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
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)
8.0.481864376904681326484697.1	x^8 - x^7 + 8327x^6 + 17x^5 + 21828560x^4 + 25765048x^3 + 18503667728x^2 + 44980143184x + 4144082243584	\( 73^{7}\cdot 457^{4} \)	$C_8$ (as 8T1)	$[26, 661882]$ (GRH)
8.0.570492119941782568590569.1	x^8 - x^7 + 7482x^6 - 14998x^5 + 4335937x^4 + 9614711x^3 + 591345284x^2 + 1502825504x + 20379696128	\( 89^{7}\cdot 337^{4} \)	$C_8$ (as 8T1)	$[9, 2728962]$ (GRH)
8.0.624672709662996662320097.4	x^8 - x^7 + 6392x^6 + 12866x^5 + 10138645x^4 + 23239495x^3 + 3636670834x^2 - 7447819272x + 82433284864	\( 113^{7}\cdot 227^{4} \)	$C_8$ (as 8T1)	$[2, 4, 4, 725636]$ (GRH)
8.0.677922439794791223113761.2	x^8 + 473x^6 + 43247x^4 - 3696749x^2 + 483032484	\( 113^{4}\cdot 401^{6} \)	$D_4$ (as 8T4)	$[838, 75420]$ (GRH)
8.0.686797756887312828619049.1	x^8 - x^7 + 7838x^6 - 15710x^5 + 4761713x^4 + 10542447x^3 + 679309680x^2 + 1726548720x + 24398622848	\( 89^{7}\cdot 353^{4} \)	$C_8$ (as 8T1)	$[13037426]$ (GRH)
8.0.902901108195372527819393.2	x^8 - 2x^7 + 1015x^6 - 4078x^5 + 386816x^4 - 1759088x^3 + 64537136x^2 - 243102432x + 3541166208	\( 193^{7}\cdot 449^{3} \)	$D_{8}$ (as 8T6)	$[2, 4, 1428144]$ (GRH)
8.0.933778758254192867986817.1	x^8 - x^7 + 7070x^6 + 14222x^5 + 12401809x^4 + 28419415x^3 + 4916130736x^2 - 10045607460x + 122142877024	\( 113^{7}\cdot 251^{4} \)	$C_8$ (as 8T1)	$[2, 16571266]$ (GRH)
8.0.1058724315790630924064057.1	x^8 - x^7 + 4209x^6 - 17071x^5 + 4138978x^4 - 34427564x^3 + 142938536x^2 - 1358015520x + 5334611456	\( 73^{4}\cdot 233^{7} \)	$C_8$ (as 8T1)	$[3, 3939366]$ (GRH)
8.0.1105084380391278819484697.1	x^8 - x^7 + 792x^6 + 32102x^5 + 28609x^4 - 7094093x^3 + 131046326x^2 + 4702687224x + 34423373696	\( 17^{7}\cdot 373^{6} \)	$C_8$ (as 8T1)	$[2, 62, 220844]$ (GRH)
8.0.1143687927954664699581929.2	x^8 - x^7 + 8906x^6 - 17846x^5 + 6158657x^4 + 13581975x^3 + 994620660x^2 + 2528561184x + 40061107712	\( 89^{7}\cdot 401^{4} \)	$C_8$ (as 8T1)	$[2, 2, 6, 593196]$ (GRH)
8.0.1237722479157127945631369.1	x^8 - x^7 + 9084x^6 - 18202x^5 + 6408925x^4 + 14125943x^3 + 1055164334x^2 + 2682567140x + 43266656312	\( 89^{7}\cdot 409^{4} \)	$C_8$ (as 8T1)	$[2, 16785154]$ (GRH)
8.0.1509019481189788057075457.1	x^8 - x^7 + 7974x^6 + 16030x^5 + 15773729x^4 + 36135959x^3 + 7045901400x^2 - 14363048180x + 195526769312	\( 113^{7}\cdot 283^{4} \)	$C_8$ (as 8T1)	$[2, 2, 6, 1806726]$ (GRH)
8.0.1554825418516488871484009.1	x^8 - x^7 + 9618x^6 - 19270x^5 + 7189633x^4 + 15821927x^3 + 1251435500x^2 + 3181841120x + 54043739648	\( 89^{7}\cdot 433^{4} \)	$C_8$ (as 8T1)	$[161, 139426]$ (GRH)
8.0.1797692516490092326428329.6	x^8 - x^7 + 9974x^6 - 19982x^5 + 7735025x^4 + 17005983x^3 + 1394952984x^2 + 3546933360x + 62269697792	\( 89^{7}\cdot 449^{4} \)	$C_8$ (as 8T1)	$[4, 4, 4, 372452]$ (GRH)
8.0.1881764443695141248264033.1	x^8 - x^7 + 4514x^6 - 36466x^5 + 3303313x^4 - 22024241x^3 + 422599756x^2 + 88680484x + 8146628864	\( 71^{4}\cdot 257^{7} \)	$C_8$ (as 8T1)	$[26454678]$ (GRH)
8.0.1929278154694333202534729.1	x^8 - x^7 + 10152x^6 - 20338x^5 + 8015197x^4 + 17614031x^3 + 1470653714x^2 + 3739511204x + 66718026728	\( 89^{7}\cdot 457^{4} \)	$C_8$ (as 8T1)	$[45350674]$ (GRH)
8.0.2089789805688316312102817.1	x^8 - x^7 + 8652x^6 + 17386x^5 + 18568445x^4 + 42530855x^3 + 8994509334x^2 - 18308244752x + 269203825184	\( 113^{7}\cdot 307^{4} \)	$C_8$ (as 8T1)	$[2, 2, 10, 1214410]$ (GRH)
8.0.2100531593677317435186049.1	x^8 - 2x^7 + 877x^6 + 568x^5 + 199260x^4 - 413184x^3 + 5678080x^2 - 58523648x + 185597952	\( 193^{6}\cdot 449^{4} \)	$C_2^3 : C_4 $ (as 8T19)	$[2, 4, 1641936]$ (GRH)
8.0.2823976507260197019317057.1	x^8 - x^7 + 9330x^6 + 18742x^5 + 21590969x^4 + 49446455x^3 + 11272853076x^2 - 22916818220x + 361965886784	\( 113^{7}\cdot 331^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 1807042]$ (GRH)
8.0.2884298661896695890615233.2	x^8 - x^7 + 5028x^6 - 40578x^5 + 4081509x^4 - 27267041x^3 + 577700798x^2 + 109717476x + 12228740792	\( 79^{4}\cdot 257^{7} \)	$C_8$ (as 8T1)	$[2, 5450646]$ (GRH)
8.0.3410884421861181521752577.1	x^8 - x^7 + 9782x^6 + 19646x^5 + 23732545x^4 + 54346135x^3 + 12987663784x^2 - 26383199892x + 435902726944	\( 113^{7}\cdot 347^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 2157202]$ (GRH)
8.0.4565663843921795982558497.1	x^8 - 3x^7 + 8530x^6 + 17246x^5 + 14862865x^4 + 91668357x^3 + 5881984412x^2 + 30776452128x + 601602283008	\( 97^{6}\cdot 353^{5} \)	$C_4\wr C_2$ (as 8T17)	$[2, 2, 4, 2536868]$ (GRH)
8.0.4854068986288568156795777.1	x^8 - x^7 + 10686x^6 + 21454x^5 + 28319441x^4 + 64839767x^3 + 16921847376x^2 - 34330294628x + 617135699552	\( 113^{7}\cdot 379^{4} \)	$C_8$ (as 8T1)	$[22214866]$ (GRH)
8.0.5490350377781466671982217.1	x^8 - x^7 + 808x^6 + 30458x^5 + 647245x^4 + 15248303x^3 + 404422218x^2 + 8768700504x + 94325352768	\( 73^{7}\cdot 89^{6} \)	$C_8$ (as 8T1)	$[2, 2, 4, 1112068]$ (GRH)
8.0.7251121733916061655801057.1	x^8 - x^7 + 11816x^6 + 23714x^5 + 34622581x^4 + 79258567x^3 + 22864387426x^2 - 46323547368x + 916950788992	\( 113^{7}\cdot 419^{4} \)	$C_8$ (as 8T1)	$[84323522]$ (GRH)
8.0.8276200136091069747575057.1	x^8 - x^7 + 5141x^6 - 20965x^5 + 7530019x^4 - 31484723x^3 + 2795041399x^2 + 11895080217x + 32108989264	\( 59^{4}\cdot 353^{7} \)	$C_8$ (as 8T1)	$[10114178]$ (GRH)
8.0.8334523244344325072849633.1	x^8 - x^7 + 6570x^6 - 52914x^5 + 6909537x^4 - 46350833x^3 + 1260018836x^2 + 186250020x + 33809184992	\( 103^{4}\cdot 257^{7} \)	$C_8$ (as 8T1)	$[74432454]$ (GRH)
8.0.9060747111652487696434817.1	x^8 - x^7 + 12494x^6 + 25070x^5 + 38708209x^4 + 88604119x^3 + 27022299040x^2 - 54709481220x + 1142625909472	\( 113^{7}\cdot 443^{4} \)	$C_8$ (as 8T1)	$[2, 17100802]$ (GRH)
8.0.11189653199087015249863457.1	x^8 - x^7 + 13172x^6 + 26426x^5 + 43021645x^4 + 98470375x^3 + 31656003934x^2 - 64050906912x + 1407595078624	\( 113^{7}\cdot 467^{4} \)	$C_8$ (as 8T1)	$[2, 2, 2, 12489266]$ (GRH)
8.0.13133295493358990410442297.1	x^8 - x^7 + 7937x^6 - 31983x^5 + 14789874x^4 - 121431628x^3 + 968630888x^2 - 9992391584x + 34660192768	\( 137^{4}\cdot 233^{7} \)	$C_8$ (as 8T1)	$[24527266]$ (GRH)
8.0.13673354476852237644358337.1	x^8 - x^7 + 13850x^6 + 27782x^5 + 47562889x^4 + 108857335x^3 + 36791276956x^2 - 74399374140x + 1716174411904	\( 113^{7}\cdot 491^{4} \)	$C_8$ (as 8T1)	$[4479, 8958]$ (GRH)
8.0.13763286441873574081256177.1	x^8 - x^7 + 5847x^6 - 23789x^5 + 9733445x^4 - 40674019x^3 + 4085538093x^2 + 17265263569x + 50203839158	\( 67^{4}\cdot 353^{7} \)	$C_8$ (as 8T1)	$[10390546]$ (GRH)
8.0.13774485566948763382269193.5	x^8 - x^7 + 677x^6 - 16515x^5 - 134234x^4 - 3678248x^3 - 80790688x^2 + 714289536x + 56703181824	\( 13^{6}\cdot 433^{7} \)	$C_8$ (as 8T1)	$[12, 1176972]$ (GRH)

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