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 53)

Label	Polynomial	Discriminant	Galois group	Class group
22.0.529866739430089519756710630129664.1	x^22 + 8x^20 + 29x^18 + 99x^16 + 222x^14 + 344x^12 + 382x^10 + 254x^8 + 145x^6 + 84x^4 + 32x^2 + 9	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.4.529866739430089519756710630129664.1	x^22 + 3x^20 + 23x^18 - 39x^16 + 58x^14 + 58x^12 - 275x^10 + 455x^8 - 258x^6 + 12x^4 + 12x^2 + 1	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.0.529866739430089519756710630129664.2	x^22 + 5x^20 - 3x^18 - 2x^16 + 35x^14 - 32x^12 + 18x^10 + 19x^8 - 11x^6 + 5x^4 + 7x^2 + 1	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (GRH)
22.4.529866739430089519756710630129664.2	x^22 - 3x^20 - x^18 + 4x^16 + 12x^14 - 14x^12 - 6x^10 + 6x^8 - 8x^6 + 11x^4 - 6x^2 + 1	\( -\,2^{22}\cdot 1831^{8} \)	22T42	Trivial (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)
22.6.9007734570311521835864080712204288.1	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)
22.6.970185999896493910674537163767414784.1	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)
22.14.95495132016543203413964761918289025880897.1	x^22 - 3x^21 - 29x^20 + 26x^19 + 420x^18 + 885x^17 - 3122x^16 - 19486x^15 - 3640x^14 + 188637x^13 + 243555x^12 - 1052571x^11 - 1941345x^10 + 3343356x^9 + 7877194x^8 - 4368623x^7 - 16343655x^6 - 3154416x^5 + 10462530x^4 + 4628676x^3 - 1677053x^2 - 994739x - 67717	\( 97\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.6.95495132016543203413964761918289025880897.1	x^22 - 9x^21 + 19x^20 + 110x^19 - 682x^18 + 489x^17 + 6037x^16 - 18540x^15 + 5911x^14 + 76660x^13 - 211000x^12 + 254168x^11 - 7956x^10 - 517531x^9 + 1351100x^8 - 2847860x^7 + 4722099x^6 - 5902951x^5 + 3241118x^4 + 3222860x^3 - 7591065x^2 + 6870510x - 2410857	\( 97\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.18.924610449303392395108565351166810367173677581.1	x^22 - 11x^21 + 44x^20 - 55x^19 - 149x^18 + 714x^17 - 1042x^16 - 742x^15 + 5168x^14 - 5630x^13 - 5248x^12 + 15888x^11 - 6710x^10 - 12738x^9 + 15541x^8 - 1265x^7 - 8234x^6 + 5083x^5 + 294x^4 - 1334x^3 + 492x^2 - 67x + 3	\( 74843^{8}\cdot 939181 \)	22T42	Trivial (GRH)
22.0.4129233136056857981979443884256982828952059904.1	x^22 + 53x^20 + 963x^18 + 8057x^16 + 34825x^14 + 83894x^12 + 119260x^10 + 102849x^8 + 53662x^6 + 16302x^4 + 2614x^2 + 169	\( -\,2^{22}\cdot 74843^{8} \)	22T42	$[193648]$ (GRH)
22.12.4129233136056857981979443884256982828952059904.1	x^22 + x^20 - 251x^18 + 474x^16 + 16151x^14 - 58074x^12 - 84453x^10 + 36512x^8 + 41198x^6 - 7092x^4 - 4293x^2 + 729	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.1	x^22 - 29x^20 + 57x^18 + 3633x^16 - 22667x^14 - 43524x^12 + 516399x^10 - 732335x^8 - 444902x^6 + 959879x^4 - 44962x^2 + 441	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.20.4129233136056857981979443884256982828952059904.1	x^22 - 68x^20 + 1749x^18 - 21878x^16 + 146579x^14 - 538577x^12 + 1028049x^10 - 796919x^8 - 100770x^6 + 299644x^4 - 34200x^2 + 729	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.4.4129233136056857981979443884256982828952059904.1	x^22 + 13x^20 - 636x^18 - 14672x^16 - 99474x^14 - 107348x^12 + 1163186x^10 + 3657772x^8 + 4010549x^6 + 1905711x^4 + 380936x^2 + 26569	\( -\,2^{22}\cdot 74843^{8} \)	22T42	$[2]$ (GRH)
22.8.4129233136056857981979443884256982828952059904.1	x^22 + 13x^20 - 175x^18 - 443x^16 + 4918x^14 + 5154x^12 - 30529x^10 - 31931x^8 - 8640x^6 - 37x^4 + 149x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.0.4129233136056857981979443884256982828952059904.2	x^22 + 53x^20 + 1109x^18 + 11954x^16 + 72629x^14 + 254808x^12 + 505403x^10 + 527803x^8 + 253819x^6 + 49582x^4 + 3337x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	$[110224]$ (GRH)
22.12.4129233136056857981979443884256982828952059904.2	x^22 + 12x^20 - 99x^18 - 1322x^16 + 2041x^14 + 33971x^12 - 1977x^10 - 65346x^8 + 6098x^6 + 23442x^4 - 4147x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.2	x^22 - 18x^20 - 120x^18 + 3945x^16 - 21338x^14 - 14989x^12 + 369623x^10 - 648901x^8 - 637282x^6 + 2623736x^4 - 2281873x^2 + 588289	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.20.4129233136056857981979443884256982828952059904.2	x^22 - 48x^20 + 773x^18 - 5165x^16 + 14676x^14 - 11976x^12 - 15879x^10 + 31691x^8 - 16674x^6 + 3536x^4 - 313x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.4.4129233136056857981979443884256982828952059904.2	x^22 + 36x^20 + 304x^18 - 824x^16 - 20222x^14 - 83254x^12 - 86677x^10 + 173346x^8 + 424981x^6 + 275162x^4 + 53257x^2 + 81	\( -\,2^{22}\cdot 74843^{8} \)	22T42	$[2]$ (GRH)
22.8.4129233136056857981979443884256982828952059904.2	x^22 - 7x^20 - 305x^18 + 1628x^16 + 16707x^14 - 32324x^12 - 356150x^10 - 370911x^8 + 918618x^6 + 1408022x^4 + 86679x^2 + 729	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.12.4129233136056857981979443884256982828952059904.3	x^22 + 8x^20 - 534x^18 + 4098x^16 + 2927x^14 - 114120x^12 + 301339x^10 - 96731x^8 - 150700x^6 - 25366x^4 + 878x^2 + 81	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.3	x^22 - 6x^20 - 335x^18 + 5050x^16 - 18019x^14 - 101105x^12 + 982641x^10 - 2621147x^8 + 1562236x^6 + 2051432x^4 - 26350x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.3	x^22 - 10x^20 - 462x^18 + 3723x^16 + 44062x^14 - 61606x^12 - 1444979x^10 - 4726237x^8 - 6044709x^6 - 2432660x^4 + 446695x^2 + 52441	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.12.4129233136056857981979443884256982828952059904.4	x^22 + 38x^20 + 282x^18 - 2354x^16 - 17471x^14 + 65238x^12 + 151346x^10 - 589814x^8 + 397693x^6 - 55679x^4 + 266x^2 + 81	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.16.4129233136056857981979443884256982828952059904.4	x^22 - 20x^20 - 141x^18 + 6373x^16 - 58122x^14 + 200198x^12 - 37877x^10 - 1451515x^8 + 3467174x^6 - 2913736x^4 + 806773x^2 + 3969	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.4	x^22 + 53x^20 + 1013x^18 + 7634x^16 + 4909x^14 - 175743x^12 - 326231x^10 + 1362553x^8 + 1192125x^6 - 2661192x^4 - 168308x^2 + 109561	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.12.4129233136056857981979443884256982828952059904.5	x^22 - 20x^20 - 127x^18 + 3357x^16 + 85x^14 - 98678x^12 + 5024x^10 + 688029x^8 + 52810x^6 - 963192x^4 + 62257x^2 + 178929	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.5	x^22 + 10x^20 - 224x^18 - 1796x^16 + 5190x^14 + 71141x^12 + 187010x^10 + 147260x^8 + 4176x^6 - 5361x^4 - 167x^2 + 1	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.12.4129233136056857981979443884256982828952059904.6	x^22 - 25x^20 + 103x^18 + 744x^16 - 2021x^14 - 11803x^12 - 14257x^10 - 905x^8 + 6312x^6 + 1126x^4 - 951x^2 + 49	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.8.4129233136056857981979443884256982828952059904.6	x^22 + 13x^20 - 136x^18 - 1229x^16 + 6421x^14 + 15324x^12 - 43922x^10 - 84593x^8 - 33311x^6 - 3209x^4 + 35x^2 + 9	\( -\,2^{22}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.10.12387699408170573945938331652770948486856179712.1	x^22 + 11x^20 + 16x^18 - 230x^16 - 1143x^14 - 1795x^12 - 203x^10 + 1583x^8 + 484x^6 - 425x^4 + 67x^2 - 3	\( 2^{22}\cdot 3\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.22.532671074551334679675348261069150784934815727616.1	x^22 - 33x^20 + 475x^18 - 3915x^16 + 20393x^14 - 69905x^12 + 159170x^10 - 237054x^8 + 220759x^6 - 116733x^4 + 27922x^2 - 1161	\( 2^{22}\cdot 3\cdot 43\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.10.730874265082063862810361567513485960724514603008.1	x^22 - 20x^18 + 143x^14 + 4x^12 - 463x^10 - 54x^8 + 691x^6 + 186x^4 - 392x^2 - 177	\( 2^{22}\cdot 3\cdot 59\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.14.1308966904130023980287483711309463556777802989568.1	x^22 - 11x^20 + 16x^18 + 142x^16 - 439x^14 - 129x^12 + 1485x^10 - 559x^8 - 1724x^6 + 871x^4 + 583x^2 - 317	\( 2^{22}\cdot 317\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.14.8454115376424649903675045731962308211426203045057.1	x^22 - 6x^21 - 84x^20 + 446x^19 + 3054x^18 - 13258x^17 - 47156x^16 + 87393x^15 + 214333x^14 + 4592960x^13 - 8169779x^12 - 97523140x^11 + 286905876x^10 + 443480439x^9 - 2833653296x^8 + 2392585056x^7 + 7429384462x^6 - 17535751907x^5 + 7148761681x^4 + 16729868412x^3 - 21211987463x^2 + 6184844508x + 940596021	\( 97^{5}\cdot 74843^{8} \)	22T42	Trivial (GRH)
22.10.309044195601903421945287518629445365867259019395072.1	x^22 - 45x^20 - 1917x^18 - 19x^16 + 630240x^14 + 8584323x^12 + 43408091x^10 + 57022357x^8 - 144688750x^6 - 213344603x^4 + 32631548x^2 - 673587	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.14.309044195601903421945287518629445365867259019395072.1	x^22 - 66x^20 + 764x^18 + 18746x^16 - 358167x^14 - 833741x^12 + 40130611x^10 - 82628849x^8 - 1347063832x^6 + 5030088709x^4 - 605479870x^2 - 113836203	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.18.309044195601903421945287518629445365867259019395072.1	x^22 - 152x^20 + 8733x^18 - 236350x^16 + 3051787x^14 - 17399125x^12 + 47374033x^10 - 62687488x^8 + 35737999x^6 - 4125223x^4 - 1571703x^2 - 74843	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.2.309044195601903421945287518629445365867259019395072.1	x^22 + 101x^20 + 4176x^18 + 91407x^16 + 1138432x^14 + 8015565x^12 + 29342566x^10 + 41164011x^8 - 37023993x^6 - 171064312x^4 - 170043296x^2 - 54560547	\( 2^{22}\cdot 74843^{9} \)	22T42	$[90]$ (GRH)
22.22.309044195601903421945287518629445365867259019395072.1	x^22 - 164x^20 + 11177x^18 - 414569x^16 + 9220027x^14 - 127930459x^12 + 1118415018x^10 - 6092366081x^8 + 20037463337x^6 - 37248632179x^4 + 34131252034x^2 - 11209161267	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.6.309044195601903421945287518629445365867259019395072.1	x^22 + 162x^20 + 8365x^18 + 150901x^16 + 603205x^14 - 6625362x^12 - 32932697x^10 + 128155464x^8 + 204536177x^6 - 619108447x^4 - 27916439x^2 - 74843	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.10.309044195601903421945287518629445365867259019395072.2	x^22 - 40x^20 - 4187x^18 - 86459x^16 - 419737x^14 + 4565971x^12 + 45230383x^10 + 7236576x^8 - 744630181x^6 - 580648009x^4 + 3448765440x^2 - 54560547	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.14.309044195601903421945287518629445365867259019395072.2	x^22 + 37x^20 - 1608x^18 - 1511x^16 + 343041x^14 - 1379182x^12 - 18048818x^10 + 125311851x^8 - 182985604x^6 - 215226104x^4 + 568433909x^2 - 260528483	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.2.309044195601903421945287518629445365867259019395072.2	x^22 + 142x^20 + 8137x^18 + 240973x^16 + 3891662x^14 + 32293812x^12 + 96833387x^10 - 243780245x^8 - 1499852584x^6 - 510354432x^4 - 18785593x^2 - 74843	\( 2^{22}\cdot 74843^{9} \)	22T42	n/a
22.6.309044195601903421945287518629445365867259019395072.2	x^22 + 2x^20 - 3444x^18 - 122572x^16 - 1108565x^14 + 16645328x^12 + 450015451x^10 + 3964896234x^8 + 16436635093x^6 + 31054897710x^4 + 18216187456x^2 - 5496544763	\( 2^{22}\cdot 74843^{9} \)	22T42	$[3]$ (GRH)
22.10.309044195601903421945287518629445365867259019395072.3	x^22 + 43x^20 - 666x^18 - 30595x^16 + 66169x^14 + 1320239x^12 - 1993079x^10 - 13734822x^8 + 23182188x^6 - 308103x^4 - 4415737x^2 - 673587	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)
22.14.309044195601903421945287518629445365867259019395072.3	x^22 - 111x^20 + 2578x^18 - 9394x^16 - 239002x^14 + 1799474x^12 + 3562740x^10 - 42068353x^8 + 14604187x^6 + 177860434x^4 - 161361508x^2 - 673587	\( 2^{22}\cdot 74843^{9} \)	22T42	Trivial (GRH)