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 )

Label	Polynomial	Discriminant	Galois group	Class group
6.0.3006256887635270172649443.1	x^6 - 111169x^3 + 1373887262639809	\( -\,3^{9}\cdot 19^{4}\cdot 5851^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 3, 3, 668163]$ (GRH)
6.0.8022101987542393844739387.1	x^6 - 3x^5 + 6x^4 + 492191x^3 - 738291x^2 - 738300x + 60565210000	\( -\,3^{11}\cdot 7^{4}\cdot 11719^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 2646, 2646]$ (GRH)
6.0.9108286536278403947566107.1	x^6 - 3x^5 + 6x^4 + 508067x^3 - 762105x^2 - 762114x + 64535305444	\( -\,3^{11}\cdot 7^{4}\cdot 12097^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3186, 3186]$ (GRH)
6.0.24032589566657975139769947.1	x^6 - 3x^5 + 6x^4 + 647535x^3 - 971307x^2 - 971316x + 104828307984	\( -\,3^{7}\cdot 7^{4}\cdot 23^{4}\cdot 2011^{4} \)	$S_3$ (as 6T2)	$[3, 6, 6, 1740, 1740]$ (GRH)
6.0.26986934371650677199689787.1	x^6 - 3x^5 + 6x^4 + 666579x^3 - 999873x^2 - 999882x + 111084890436	\( -\,3^{7}\cdot 23^{4}\cdot 43^{4}\cdot 337^{4} \)	$S_3$ (as 6T2)	$[3, 6, 6, 1596, 1596]$ (GRH)
6.0.43640378966014176369738672.1	x^6 - 3x^5 + 6x^4 + 751685x^3 - 1127532x^2 - 1127541x + 141260967409	\( -\,2^{4}\cdot 3^{11}\cdot 37^{4}\cdot 1693^{4} \)	$S_3$ (as 6T2)	$[3, 3, 6, 18, 414, 414]$ (GRH)
8.0.25592429020084354212450313.1	x^8 - x^7 + 881x^6 + 20093x^5 + 1109222x^4 - 5894476x^3 + 95433112x^2 + 5333705760x + 33591285504	\( 37^{6}\cdot 193^{7} \)	$C_8$ (as 8T1)	$[11, 21919612]$ (GRH)
8.0.38498131577792085798402593.1	x^8 - x^7 + 9654x^6 - 77586x^5 + 14786073x^4 - 99617681x^3 + 3903207296x^2 + 399712164x + 148887867824	\( 151^{4}\cdot 257^{7} \)	$C_8$ (as 8T1)	$[120043158]$ (GRH)
8.0.57944133222407328636664193.1	x^8 - 3x^7 + 12376x^6 - 24734x^5 + 22720489x^4 + 32175201x^3 + 11819644958x^2 + 63691264512x + 944227994976	\( 193^{6}\cdot 257^{5} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 4, 7602920]$ (GRH)
8.0.120768260928169151858067641.3	x^8 - x^7 + 333x^6 - 30679x^5 - 287030x^4 - 9799184x^3 + 278703872x^2 + 4915236864x + 58573389824	\( 17^{7}\cdot 313^{7} \)	$C_8$ (as 8T1)	$[89, 2011400]$ (GRH)
8.0.629221272157210282490919889.1	x^8 - 3x^7 + 5463x^6 + 5095x^5 + 15806616x^4 + 51182956x^3 + 11178650784x^2 + 450158768448x + 9904759495168	\( 73^{6}\cdot 401^{6} \)	$Q_8$ (as 8T5)	$[30, 2490, 2490]$ (GRH)
8.0.783242835309646294823246161.2	x^8 - 3x^7 + 5671x^6 - 55449x^5 + 17412064x^4 + 123908628x^3 + 9794653488x^2 + 598996548288x + 9286969469184	\( 97^{6}\cdot 313^{6} \)	$Q_8$ (as 8T5)	$[2, 7342, 7342]$ (GRH)
8.0.884137376053502406583563913.1	x^8 - x^7 + 1801x^6 - 53291x^5 + 5308046x^4 - 20768516x^3 + 3192104472x^2 + 52057482048x + 374374573056	\( 97^{7}\cdot 149^{6} \)	$C_8$ (as 8T1)	$[463033828]$ (GRH)
8.0.1046585023211040080984056249.3	x^8 - x^7 + 1582x^6 + 32742x^5 - 935391x^4 + 48408231x^3 - 391513312x^2 + 13294112308x + 1810372179920	\( 53^{6}\cdot 241^{7} \)	$C_8$ (as 8T1)	$[4, 43518148]$ (GRH)
8.0.1466738876545061826724888576.43	x^8 + 2824x^6 + 2514772x^4 + 702752400x^2 + 2895041250	\( 2^{31}\cdot 353^{7} \)	$C_8$ (as 8T1)	$[4, 4, 8383720]$ (GRH)
8.0.1767647026420274120972649193.2	x^8 - x^7 + 2122x^6 + 96742x^5 + 4553037x^4 + 167153419x^3 + 3478748744x^2 + 220978113776x + 4614197571584	\( 73^{7}\cdot 233^{6} \)	$C_8$ (as 8T1)	$[5, 78571940]$ (GRH)
8.0.3056865062754860321468317696.6	x^8 + 11333560x^4 + 32139386443921	\( 2^{24}\cdot 2381^{6} \)	$C_4\times C_2$ (as 8T2)	$[5, 21052460]$ (GRH)
8.0.3436420224867951431627682041.1	x^8 - x^7 + 27837x^6 - 55783x^5 + 184383538x^4 - 155921032x^3 + 402434045312x^2 + 362200624640x + 280968888541184	\( 281^{7}\cdot 397^{4} \)	$C_8$ (as 8T1)	$[2, 2, 34, 1060834]$ (GRH)
8.0.4087102501534337018181988513.1	x^8 - 3x^7 + 26327x^6 - 210849x^5 + 186682040x^4 - 1443989756x^3 + 486265872848x^2 - 2432475898752x + 410307009155072	\( 313^{6}\cdot 337^{5} \)	$C_4\wr C_2$ (as 8T17)	$[2, 60113386]$ (GRH)
8.0.4345828890015370938034129241.1	x^8 - x^7 + 29523x^6 - 59155x^5 + 207419356x^4 - 175461772x^3 + 480109130864x^2 + 431596924160x + 354721068818432	\( 281^{7}\cdot 421^{4} \)	$C_8$ (as 8T1)	$[4, 4, 4, 4956488]$ (GRH)
8.0.5438735522878372046665954057.1	x^8 - x^7 + 2560x^6 - 149998x^5 + 6366649x^4 - 153612085x^3 + 13255134606x^2 - 512228191932x + 6465100556952	\( 73^{7}\cdot 281^{6} \)	$C_8$ (as 8T1)	$[3, 44828268]$ (GRH)
8.0.9196155263122253470427891561.1	x^8 - x^7 + 618x^6 + 83834x^5 - 2319695x^4 - 33901945x^3 + 2025490148x^2 - 27841538560x + 184031513600	\( 41^{7}\cdot 241^{7} \)	$C_8$ (as 8T1)	$[2, 4, 13867240]$ (GRH)
8.0.9196155263122253470427891561.3	x^8 - x^7 + 618x^6 + 83834x^5 - 778259x^4 + 47319875x^3 + 1858422200x^2 - 29799043708x + 1248004155440	\( 41^{7}\cdot 241^{7} \)	$C_8$ (as 8T1)	$[2, 4, 39374120]$ (GRH)
8.0.13787434170228251520116680169.1	x^8 - x^7 + 14531x^6 + 177721x^5 + 63788428x^4 + 1354550168x^3 + 84318366032x^2 + 1043774396368x + 9232442195264	\( 137^{7}\cdot 433^{5} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 16083748]$ (GRH)
8.0.14043700881105708763602116473.1	x^8 - x^7 + 27449x^6 + 302641x^5 + 129543474x^4 + 1132481969x^3 + 170051152183x^2 + 837113334012x + 8888586604571	\( 241^{4}\cdot 457^{7} \)	$C_8$ (as 8T1)	$[2, 10, 20, 275060]$ (GRH)
8.0.16726853867309592405065509153.5	x^8 - 3x^7 + 32912x^6 - 98793x^5 + 239357760x^4 - 1502459109x^3 + 477022089020x^2 - 4559653374927x + 39093600296275	\( 313^{5}\cdot 421^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 45547970]$ (GRH)
8.0.18072396243720043020540182257.1	x^8 - 3x^7 + 33714x^6 - 303982x^5 + 295638945x^4 - 4095106094x^3 + 215969743760x^2 - 665640250816x + 20476799325040	\( 337^{5}\cdot 401^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 2, 15099530]$ (GRH)
8.0.19829803394853790928098618049.3	x^8 - 4x^7 + 1806x^6 - 5404x^5 + 722849x^4 - 1436696x^3 + 95190632x^2 - 94473184x + 2950956496	\( 193^{5}\cdot 257^{7} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 8, 14054736]$ (GRH)
8.0.19829803394853790928098618049.4	x^8 - 2x^7 + 3407x^6 + 18214x^5 + 2730812x^4 + 27195240x^3 + 676416224x^2 + 4405144448x + 12034606592	\( 193^{5}\cdot 257^{7} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[2, 2, 8, 8446704]$ (GRH)
8.0.21375104822753880495301608313.2	x^8 - x^7 + 3217x^6 + 159449x^5 + 10556338x^4 + 453435548x^3 + 8938293768x^2 + 844211062080x + 24064659702144	\( 73^{7}\cdot 353^{6} \)	$C_8$ (as 8T1)	$[6, 21201996]$ (GRH)
8.0.25896420426804374008603082752.11	x^8 + 5188x^6 + 376130x^4 + 6910416x^2 + 1680912	\( 2^{22}\cdot 1297^{7} \)	$C_8$ (as 8T1)	$[2, 65524316]$ (GRH)
8.0.25896420426804374008603082752.12	x^8 + 5188x^6 + 6913010x^4 + 477565776x^2 + 1680912	\( 2^{22}\cdot 1297^{7} \)	$C_8$ (as 8T1)	$[10, 18512780]$ (GRH)
8.0.30950185120418202714623515969.1	x^8 - 3x^7 + 10476x^6 - 354510x^5 + 58301745x^4 - 1978714783x^3 + 171186449570x^2 - 7442730006896x + 202589282336864	\( 137^{6}\cdot 409^{6} \)	$Q_8$ (as 8T5)	$[6, 4374, 4374]$ (GRH)
8.0.41468252123822947209337372672.4	x^8 + 4552x^6 + 5856148x^4 + 2509290000x^2 + 241016802642	\( 2^{31}\cdot 569^{7} \)	$C_8$ (as 8T1)	$[2, 4, 4, 12, 311088]$ (GRH)
8.0.45497113695130083887456829001.1	x^8 - x^7 + 11169x^6 + 45771x^5 + 69712610x^4 + 203660475x^3 + 132729039125x^2 - 172383112500x + 273542293828125	\( 149^{6}\cdot 401^{6} \)	$C_4\times C_2$ (as 8T2)	$[6, 270, 188190]$ (GRH)
8.0.50124209986911477351431969881.1	x^8 - x^7 + 3028x^6 + 86726x^5 - 10382591x^4 - 151933141x^3 + 16462000842x^2 + 101776517136x + 176568665184	\( 101^{6}\cdot 241^{7} \)	$C_8$ (as 8T1)	$[11, 12976172]$ (GRH)
8.0.55374869931911176637472833536.30	x^8 + 4744x^6 + 1036564x^4 + 74547216x^2 + 1750802850	\( 2^{31}\cdot 593^{7} \)	$C_8$ (as 8T1)	$[2, 12, 4198704]$ (GRH)
8.0.60467351645799489443637231616.19	x^8 + 4804x^6 + 2044102x^4 + 56730436x^2 + 141296449	\( 2^{24}\cdot 1201^{7} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[4, 8, 8, 40, 15840]$ (GRH)
8.0.60467351645799489443637231616.46	x^8 + 4804x^6 + 4811206x^4 + 1330213188x^2 + 27936856129	\( 2^{24}\cdot 1201^{7} \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	$[4, 4, 8, 40, 46000]$ (GRH)
8.0.63285718843729333630079120593.1	x^8 + 3617x^6 + 3704863x^4 + 1329681947x^2 + 113833013668	\( 401^{6}\cdot 433^{5} \)	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30)	$[3, 45553872]$ (GRH)
8.0.63285718843729333630079120593.2	x^8 + 4469x^6 + 1501603x^4 + 87184983x^2 + 79318672	\( 401^{6}\cdot 433^{5} \)	$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30)	$[3, 37640400]$ (GRH)
8.0.67616771774330032136621391872.44	x^8 + 14216x^6 + 63154580x^4 + 89780550928x^2 + 39883184582402	\( 2^{31}\cdot 1777^{6} \)	$C_8$ (as 8T1)	$[2, 2, 2, 4, 6747380]$ (GRH)
8.0.69847873265392348663346364416.11	x^8 + 4904x^6 + 7515380x^4 + 3685542352x^2 + 460692794	\( 2^{31}\cdot 613^{7} \)	$C_8:C_2$ (as 8T7)	$[5, 67510340]$ (GRH)
8.0.70403120507437021940708016128.6	x^8 + 14312x^6 + 64010420x^4 + 91611713104x^2 + 11136283230962	\( 2^{31}\cdot 1789^{6} \)	$C_8$ (as 8T1)	$[17, 14240900]$ (GRH)
8.0.70403120507437021940708016128.7	x^8 + 14312x^6 + 64010420x^4 + 91611713104x^2 + 29837055454802	\( 2^{31}\cdot 1789^{6} \)	$C_8$ (as 8T1)	$[7, 47242300]$ (GRH)
8.0.73284502256972228114983682048.17	x^8 + 14408x^6 + 64872020x^4 + 93467606416x^2 + 6895642725122	\( 2^{31}\cdot 1801^{6} \)	$C_8$ (as 8T1)	$[6, 23955852]$ (GRH)
8.0.73284502256972228114983682048.24	x^8 + 14408x^6 + 65304260x^4 + 96581463376x^2 + 23939338795682	\( 2^{31}\cdot 1801^{6} \)	$C_8:C_2$ (as 8T7)	$[6, 17007036]$ (GRH)
8.0.97571192547662768845333987328.43	x^8 + 15112x^6 + 59186148x^4 + 88779826480x^2 + 45644827505922	\( 2^{31}\cdot 1889^{6} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 4, 4, 8, 218312]$ (GRH)
8.0.101607152365651410251334638729.1	x^8 - 3x^7 + 47221x^6 - 47104x^5 + 707807472x^4 - 507993600x^3 + 3620099355712x^2 - 2416786119104x + 2414998364904384	\( 421^{6}\cdot 449^{5} \)	$C_4\wr C_2$ (as 8T17)	$[4, 8, 8, 852616]$ (GRH)
8.0.113083496445947575098203439104.41	x^8 + 6404x^6 + 3358898x^4 + 460678144x^2 + 104923136	\( 2^{22}\cdot 1601^{7} \)	$C_8$ (as 8T1)	$[2, 2, 40, 941360]$ (GRH)

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