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 85)

Label	Polynomial	Discriminant	Galois group	Class group
22.6.440358787157109245022232573.1	x^22 - 11x^21 + 64x^20 - 255x^19 + 770x^18 - 1857x^17 + 3688x^16 - 6146x^15 + 8690x^14 - 10480x^13 + 10777x^12 - 9386x^11 + 6807x^10 - 3960x^9 + 1680x^8 - 341x^7 - 170x^6 + 212x^5 - 109x^4 + 28x^3 + 3x^2 - 5x + 1	\( 37\cdot 163^{2}\cdot 14281\cdot 177106931^{2} \)	22T53	Trivial (GRH)
22.6.1447402975463751668017578125.1	x^22 - 2x^21 - x^20 + 18x^19 - 17x^18 - 44x^17 + 110x^16 - 3x^15 - 254x^14 + 59x^13 + 240x^12 - 102x^11 - 552x^10 - 230x^9 + 307x^8 + 320x^7 - 3x^6 - 154x^5 - 62x^4 + 18x^3 + 19x^2 + 2x - 1	\( 5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4} \)	22T46	Trivial (GRH)
22.6.2613825179875044875466440704.1	x^22 - 6x^20 + 16x^18 - 18x^16 + 4x^14 - 6x^12 + 25x^10 - 3x^8 - 19x^6 + 4x^4 + 4x^2 - 1	\( 2^{22}\cdot 971^{2}\cdot 25709231^{2} \)	22T51	Trivial (GRH)
22.6.3029890053010200585803137024.1	x^22 - x^18 - x^16 - 2x^14 + x^10 + 2x^8 + 2x^6 - 1	\( 2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2} \)	22T51	Trivial (GRH)
22.6.4525438563861162255210415625.1	x^22 - 3x^21 - 5x^20 + 20x^19 + 6x^18 - 46x^17 - 22x^16 + 88x^15 + 102x^14 - 250x^13 - 116x^12 + 460x^11 - 50x^10 - 559x^9 + 321x^8 + 395x^7 - 287x^6 - 315x^5 + 200x^4 + 136x^3 + 14x^2 - 70x + 5	\( 5^{5}\cdot 7^{6}\cdot 83^{4}\cdot 127^{4}\cdot 997 \)	22T52	Trivial (GRH)
22.6.11179894991688395891652264149.1	x^22 - 11x^21 + 44x^20 - 55x^19 - 111x^18 + 372x^17 - 61x^16 - 838x^15 + 563x^14 + 1153x^13 - 1030x^12 - 1191x^11 + 1050x^10 + 987x^9 - 634x^8 - 630x^7 + 192x^6 + 264x^5 - 3x^4 - 53x^3 - 10x^2 + x - 1	\( 83\cdot 199\cdot 937\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2} \)	22T53	Trivial (GRH)
22.6.18415764278243178646713405625.1	x^22 - 7x^21 + 16x^20 - 3x^19 - 51x^18 + 101x^17 - 62x^16 - 50x^15 + 49x^14 + 124x^13 - 271x^12 + 166x^11 + 113x^10 - 102x^9 - 51x^8 - 34x^7 + 128x^6 - 78x^5 - 37x^4 + 36x^3 + 14x^2 - 8x + 1	\( 5^{4}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}\cdot 997^{2} \)	22T49	Trivial (GRH)
22.6.30428929951449912919970703125.1	x^22 - 8x^19 - 4x^16 + 116x^15 - 47x^14 - 228x^13 + 179x^12 + 177x^11 - 108x^10 + 58x^9 + 78x^8 + 4x^7 + 37x^6 - 13x^5 - 40x^4 - x^3 + 10x^2 + x - 1	\( 5^{11}\cdot 971^{2}\cdot 25709231^{2} \)	22T47	Trivial (GRH)
22.6.31524414620673611592542191616.1	x^22 - 6x^20 + 14x^18 - 15x^16 - 6x^14 + 47x^12 - 75x^10 + 21x^8 + 101x^6 - 110x^4 + 55x^2 - 11	\( 2^{24}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4} \)	22T52	Trivial (GRH)
22.6.33458177485426043697705078125.1	x^22 - 3x^20 - 4x^19 - 13x^18 + x^17 + 41x^16 + 85x^15 - 10x^14 - 177x^13 + 9x^12 + 233x^11 - 32x^10 - 26x^9 + 38x^8 - 74x^7 + 18x^6 + 22x^5 - 25x^4 + 6x^2 - 1	\( 5^{11}\cdot 14851^{2}\cdot 1762627^{2} \)	22T47	Trivial (GRH)
22.6.45853693993707071407334096896.1	x^22 - 12x^20 + 59x^18 - 154x^16 + 229x^14 - 193x^12 + 96x^10 - 57x^8 + 54x^6 - 24x^4 + x^2 - 1	\( 2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4} \)	22T49	Trivial (GRH)
22.6.1562900555060447098970765787136.1	x^22 + x^20 - 4x^18 - x^16 + 5x^14 - 7x^12 - 7x^10 + 5x^8 + 7x^6 + 3x^4 - x^2 - 1	\( 2^{22}\cdot 610429790897^{2} \)	22T51	Trivial (GRH)
22.6.1572374828482515451166834294784.1	x^22 - 4x^21 + 8x^20 - 8x^19 - 2x^18 + 20x^17 - 32x^16 + 22x^15 + 9x^14 - 38x^13 + 40x^12 - 12x^11 - 20x^10 + 30x^9 - 15x^8 - 6x^7 + 12x^6 - 8x^5 - x^4 + 4x^3 - 2x^2 + 1	\( 2^{33}\cdot 3^{2}\cdot 47\cdot 311\cdot 1391443157437409 \)	22T57	Trivial (GRH)
22.6.1815714277580347556883155703869.1	x^22 - 11x^21 + 64x^20 - 255x^19 + 769x^18 - 1848x^17 + 3647x^16 - 6022x^15 + 8418x^14 - 10032x^13 + 10228x^12 - 8926x^11 + 6647x^10 - 4183x^9 + 2160x^8 - 829x^7 + 136x^6 + 111x^5 - 114x^4 + 47x^3 - 3x^2 - 5x + 1	\( 71^{2}\cdot 73^{2}\cdot 1408829\cdot 219034943^{2} \)	22T53	Trivial (GRH)
22.6.2741869623221317890608793124864.1	x^22 + 2x^20 - x^18 - 4x^16 - x^14 + 5x^12 - x^10 - 8x^8 + 3x^6 + 5x^4 - x^2 - 1	\( 2^{22}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2} \)	22T51	Trivial (GRH)
22.6.3790988231418101231518884499009.1	x^22 - x^21 + 5x^20 - 13x^19 + 3x^18 - 23x^17 - 63x^16 + 117x^15 + 79x^14 + 221x^13 + 156x^12 + 15x^11 - 1069x^10 - 1131x^9 - 164x^8 + 1812x^7 + 1646x^6 - 690x^5 - 1234x^4 - 363x^3 - 6x^2 + 10x + 1	\( 23^{20}\cdot 47^{2} \)	22T23	Trivial (GRH)
22.6.17629227795712151522876415102277.1	x^22 - 11x^21 + 64x^20 - 255x^19 + 769x^18 - 1848x^17 + 3645x^16 - 6006x^15 + 8346x^14 - 9808x^13 + 9702x^12 - 7954x^11 + 5209x^10 - 2471x^9 + 537x^8 + 363x^7 - 501x^6 + 318x^5 - 120x^4 + 16x^3 + 13x^2 - 9x + 1	\( 349^{2}\cdot 1697\cdot 1949\cdot 6615221297^{2} \)	22T53	Trivial (GRH)
22.6.19942830400383601345661142929337.1	x^22 - 3x^21 + 7x^20 - 13x^19 + 18x^18 - 21x^17 + 18x^16 - 9x^15 - 5x^14 + 16x^13 - 24x^12 + 25x^11 - 16x^10 + 6x^9 + 3x^8 - 12x^7 + 9x^6 - 6x^5 + 4x^4 + 2x^3 - x^2 + x - 1	\( 3^{4}\cdot 7^{2}\cdot 59\cdot 5851\cdot 36319\cdot 400764924995207263 \)	22T59	Trivial (GRH)
22.6.32352556342113252227121422532608.1	x^22 - 10x^20 + 20x^18 + 38x^16 + 30x^14 - 676x^12 + 645x^10 + 720x^8 - 79x^6 - 2438x^4 + 2236x^2 - 648	\( 2^{43}\cdot 43793^{4} \)	22T46	Trivial (GRH)
22.6.190519758499542040030540538748229.1	x^22 - x^21 - 2x^20 + 6x^19 - 4x^18 - 5x^17 + 13x^16 - 11x^15 + 13x^13 - 18x^12 + 11x^11 + 3x^10 - 14x^9 + 15x^8 - 7x^7 - 3x^6 + 8x^5 - 8x^4 + 2x^3 + x^2 - 2x + 1	\( 1671032183\cdot 114013219157456550332963 \)	22T59	Trivial (GRH)
22.6.237871803919090816246272099352576.1	x^22 + 12x^20 + 59x^18 + 151x^16 + 204x^14 + 106x^12 - 64x^10 - 101x^8 - 19x^6 + 16x^4 + 3x^2 - 1	\( 2^{22}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2} \)	22T51	Trivial (GRH)
22.6.529866739430089519756710630129664.1	x^22 - 13x^20 + 76x^18 - 269x^16 + 659x^14 - 1206x^12 + 1700x^10 - 1829x^8 + 1455x^6 - 817x^4 + 293x^2 - 49	\( 2^{22}\cdot 1831^{8} \)	22T39	Trivial (GRH)
22.6.529866739430089519756710630129664.2	x^22 - 5x^20 - 3x^18 + 2x^16 + 35x^14 + 32x^12 + 18x^10 - 19x^8 - 11x^6 - 5x^4 + 7x^2 - 1	\( 2^{22}\cdot 1831^{8} \)	22T39	Trivial (GRH)
22.6.1288033148279983900699565800554496.1	x^22 + 8x^20 + 24x^18 + 28x^16 - 12x^14 - 66x^12 - 48x^10 + 28x^8 + 43x^6 + 3x^4 - 7x^2 - 1	\( 2^{22}\cdot 17524013040643^{2} \)	22T51	Trivial (GRH)
22.6.2235701649852680852322529969176576.1	x^22 - 2x^21 - x^20 + 8x^19 - 9x^18 - 2x^17 + 15x^16 - 16x^15 + 8x^14 + 2x^13 - 14x^12 + 22x^11 - 13x^10 - 6x^9 + 13x^8 - 10x^7 + 4x^6 - 5x^4 + 6x^3 - x^2 - 2x + 1	\( 2^{33}\cdot 3^{2}\cdot 11^{2}\cdot 241\cdot 991697156691810497 \)	22T57	Trivial (GRH)
22.6.4098058278162967431271914143428729.1	x^22 - x^21 + x^20 - x^19 - 22x^18 - x^17 - 114x^16 + 160x^15 - 22x^14 + 390x^13 + 806x^12 + 712x^11 + 1174x^10 - 5015x^9 - 2690x^8 - 5866x^7 + 10213x^6 - 2646x^5 + 2232x^4 - 12927x^3 + 6786x^2 - 806x + 47	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.6.4098058278162967431271914143428729.3	x^22 - 5x^21 + 2x^20 + 36x^19 - 88x^18 + 95x^17 - 15x^16 - 224x^15 + 108x^14 + 58x^13 + 1642x^12 - 5082x^11 + 6435x^10 + 1474x^9 - 21998x^8 + 40783x^7 - 25274x^6 - 17265x^5 + 57828x^4 - 81220x^3 + 54660x^2 - 19173x + 7499	\( 23^{21}\cdot 47^{3} \)	22T28	Trivial (GRH)
22.6.5846186244289687455223944279228416.1	x^22 + 2x^20 - 4x^19 - 3x^18 - 6x^17 + 12x^15 + 10x^14 + 12x^13 - 9x^12 - 16x^11 - 16x^10 - 8x^9 + 11x^8 + 10x^7 + 9x^6 + 2x^5 - 5x^4 - 2x^3 - 2x^2 + 1	\( 2^{33}\cdot 7\cdot 39297136127\cdot 2474137595057 \)	22T57	Trivial (GRH)
22.6.6168460699614248235671671923828125.1	x^22 - 2x^21 - x^20 - 18x^19 + 62x^18 - 94x^16 - 181x^15 + 176x^14 + 109x^13 - 688x^12 - 104x^11 + 486x^10 - 327x^9 - 459x^8 + 239x^7 + 157x^6 - 80x^5 - 7x^4 + 30x^3 + 13x^2 - 2x - 1	\( 5^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.6.6168460699614248235671671923828125.2	x^22 - 2x^21 + 5x^20 + 14x^19 - 14x^18 + 142x^17 - 5x^16 + 272x^15 + 173x^14 + 218x^13 + 72x^12 + 64x^11 - 24x^10 - 523x^9 - 90x^8 - 459x^7 + 102x^6 - 56x^5 + 85x^4 + 4x^3 + 7x^2 - 4x - 1	\( 5^{11}\cdot 1831^{8} \)	22T13	Trivial (GRH)
22.6.6719996816960288878148142661369856.1	x^22 - 2x^21 - x^20 + 10x^19 - 11x^18 - 8x^17 + 30x^16 - 20x^15 - 16x^14 + 34x^13 - 18x^12 - 4x^11 + 13x^10 - 16x^9 + 13x^8 - 12x^6 + 8x^5 - 2x^4 + x^2 - 2x + 1	\( 2^{33}\cdot 2399\cdot 3769\cdot 593353\cdot 145817511551 \)	22T57	Trivial (GRH)
22.6.7198079267989980836471065337135104.1	x^22 + 13x^20 + 58x^18 + 76x^16 - 157x^14 - 555x^12 - 497x^10 - 62x^8 + 93x^6 + 22x^4 - 4x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.6.7198079267989980836471065337135104.2	x^22 + 16x^20 + 85x^18 + 166x^16 - 21x^14 - 476x^12 - 477x^10 + 83x^8 + 328x^6 + 143x^4 + 14x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.6.7198079267989980836471065337135104.3	x^22 + 9x^20 + 18x^18 - 52x^16 - 221x^14 - 121x^12 + 384x^10 + 550x^8 + 179x^6 - 39x^4 - 16x^2 - 1	\( 2^{22}\cdot 23^{20} \)	22T23	Trivial (GRH)
22.6.8147930264446686251430802882822144.1	x^22 + 6x^20 + 3x^18 - 36x^16 - 53x^14 + 44x^12 + 116x^10 + 29x^8 - 55x^6 - 42x^4 - 11x^2 - 1	\( 2^{18}\cdot 7786721^{2}\cdot 22641181^{2} \)	22T51	Trivial (GRH)
22.6.9007734570311521835864080712204288.1	x^22 - 9x^20 + 38x^18 - 104x^16 + 209x^14 - 331x^12 + 429x^10 - 453x^8 + 376x^6 - 227x^4 + 89x^2 - 17	\( 2^{22}\cdot 17\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.6.165555823163769559238834502754107392.1	x^22 - 46x^18 - 69x^16 + 529x^14 + 1242x^12 - 1196x^10 - 5336x^8 - 4922x^6 - 1932x^4 - 345x^2 - 23	\( 2^{22}\cdot 23^{21} \)	22T28	Trivial (GRH)
22.6.970185999896493910674537163767414784.1	x^22 + 16x^20 + 148x^18 + 671x^16 + 1205x^14 - 5770x^12 - 13367x^10 - 3297x^8 + 124727x^6 - 177384x^4 + 91550x^2 - 16479	\( 2^{22}\cdot 1831^{9} \)	22T42	Trivial (GRH)
22.6.2661248664423333685102326194280333312.1	x^22 - 11x^21 + 44x^20 - 44x^19 - 231x^18 + 825x^17 - 550x^16 - 1540x^15 - 968x^14 + 23056x^13 - 65956x^12 + 98910x^11 - 90409x^10 + 22077x^9 + 172414x^8 - 515240x^7 + 704264x^6 - 400400x^5 - 37840x^4 + 72512x^3 + 32560x^2 + 3696x - 9888	\( 2^{24}\cdot 3^{11}\cdot 11^{23} \)	22T14	Trivial (GRH)
22.6.22661033510180079603495293971842498241.2	x^22 - x^21 - 11x^20 + 37x^19 - 125x^18 - 206x^17 + 947x^16 - 1002x^15 + 693x^14 - 867x^13 - 2005x^12 + 50723x^11 - 26677x^10 - 11638x^9 + 87302x^8 + 129837x^7 + 279630x^6 - 109510x^5 - 453150x^4 - 37802x^3 + 155367x^2 - 17135x - 36319	\( 1297^{12} \)	22T30	Trivial (GRH)
22.6.56501459388151144478039723653407440896.1	x^22 + 26x^20 + 246x^18 + 992x^16 + 1270x^14 - 1382x^12 - 3114x^10 - 1149x^8 + 264x^6 + 117x^4 - 5x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.6.56501459388151144478039723653407440896.2	x^22 + 25x^20 + 230x^18 + 924x^16 + 1202x^14 - 2380x^12 - 9046x^10 - 8766x^8 - 865x^6 + 1915x^4 + 68x^2 - 1	\( 2^{22}\cdot 1297^{10} \)	22T30	Trivial (GRH)
22.6.113420524920318543882697355574770703125.1	x^22 - 9x^21 + 41x^20 - 140x^19 + 383x^18 - 720x^17 + 530x^16 + 1506x^15 - 7373x^14 + 22033x^13 - 51771x^12 + 76979x^11 - 19458x^10 - 188822x^9 + 431163x^8 - 422621x^7 + 84439x^6 + 244344x^5 - 239399x^4 + 37800x^3 + 53515x^2 - 17850x - 6300	\( 5^{8}\cdot 7^{15}\cdot 11^{19} \)	22T14	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)
22.6.4299288794103243236127943577240214703609.1	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)
22.6.4299288794103243236127943577240214703609.2	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)
22.6.6172475179135960522642404800603172634624.1	x^22 + 22x^20 - 44x^19 + 176x^18 - 242x^17 + 506x^16 - 726x^15 + 528x^14 - 5214x^13 + 3894x^12 + 316x^11 - 23716x^10 - 10472x^9 + 82962x^8 + 101090x^7 - 82456x^6 - 170368x^5 - 12100x^4 + 75504x^3 + 37510x^2 + 6776x + 242	\( 2^{28}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.6.6172475179135960522642404800603172634624.2	x^22 - 308x^18 - 3080x^16 - 7040x^14 + 42944x^12 + 292600x^10 + 659120x^8 + 536096x^6 - 125532x^4 - 335060x^2 - 70756	\( 2^{28}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (GRH)
22.6.24689900716543842090569619202412690538496.1	x^22 - 22x^18 + 88x^16 - 484x^15 - 1232x^14 - 352x^13 - 8448x^12 - 11888x^11 + 8712x^10 - 54208x^9 + 42592x^8 + 256608x^7 - 547888x^6 - 399168x^5 + 878944x^4 - 1636800x^3 - 2798048x^2 + 297088x + 734816	\( 2^{30}\cdot 7^{10}\cdot 11^{22} \)	22T34	Trivial (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)