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 all 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.11817921128801381191090366840832.1	x^22 + 9x^20 + 37x^18 + 74x^16 + 22x^14 - 217x^12 - 442x^10 - 261x^8 + 291x^6 + 663x^4 + 501x^2 + 167	\( -\,2^{22}\cdot 167^{11} \)	22T29	Trivial (GRH)
22.0.11817921128801381191090366840832.2	x^22 - 6x^20 + 19x^18 - 15x^16 - 90x^14 + 259x^12 - 217x^10 + 142x^8 - 495x^6 + 761x^4 - 501x^2 + 167	\( -\,2^{22}\cdot 167^{11} \)	22T29	Trivial (GRH)
22.10.17471883970840462300304775614373553.1	x^22 - 2x^21 - 2x^20 + 24x^19 - 83x^18 - 30x^17 + 161x^16 + 292x^15 + 431x^14 - 4032x^13 + 7422x^12 - 3707x^11 - 11808x^10 + 25440x^9 - 18429x^8 + 765x^7 + 7197x^6 - 4873x^5 + 1431x^4 - 165x^3 - 15x^2 + 8x - 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.14.17471883970840462300304775614373553.1	x^22 - 8x^21 + 12x^20 + 43x^19 - 133x^18 + 143x^17 - 51x^16 - 1197x^15 + 2298x^14 + 2198x^13 - 4854x^12 - 1488x^11 + 3269x^10 - 955x^9 - 610x^8 + 2045x^7 + 101x^6 - 1059x^5 - 151x^4 + 211x^3 + 62x^2 - x - 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.10.17471883970840462300304775614373553.2	x^22 - 4x^21 - 12x^20 + 79x^19 - 46x^18 - 417x^17 + 999x^16 - 364x^15 - 2461x^14 + 6453x^13 - 7803x^12 + 1855x^11 + 10460x^10 - 21218x^9 + 23963x^8 - 17867x^7 + 7632x^6 - 1285x^5 - 15x^4 + 157x^3 - 73x^2 - 10x + 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.14.17471883970840462300304775614373553.2	x^22 - x^21 - 14x^20 + 62x^18 + 129x^17 - 52x^16 - 983x^15 + 160x^14 + 2384x^13 - 603x^12 - 2192x^11 - 1350x^10 + 4200x^9 + 91x^8 - 3234x^7 + 1064x^6 + 775x^5 - 416x^4 - 33x^3 + 39x^2 - x - 1	\( 1297^{11} \)	22T29	Trivial (GRH)
22.14.17471883970840462300304775614373553.3	x^22 - x^21 - 26x^20 + 49x^19 + 237x^18 - 701x^17 - 634x^16 + 4156x^15 - 2565x^14 - 9376x^13 + 16978x^12 - 1217x^11 - 24957x^10 + 25854x^9 + 3793x^8 - 25081x^7 + 13524x^6 + 5616x^5 - 7257x^4 + 961x^3 + 908x^2 - 278x + 11	\( 1297^{11} \)	22T29	Trivial (GRH)
22.10.4299288794103243236127943577240214703609.1	x^22 - 8x^21 - 5x^20 + 179x^19 - 137x^18 - 2169x^17 + 1761x^16 + 18883x^15 - 4278x^14 - 98036x^13 - 50230x^12 + 300890x^11 + 273099x^10 - 507315x^9 - 680178x^8 + 245730x^7 + 848289x^6 + 558904x^5 + 116201x^4 - 37579x^3 - 28495x^2 - 7129x - 721	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.14.4299288794103243236127943577240214703609.1	x^22 - 9x^21 - 5x^20 + 230x^19 - 343x^18 - 2094x^17 + 5295x^16 + 8119x^15 - 33602x^14 - 6253x^13 + 119287x^12 - 91272x^11 - 182743x^10 + 403919x^9 - 287584x^8 - 116709x^7 + 557374x^6 - 666253x^5 + 340515x^4 + 15415x^3 - 98010x^2 + 39788x - 5047	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.18.4299288794103243236127943577240214703609.1	x^22 - 5x^21 - 49x^20 + 149x^19 + 1117x^18 - 1000x^17 - 12006x^16 - 3533x^15 + 64273x^14 + 63958x^13 - 171145x^12 - 263217x^11 + 207316x^10 + 471355x^9 - 84325x^8 - 394692x^7 + 1221x^6 + 166543x^5 + 881x^4 - 34179x^3 + 1826x^2 + 2665x - 347	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.6.4299288794103243236127943577240214703609.1	x^22 - 7x^21 + 19x^20 - 278x^18 + 1133x^17 - 2011x^16 + 888x^15 + 8287x^14 - 39621x^13 + 120190x^12 - 205304x^11 + 49905x^10 + 471482x^9 - 1443152x^8 + 2814323x^7 - 4045900x^6 + 3758973x^5 - 1667602x^4 + 1178692x^3 + 478694x^2 - 640688x + 244927	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.14.4299288794103243236127943577240214703609.2	x^22 - 6x^21 - 17x^20 + 128x^19 + 36x^18 - 939x^17 + 1324x^16 + 1351x^15 - 14113x^14 + 19961x^13 + 63677x^12 - 139022x^11 - 153919x^10 + 426871x^9 + 228955x^8 - 682443x^7 - 246758x^6 + 494621x^5 + 166486x^4 - 90530x^3 - 15247x^2 + 1575x + 49	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.6.4299288794103243236127943577240214703609.2	x^22 - 4x^21 - 27x^20 + 143x^19 - 1474x^17 + 5043x^16 - 4253x^15 - 22763x^14 + 75962x^13 - 70679x^12 - 119358x^11 + 468438x^10 - 582606x^9 + 180283x^8 + 170530x^7 - 66816x^6 - 13600x^5 - 27878x^4 + 5391x^3 - 1956x^2 - 665x + 19	\( 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.10.29391360462703563245733396281479720218577.1	x^22 - 7x^21 + 20x^20 - 37x^19 - 6x^18 - 96x^17 - 601x^16 + 4887x^15 - 10409x^14 + 17140x^13 + 61830x^12 - 229061x^11 + 473100x^10 - 93708x^9 - 2265797x^8 + 4028576x^7 - 8303052x^6 + 265807x^5 + 2580052x^4 - 854179x^3 + 69971x^2 + 4729x - 635	\( 1297^{13} \)	22T29	Trivial (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)
22.6.29391360462703563245733396281479720218577.2	x^22 - 4x^21 - 15x^20 + 186x^19 - 340x^18 - 190x^17 + 1474x^16 - 16339x^15 + 54779x^14 - 48760x^13 - 60506x^12 + 162742x^11 - 382113x^10 + 377976x^9 + 812112x^8 - 662419x^7 + 800005x^6 + 1654250x^5 - 632588x^4 - 210361x^3 + 534728x^2 + 1099550x + 328525	\( 1297^{13} \)	22T29	Trivial (GRH)
22.10.29391360462703563245733396281479720218577.3	x^22 - 2x^21 - 5x^20 + 63x^19 - 277x^18 - 763x^17 + 1430x^16 - 4519x^15 - 12215x^14 + 55828x^13 + 211576x^12 + 329486x^11 + 565827x^10 + 1673022x^9 + 1315125x^8 - 4385689x^7 - 9574393x^6 - 2442233x^5 + 9228793x^4 + 6912958x^3 - 1578970x^2 - 2159051x - 187717	\( 1297^{13} \)	22T29	Trivial (GRH)
22.10.29391360462703563245733396281479720218577.4	x^22 - 2x^21 - x^20 - 27x^19 - 123x^18 + 557x^17 - 15x^16 + 3931x^15 - 14708x^14 + 14397x^13 - 67597x^12 + 333066x^11 - 708951x^10 + 533647x^9 - 501187x^8 + 1877976x^7 + 4952836x^6 - 26543542x^5 + 33271030x^4 - 4722738x^3 - 22835725x^2 + 20238011x - 5825245	\( 1297^{13} \)	22T29	Trivial (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)
22.22.18032524186262409518264378257792941492206043136.1	x^22 - 40x^20 + 653x^18 - 5754x^16 + 30641x^14 - 103997x^12 + 229463x^10 - 327203x^8 + 291804x^6 - 151698x^4 + 40090x^2 - 4009	\( 2^{22}\cdot 19^{11}\cdot 211^{11} \)	22T29	Trivial (GRH)
22.22.1763538487452830226245963748900352261772304973824.1	x^22 - 89x^20 + 3150x^18 - 57580x^16 + 598262x^14 - 3693531x^12 + 13804717x^10 - 31161425x^8 + 41221734x^6 - 29534937x^4 + 9303930x^2 - 492561	\( 2^{22}\cdot 3^{11}\cdot 2027^{11} \)	22T29	Trivial (GRH)