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 736)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.1767647026420274120972649193.1	x^8 - x^7 + 2122x^6 - 39330x^5 + 4144821x^4 + 24141747x^3 + 1540947392x^2 - 171927064784x + 3339224703104	\( 73^{7}\cdot 233^{6} \)	$C_8$ (as 8T1)	$[5513055508]$ (GRH)
8.0.8656391633739689127939614209.1	x^8 - 3x^7 + 8468x^6 - 150738x^5 + 22418861x^4 + 396498613x^3 - 32011251778x^2 - 848649683424x + 28742837126528	\( 113^{6}\cdot 401^{6} \)	$Q_8$ (as 8T5)	$[2, 4522, 203490]$ (GRH)
8.0.2796208786031806116389676225641.2	x^8 - x^7 + 5439x^6 + 549113x^5 + 29196988x^4 + 1307717844x^3 + 133263372368x^2 + 7230689962880x + 161758275770368	\( 109^{6}\cdot 401^{7} \)	$C_8$ (as 8T1)	$[4, 332754580]$ (GRH)
8.0.3275381636640984798566041763497.4	x^8 - x^7 + 1430x^6 - 286270x^5 - 6455491x^4 - 308590549x^3 + 21350056300x^2 + 1051286540820x + 10486122964416	\( 89^{7}\cdot 257^{7} \)	$C_8$ (as 8T1)	$[2, 4, 145744728]$ (GRH)
8.0.3905284068350630918099056615049.1	x^8 - x^7 + 5641x^6 + 671753x^5 - 7546954x^4 - 2049624728x^3 - 40387406944x^2 + 1711530984976x + 64650867436256	\( 101^{6}\cdot 449^{7} \)	$C_8$ (as 8T1)	$[68, 28851380]$ (GRH)
8.0.4786017277896748306090327094857.1	x^8 - x^7 + 5873x^6 - 421803x^5 - 27870482x^4 + 1125604804x^3 + 33899521688x^2 - 2233056627168x + 108461951237376	\( 109^{6}\cdot 433^{7} \)	$C_8$ (as 8T1)	$[2, 2, 266466436]$ (GRH)
8.0.5235505260467902422785504364889.2	x^8 - x^7 + 24662x^6 + 1813972x^5 + 210268857x^4 - 3890248614x^3 - 81144892584x^2 - 19047412684944x + 2101736448182448	\( 313^{6}\cdot 421^{6} \)	$C_4\times C_2$ (as 8T2)	$[2, 2, 8, 8, 4586160]$ (GRH)
8.0.5453424776560798429911468532201.1	x^8 - x^7 + 1538x^6 + 356330x^5 - 16290799x^4 - 408639337x^3 + 33360459244x^2 - 642996773760x + 4291557679872	\( 73^{7}\cdot 337^{7} \)	$C_8$ (as 8T1)	$[2980610152]$ (GRH)
8.0.5453424776560798429911468532201.4	x^8 - x^7 + 1538x^6 + 356330x^5 - 6548803x^4 + 373377251x^3 + 28692271888x^2 - 1163044889868x + 28504814036976	\( 73^{7}\cdot 337^{7} \)	$C_8$ (as 8T1)	$[2785668392]$ (GRH)
8.0.7386062380882957944509679271936.1	x^8 + 9544x^6 + 10617700x^4 + 3328470000x^2 + 244602281250	\( 2^{31}\cdot 1193^{7} \)	$C_8$ (as 8T1)	$[2, 4286244040]$ (GRH)
8.0.7739821010662334648785565646848.16	x^8 + 9608x^6 + 29232340x^4 + 31644274672x^2 + 7016429858018	\( 2^{31}\cdot 1201^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 2, 2, 4, 8, 16, 610240]$ (GRH)
8.0.7739821010662334648785565646848.35	x^8 + 9608x^6 + 946388x^4 + 23539600x^2 + 5767202	\( 2^{31}\cdot 1201^{7} \)	$C_8$ (as 8T1)	$[2, 2, 2, 2, 8, 8, 1463120]$ (GRH)
8.0.7739821010662334648785565646848.36	x^8 + 9608x^6 + 23544404x^4 + 2238145168x^2 + 5767202	\( 2^{31}\cdot 1201^{7} \)	$C_8$ (as 8T1)	$[2, 2, 2, 2, 8, 8, 3369680]$ (GRH)
8.0.7739821010662334648785565646848.45	x^8 + 9608x^6 + 28848020x^4 + 27717177616x^2 + 3464647202	\( 2^{31}\cdot 1201^{7} \)	$C_8:C_2$ (as 8T7)	$[2, 4, 4, 4, 8, 16, 130960]$ (GRH)
8.0.13547867530592509401139876200448.12	x^8 + 10408x^6 + 33852020x^4 + 35233182416x^2 + 4404147802	\( 2^{31}\cdot 1301^{7} \)	$C_8:C_2$ (as 8T7)	$[1145772020]$ (GRH)
8.0.18244342591747163638870188429401.1	x^8 - x^7 + 7444x^6 + 780490x^5 + 51900405x^4 + 2217754863x^3 + 234821135222x^2 + 20637311571272x + 532351922168960	\( 149^{6}\cdot 401^{7} \)	$C_8$ (as 8T1)	$[2, 2, 745336820]$ (GRH)
8.0.19082143100442103109705931158249.1	x^8 - x^7 + 40727x^6 - 163063x^5 + 247972964x^4 - 63041308x^3 + 339739632560x^2 - 4749902474240x + 63545277135872	\( 401^{7}\cdot 409^{5} \)	$C_4\wr C_2$ (as 8T17)	$[4, 4, 154279060]$ (GRH)
8.0.21330346599403509883644513084409.2	x^8 - x^7 + 8330x^6 - 229466x^5 - 56166807x^4 - 310527529x^3 + 199114343500x^2 - 9386483978364x + 584194567641536	\( 241^{7}\cdot 277^{6} \)	$C_8$ (as 8T1)	$[2, 2, 2, 2, 28, 3291064]$ (GRH)
8.0.24969423926841105551040628528649.2	x^8 - x^7 + 7845x^6 - 405267x^5 + 66210090x^4 - 2848018388x^3 + 76480434632x^2 - 19422288907392x + 816267426117248	\( 157^{6}\cdot 401^{7} \)	$C_8$ (as 8T1)	$[1047824020]$ (GRH)
8.0.33559484046234370382183822000128.21	x^8 + 11848x^6 + 40052164x^4 + 45081237168x^2 + 9136527503202	\( 2^{31}\cdot 1481^{7} \)	$C_8$ (as 8T1)	$[2, 801216120]$ (GRH)
8.0.34561992451373371988963929807177.3	x^8 - x^7 + 9373x^6 - 2041147x^5 + 84364018x^4 + 213260884x^3 + 20608946088x^2 - 9015145181408x + 314486677270784	\( 193^{7}\cdot 389^{6} \)	$C_8$ (as 8T1)	$[2, 2, 2, 4, 34415428]$ (GRH)
8.0.55096283096198945191473583485401.1	x^8 - x^7 + 8784x^6 - 1105838x^5 - 41710915x^4 + 7420291295x^3 - 104734544334x^2 - 12537439675376x + 407608692541952	\( 157^{6}\cdot 449^{7} \)	$C_8$ (as 8T1)	$[3, 908259612]$ (GRH)
8.0.81729569074669588344431934238657.2	x^8 - x^7 + 16128x^6 - 637651x^5 + 138292271x^4 - 2575089632x^3 + 241749991220x^2 - 8775142779728x + 739277270681216	\( 193^{7}\cdot 449^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 2, 4, 16378080]$ (GRH)
8.0.81729569074669588344431934238657.3	x^8 - x^7 + 16128x^6 + 402233x^5 + 106055867x^4 - 194795156x^3 + 117877276000x^2 - 3675683362368x + 988078947349328	\( 193^{7}\cdot 449^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 2, 4, 21931104]$ (GRH)
8.0.96027574156103099500532510752768.18	x^8 + 13768x^6 + 59099140x^4 + 84225216816x^2 + 20711409061122	\( 2^{31}\cdot 1721^{7} \)	$C_8$ (as 8T1)	$[5, 5, 170, 720120]$ (GRH)
8.0.96027574156103099500532510752768.28	x^8 + 13768x^6 + 59236820x^4 + 81557253776x^2 + 13616968482	\( 2^{31}\cdot 1721^{7} \)	$C_8:C_2$ (as 8T7)	$[5, 10, 36191640]$ (GRH)
8.0.104116908284538646543243661017088.21	x^8 + 13928x^6 + 60621620x^4 + 84433792336x^2 + 10554224042	\( 2^{31}\cdot 1741^{7} \)	$C_8:C_2$ (as 8T7)	$[1492416060]$ (GRH)
8.0.154691088673896293052793942309897.2	x^8 - x^7 + 2480x^6 + 396110x^5 - 11857171x^4 + 1567646351x^3 + 82900732570x^2 - 2598191444700x + 321922277979336	\( 97^{7}\cdot 409^{7} \)	$C_8$ (as 8T1)	$[1166589912]$ (GRH)
8.0.154691088673896293052793942309897.3	x^8 - x^7 + 2480x^6 + 396110x^5 - 36137047x^4 - 2238581269x^3 + 127500008326x^2 - 272737761048x + 549334612224	\( 97^{7}\cdot 409^{7} \)	$C_8$ (as 8T1)	$[2708341656]$ (GRH)
8.0.166017732349269837601386065297408.21	x^8 + 14888x^6 + 69266420x^4 + 103123846096x^2 + 12890480762	\( 2^{31}\cdot 1861^{7} \)	$C_8:C_2$ (as 8T7)	$[2807844260]$ (GRH)
8.0.184311982722534970348835902062592.46	x^8 + 15112x^6 + 46280500x^4 + 47034014544x^2 + 14556850588962	\( 2^{31}\cdot 1889^{7} \)	$C_8$ (as 8T1)	$[2, 4, 8, 8, 56, 39536]$ (GRH)
8.0.202639285074291217926031129154249.4	x^8 - x^7 + 11820x^6 - 53254x^5 + 107726457x^4 - 11863904333x^3 - 294112054190x^2 - 35883020751500x + 3843302866625000	\( 281^{7}\cdot 337^{6} \)	$C_8:C_2$ (as 8T7)	$[4, 901965380]$ (GRH)
8.0.403855819100833706490759181500416.31	x^8 + 16904x^6 + 95110356x^4 + 178193955504x^2 + 549114611426	\( 2^{31}\cdot 2113^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	$[4, 204, 4263600]$ (GRH)
8.0.403855819100833706490759181500416.70	x^8 + 16904x^6 + 33715028x^4 + 17966686864x^2 + 3902799746	\( 2^{31}\cdot 2113^{7} \)	$C_8$ (as 8T1)	$[4, 172, 3941552]$ (GRH)
8.0.403855819100833706490759181500416.71	x^8 + 16904x^6 + 86455508x^4 + 119333889424x^2 + 3902799746	\( 2^{31}\cdot 2113^{7} \)	$C_8$ (as 8T1)	$[4, 164, 4471952]$ (GRH)
8.0.403855819100833706490759181500416.76	x^8 + 16904x^6 + 89295380x^4 + 150944910352x^2 + 18868113794	\( 2^{31}\cdot 2113^{7} \)	$C_8:C_2$ (as 8T7)	$[4, 4, 192871120]$ (GRH)
8.0.425754743838724234995143469432832.5	x^8 + 17032x^6 + 90550628x^4 + 188847716176x^2 + 130808419244482	\( 2^{31}\cdot 2129^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	$[2, 4, 232967280]$ (GRH)
8.0.425754743838724234995143469432832.33	x^8 + 17032x^6 + 90652820x^4 + 154399883024x^2 + 5577695774242	\( 2^{31}\cdot 2129^{7} \)	$C_8:C_2$ (as 8T7)	$[2, 4, 285315472]$ (GRH)
8.0.430146603940909544066530986816769.1	x^8 - x^7 + 20139x^6 - 1195635x^5 + 4620141x^4 + 6107597937x^3 + 185254438802x^2 - 28534270584992x + 567491024552352	\( 241^{7}\cdot 457^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 388156720]$ (GRH)
8.0.430146603940909544066530986816769.2	x^8 - x^7 + 20139x^6 + 566557x^5 + 97135221x^4 - 10433217271x^3 - 45837217338x^2 - 3307158125648x + 1371649337674496	\( 241^{7}\cdot 457^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 167502832]$ (GRH)
8.0.460508949164024406508986513227776.43	x^8 + 17224x^6 + 80444692x^4 + 113913507600x^2 + 1430240591250	\( 2^{31}\cdot 2153^{7} \)	$C_8$ (as 8T1)	$[4, 4, 107777960]$ (GRH)
8.0.531817867910855374307466941229217.3	x^8 - x^7 + 20052x^6 + 1695203x^5 + 100860172x^4 + 15081515535x^3 + 1457471142007x^2 + 61677611886608x + 1051286976413904	\( 313^{7}\cdot 349^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 2, 2, 46638568]$ (GRH)
8.0.715744877799290519974671691022336.1	x^8 + 18344x^6 + 105156980x^4 + 192899964112x^2 + 101875293546650	\( 2^{31}\cdot 2293^{7} \)	$C_8:C_2$ (as 8T7)	$[3664993460]$ (GRH)
8.0.815672190875500670698774526868313.1	x^8 - x^7 + 19223x^6 + 236833x^5 + 26467124x^4 - 6296099188x^3 + 396735275936x^2 + 56554290235456x + 1164688751606272	\( 241^{6}\cdot 457^{7} \)	$QD_{16}$ (as 8T8)	$[2, 2, 2, 524046544]$ (GRH)
8.0.931634651445673270453256247574528.19	x^8 + 19048x^6 + 113383220x^4 + 215972357456x^2 + 26996544682	\( 2^{31}\cdot 2381^{7} \)	$C_8:C_2$ (as 8T7)	$[17, 513086860]$ (GRH)
8.0.1510269940117393787434340294825833.2	x^8 - x^7 + 3434x^6 + 466106x^5 - 46189007x^4 + 4853572775x^3 + 291843263844x^2 - 15966068329056x + 188675512537088	\( 137^{7}\cdot 401^{7} \)	$C_8$ (as 8T1)	$[1031972968]$ (GRH)
8.0.1710436336269048136563476916048313.5	x^8 - x^7 + 16366x^6 - 1696000x^5 + 230733571x^4 - 30103158100x^3 + 1419762761784x^2 - 275329019071512x + 18516155826524688	\( 337^{7}\cdot 389^{6} \)	$C_8$ (as 8T1)	$[2, 2, 2, 4, 12, 2771544]$ (GRH)
8.0.2442249411187595453666738609664209.1	x^8 - 3x^7 + 25292x^6 - 314506x^5 + 304952061x^4 - 9530005755x^3 - 18120265290x^2 - 77700032311928x + 3012242485874816	\( 337^{6}\cdot 401^{7} \)	$QD_{16}$ (as 8T8)	$[2, 4, 12, 25832136]$ (GRH)
8.0.2534179808189051984944868707137137.1	x^8 - 3x^7 + 3701x^6 - 1733001x^5 + 162671589x^4 - 3353508043x^3 + 4490819278x^2 + 273114940000x + 2313942927232	\( 149^{7}\cdot 397^{7} \)	$C_8:C_2$ (as 8T7)	$[15, 158109180]$ (GRH)
8.0.2584992245141924649255156248205641.2	x^8 - x^7 + 3708x^6 + 58394x^5 + 104488525x^4 - 9560210377x^3 + 759346141238x^2 - 24266869427536x + 427470263382272	\( 137^{7}\cdot 433^{7} \)	$(C_8:C_2):C_2$ (as 8T16)	$[4, 4, 356300360]$ (GRH)