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
4.0.34060633877926656000.51	x^4 + 65063988990	\( 2^{11}\cdot 3^{3}\cdot 5^{3}\cdot 7^{3}\cdot 11^{3}\cdot 13^{3}\cdot 17^{3} \)	$D_{4}$ (as 4T3)	$[2, 4, 4, 4, 4, 29372]$ (GRH)
6.0.666962499705409191375.1	x^6 - 3x^5 - 10029x^4 - 263493x^3 + 27354072x^2 + 1540417020x + 22520129696	\( -\,3^{8}\cdot 5^{3}\cdot 7^{5}\cdot 13^{5}\cdot 19^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 3, 3, 18, 8190]$ (GRH)
6.0.4038712184239968337947.1	x^6 + x^4 - 73727x^2 + 452984832	\( -\,3^{3}\cdot 13^{4}\cdot 47^{4}\cdot 181^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 702, 702]$ (GRH)
6.0.7727379786207456600267.1	x^6 + x^4 - 86711x^2 + 626580912	\( -\,3^{3}\cdot 7^{4}\cdot 17^{4}\cdot 1093^{4} \)	$S_3$ (as 6T2)	$[6, 6, 372, 1116]$ (GRH)
6.0.9039759615677114306667.1	x^6 + x^4 - 90179x^2 + 677702700	\( -\,3^{3}\cdot 17^{4}\cdot 73^{4}\cdot 109^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 1143, 1143]$ (GRH)
6.0.10953436997874693548187.1	x^6 - 3x^5 + 6x^4 + 94607x^3 - 141915x^2 - 141924x + 2238046864	\( -\,3^{11}\cdot 13^{4}\cdot 1213^{4} \)	$S_3$ (as 6T2)	$[3, 3, 735, 2205]$ (GRH)
6.0.15410603129491228573872.1	x^6 + 884838828	\( -\,2^{4}\cdot 3^{11}\cdot 31^{4}\cdot 277^{4} \)	$S_3$ (as 6T2)	$[3, 3, 6, 6, 114, 342]$ (GRH)
6.0.29600300339450887234347.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 60653x^2 + 60654x + 1226302572	\( -\,3^{3}\cdot 19^{4}\cdot 61^{4}\cdot 157^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 735, 735]$ (GRH)
6.0.30621503739225077078643.1	x^6 - 35317x^3 + 44050558200013	\( -\,3^{9}\cdot 35317^{4} \)	$C_6$ (as 6T1)	$[6, 6, 30, 16410]$ (GRH)
6.0.34060398829422910760907.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 62819x^2 + 62820x + 1315450800	\( -\,3^{3}\cdot 7^{4}\cdot 13^{4}\cdot 19^{4}\cdot 109^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 354, 354]$ (GRH)
6.0.59884547451490237421232.1	x^6 - 3x^5 + 6x^4 + 144669x^3 - 217008x^2 - 217017x + 5232930921	\( -\,2^{4}\cdot 3^{7}\cdot 7^{4}\cdot 5167^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 612, 612]$ (GRH)
6.0.72449856531798127834032.1	x^6 - 3x^5 + 6x^4 + 151725x^3 - 227592x^2 - 227601x + 5755801689	\( -\,2^{4}\cdot 3^{7}\cdot 7^{4}\cdot 5419^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 666, 666]$ (GRH)
6.0.105072746302804719616875.1	x^6 - 3x^5 + 6x^4 + 832543x^3 - 1248819x^2 - 1248828x + 173285708176	\( -\,3^{7}\cdot 5^{4}\cdot 16651^{4} \)	$S_3$ (as 6T2)	$[2, 6, 1548, 1548]$ (GRH)
6.0.137927869762935648166875.1	x^6 - 3x^5 + 6x^4 + 178223x^3 - 267339x^2 - 267348x + 7941661456	\( -\,3^{11}\cdot 5^{4}\cdot 13^{4}\cdot 457^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 231, 693]$ (GRH)
6.0.150066562433717068059375.1	x^6 + 1478295	\( -\,3^{10}\cdot 5^{5}\cdot 7^{5}\cdot 13^{5}\cdot 19^{4} \)	$D_{6}$ (as 6T3)	$[3, 3, 6, 6, 72, 1080]$ (GRH)
6.0.164763093048738239266875.1	x^6 - 3x^5 + 6x^4 + 186323x^3 - 279489x^2 - 279498x + 8679903556	\( -\,3^{11}\cdot 5^{4}\cdot 6211^{4} \)	$S_3$ (as 6T2)	$[3, 9, 990, 990]$ (GRH)
6.0.198551646349438516151472.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 195224x^2 + 195225x + 12704266875	\( -\,2^{4}\cdot 3^{3}\cdot 7^{4}\cdot 13^{4}\cdot 1609^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 429, 1287]$ (GRH)
6.0.218391067782294490287792.1	x^6 - 3x^5 + 4x^4 - 3x^3 - 199928x^2 + 199929x + 13323868347	\( -\,2^{4}\cdot 3^{3}\cdot 7^{4}\cdot 31^{4}\cdot 691^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 294, 294]$ (GRH)
6.0.278298213467874667470000.1	x^6 - 3x^5 + 6x^4 + 424833x^3 - 637254x^2 - 637263x + 45122681241	\( -\,2^{4}\cdot 3^{7}\cdot 5^{4}\cdot 13^{4}\cdot 19^{4}\cdot 43^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 6, 6, 42, 42]$ (GRH)
6.0.286680761872911663511203.1	x^6 - 61777x^3 + 235765602504433	\( -\,3^{9}\cdot 163^{4}\cdot 379^{4} \)	$C_6$ (as 6T1)	$[3, 3, 3, 3, 3, 3, 58653]$ (GRH)
6.0.303058187263987335900963.1	x^6 - 62641x^3 + 245796699240721	\( -\,3^{9}\cdot 37^{4}\cdot 1693^{4} \)	$C_6$ (as 6T1)	$[3, 3, 12, 12, 36, 684]$ (GRH)
6.0.317992113503391600270000.1	x^6 - 3x^5 + 6x^4 + 439233x^3 - 658854x^2 - 658863x + 48233383641	\( -\,2^{4}\cdot 3^{7}\cdot 5^{4}\cdot 79^{4}\cdot 139^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 288, 288]$ (GRH)
6.0.462527096236404265312587.1	x^6 - 3x^5 + 6x^4 + 4582527x^3 - 6873795x^2 - 6873804x + 5249909047824	\( -\,3^{7}\cdot 11^{4}\cdot 19^{4}\cdot 577^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 387, 387]$ (GRH)
6.0.2883569911983446978703843.1	x^6 - 110017x^3 + 1331617195374913	\( -\,3^{9}\cdot 110017^{4} \)	$C_6$ (as 6T1)	$[12, 4285092]$ (GRH)
6.2.3459612694664949600960000.1	x^6 - 4602x^4 - 35490x^3 + 7059468x^2 - 163324980x - 3294856279	\( 2^{9}\cdot 3^{10}\cdot 5^{4}\cdot 7^{4}\cdot 13^{5}\cdot 59^{3} \)	$D_{6}$ (as 6T3)	$[3, 3, 42, 27300]$ (GRH)
6.0.4094671299178657790511792.1	x^6 + 57693098928	\( -\,2^{4}\cdot 3^{11}\cdot 37^{4}\cdot 937^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 468, 1404]$ (GRH)
6.0.4409496538448411099324592.1	x^6 + 59869943472	\( -\,2^{4}\cdot 3^{11}\cdot 35317^{4} \)	$S_3$ (as 6T2)	$[6, 6, 900, 2700]$ (GRH)
6.0.14060108353356563488013232.1	x^6 - 3x^5 + 6x^4 + 566317x^3 - 849480x^2 - 849489x + 80181284569	\( -\,2^{4}\cdot 3^{7}\cdot 11^{4}\cdot 61^{4}\cdot 211^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 6, 6, 300, 300]$ (GRH)
6.0.15871954977200820975195312.1	x^6 - 3x^5 + 6x^4 + 583741x^3 - 875616x^2 - 875625x + 85191015625	\( -\,2^{4}\cdot 3^{7}\cdot 11^{4}\cdot 13267^{4} \)	$S_3$ (as 6T2)	$[3, 6, 6, 912, 912]$ (GRH)
6.2.17094879279465894849600000.1	x^6 - 6030x^4 - 53550x^3 + 12120300x^2 - 322906500x - 7403700375	\( 2^{9}\cdot 3^{11}\cdot 5^{5}\cdot 7^{4}\cdot 17^{4}\cdot 67^{3} \)	$D_{6}$ (as 6T3)	$[2, 12, 12, 35664]$ (GRH)
6.0.41282029709699279545613232.1	x^6 - 3x^5 + 6x^4 + 741317x^3 - 1111980x^2 - 1111989x + 137391059569	\( -\,2^{4}\cdot 3^{11}\cdot 163^{4}\cdot 379^{4} \)	$S_3$ (as 6T2)	$[3, 3, 3, 3, 3, 609, 609]$ (GRH)
6.2.85230795183543158110714368.1	x^6 - 7854x^4 - 79186x^3 + 20561772x^2 - 621926844x - 16375967383	\( 2^{9}\cdot 3^{6}\cdot 7^{3}\cdot 11^{3}\cdot 17^{5}\cdot 137^{4} \)	$D_{6}$ (as 6T3)	$[2, 2, 2, 4, 466272]$ (GRH)
6.2.430205471990113348029676032.1	x^6 - 40683782568	\( 2^{9}\cdot 3^{11}\cdot 11^{3}\cdot 13^{5}\cdot 313^{4} \)	$D_{6}$ (as 6T3)	$[2, 2, 2, 24, 132720]$ (GRH)
8.0.51505726964824253923328.6	x^8 + 17704x^6 + 97947380x^4 + 173406041552x^2 + 47968446244322	\( 2^{31}\cdot 2213^{4} \)	$C_8$ (as 8T1)	$[12040802]$ (GRH)
8.0.61041556230067535740928.4	x^8 + 18472x^6 + 106629620x^4 + 196966234064x^2 + 56849379306722	\( 2^{31}\cdot 2309^{4} \)	$C_8$ (as 8T1)	$[5, 2339930]$ (GRH)
8.0.68556177175929964986368.4	x^8 + 19016x^6 + 113002580x^4 + 214885706128x^2 + 63847915433282	\( 2^{31}\cdot 2377^{4} \)	$C_8$ (as 8T1)	$[2, 5457346]$ (GRH)
8.0.69250997748090124894208.4	x^8 + 19064x^6 + 113573780x^4 + 216517054192x^2 + 64495017517442	\( 2^{31}\cdot 2383^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 1419266]$ (GRH)
8.0.72563581026030917255168.4	x^8 + 19288x^6 + 116258420x^4 + 224239240496x^2 + 67580101104482	\( 2^{31}\cdot 2411^{4} \)	$C_8$ (as 8T1)	$[10725458]$ (GRH)
8.0.77326569182093542191169.1	x^8 - 2x^7 + 356x^6 - 730x^5 + 65271x^4 - 13140x^3 + 6749348x^2 + 4696368x + 277001984	\( 113^{6}\cdot 439^{4} \)	$C_4\times C_2$ (as 8T2)	$[5, 2081820]$ (GRH)
8.0.109600545209715828752929.1	x^8 - 2x^7 + 396x^6 - 790x^5 + 78231x^4 - 22120x^3 + 8567148x^2 + 5233648x + 374827264	\( 113^{6}\cdot 479^{4} \)	$C_4\times C_2$ (as 8T2)	$[10232775]$ (GRH)
8.0.130362815225443624625609.2	x^8 - x^7 + 5168x^6 - 10370x^5 + 2054333x^4 + 4625727x^3 + 196389450x^2 + 498535620x + 4913336648	\( 89^{7}\cdot 233^{4} \)	$C_8$ (as 8T1)	$[6, 1887558]$ (GRH)
8.0.142488437572306293981817.1	x^8 - x^7 + 6137x^6 + 17x^5 + 11853110x^4 + 14017888x^3 + 7403924288x^2 + 18023958784x + 1237516486144	\( 73^{7}\cdot 337^{4} \)	$C_8$ (as 8T1)	$[10363058]$ (GRH)
8.0.149210098413026196049769.1	x^8 - x^7 + 5346x^6 - 10726x^5 + 2199937x^4 + 4945415x^3 + 217205660x^2 + 551451104x + 5591877632	\( 89^{7}\cdot 241^{4} \)	$C_8$ (as 8T1)	$[9, 1704258]$ (GRH)
8.0.168630239892922523260609.4	x^8 - 2x^7 - 290x^6 + 4924x^5 + 25657x^4 - 1755674x^3 + 35342184x^2 - 200704608x + 375083136	\( 193^{6}\cdot 239^{4} \)	$D_4$ (as 8T4)	$[10, 70, 15960]$ (GRH)
8.0.275775274873230615401609.1	x^8 - x^7 + 6236x^6 - 12506x^5 + 3002717x^4 + 6704055x^3 + 343554510x^2 + 872685924x + 10092525752	\( 89^{7}\cdot 281^{4} \)	$C_8$ (as 8T1)	$[17599874]$ (GRH)
8.0.285652159299235394194297.1	x^8 - x^7 + 7305x^6 + 17x^5 + 16797254x^4 + 19841536x^3 + 12490358720x^2 + 30379679488x + 2466142301696	\( 73^{7}\cdot 401^{4} \)	$C_8$ (as 8T1)	$[2, 2, 178, 15842]$ (GRH)
8.0.309138612153342029256217.1	x^8 - x^7 + 7451x^6 + 17x^5 + 17475716x^4 + 20640448x^3 + 13254714272x^2 + 32235877936x + 2667266809216	\( 73^{7}\cdot 409^{4} \)	$C_8$ (as 8T1)	$[10833266]$ (GRH)
8.0.361346036193935794388033.1	x^8 - x^7 + 2972x^6 - 24130x^5 + 1462165x^4 - 9651233x^3 + 127336054x^2 + 38991076x + 1730582744	\( 47^{4}\cdot 257^{7} \)	$C_8$ (as 8T1)	$[21336918]$ (GRH)
8.0.388339535004847851935737.1	x^8 - x^7 + 7889x^6 + 17x^5 + 19591694x^4 + 23131792x^3 + 15733563008x^2 + 38254933504x + 3344885774848	\( 73^{7}\cdot 433^{4} \)	$C_8$ (as 8T1)	$[16374434]$ (GRH)
8.0.448999011478441266749497.1	x^8 - x^7 + 8181x^6 + 17x^5 + 21069506x^4 + 24871528x^3 + 17546939072x^2 + 42657527296x + 3863341838336	\( 73^{7}\cdot 449^{4} \)	$C_8$ (as 8T1)	$[18262642]$ (GRH)

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