 - 317966x - 17727	\( 2^{26}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.0.129045097915537907803232946851577207980032.1	x^22 - 11x^20 + 99x^18 - 33x^16 - 726x^14 + 23474x^12 - 4096x^11 + 25894x^10 + 22528x^9 + 141086x^8 + 540672x^7 + 2309285x^6 + 315392x^5 + 5775209x^4 - 7434240x^3 + 5021863x^2 - 9168896x + 5643763	\( -\,2^{57}\cdot 11^{23} \)	22T41	$[2]$ (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)
22.22.341419566026798986253349758444608447265625.1	x^22 - x^21 - 91x^20 + 91x^19 + 3589x^18 - 3589x^17 - 80315x^16 + 80315x^15 + 1120837x^14 - 1120837x^13 - 10089915x^12 + 10089915x^11 + 58493509x^10 - 58493509x^9 - 210941371x^8 + 210941371x^7 + 435702341x^6 - 435702341x^5 - 426489275x^4 + 426489275x^3 + 104090181x^2 - 104090181x + 7621189	\( 3^{11}\cdot 5^{11}\cdot 23^{21} \)	$C_{22}$ (as 22T1)	$[2]$ (GRH)
22.10.475280588793468960243465169646444292866048.1	x^22 - 22x^20 + 110x^18 - 198x^17 - 1232x^16 + 880x^15 + 6072x^14 + 17732x^13 + 40128x^12 - 32728x^11 - 351384x^10 - 402776x^9 + 530464x^8 + 1234640x^7 + 593560x^6 - 1300112x^5 - 1035144x^4 + 2519792x^3 - 1050016x^2 - 2919664x + 1889288	\( 2^{28}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.14.475280588793468960243465169646444292866048.1	x^22 - 11x^20 - 44x^19 - 231x^18 + 176x^17 + 2981x^16 + 6996x^15 + 9812x^14 - 22990x^13 - 153714x^12 - 146644x^11 + 441386x^10 + 840818x^9 - 432300x^8 - 1836406x^7 - 559647x^6 + 1382480x^5 + 980903x^4 - 102718x^3 - 185581x^2 - 11440x + 7375	\( 2^{28}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.10.475280588793468960243465169646444292866048.2	x^22 - 11x^20 - 33x^18 + 495x^16 + 506x^14 - 6446x^12 - 6226x^10 + 13486x^8 + 7029x^6 - 1815x^4 - 957x^2 - 77	\( 2^{28}\cdot 7^{11}\cdot 11^{23} \)	22T35	$[2]$ (GRH)
22.6.672296453286415084930139988327026367187500.1	x^22 - 24x^20 - 495x^18 + 1650x^16 + 36795x^14 + 82962x^12 - 186318x^10 - 833085x^8 - 1007325x^6 - 539055x^4 - 131769x^2 - 11979	\( 2^{2}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17} \)	22T36	$[2]$ (GRH)
22.16.840370566608018856162674985408782958984375.1	x^22 - 25x^20 + 130x^18 + 975x^16 - 8280x^14 - 5580x^12 + 129810x^10 - 86460x^8 - 586080x^6 + 671935x^4 - 203995x^2 + 10780	\( -\,3^{20}\cdot 5^{21}\cdot 11^{17} \)	22T36	$[2]$ (GRH)
22.10.916767890845111479450190893173217773437500.1	x^22 - 10x^21 + 30x^20 - 25x^19 + 325x^18 - 3180x^17 + 11340x^16 - 9885x^15 - 62595x^14 + 261085x^13 - 416755x^12 - 26220x^11 + 1674680x^10 - 3966065x^9 + 2285520x^8 + 10714185x^7 - 18884505x^6 - 17519370x^5 + 28233430x^4 + 23392400x^3 - 5493645x^2 - 6705550x - 1073090	\( 2^{2}\cdot 3^{21}\cdot 5^{21}\cdot 11^{16} \)	22T36	$[2]$ (GRH)
22.0.1501432338263855459795691706544981028065347.1	x^22 - 3x + 4	\( -\,59\cdot 71693\cdot 246874073979902203\cdot 1437810054059874727 \)	22T59	$[2]$ (GRH)
22.0.1501615684835344357305146813744922493552315.1	x^22 - x + 4	\( -\,5\cdot 356579\cdot 842234503341668666581681374250823797 \)	22T59	$[2]$ (GRH)