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 all 25 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.332785995090979306640625.1	x^16 - x^15 + 13x^14 - 29x^13 + 90x^12 - 249x^11 + 635x^10 - 1434x^9 + 2823x^8 - 5810x^7 + 6775x^6 - 6294x^5 + 14389x^4 - 7259x^3 + 6974x^2 - 9864x + 10729	\( 3^{4}\cdot 5^{10}\cdot 29^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2, 10]$ (GRH)
16.16.332785995090979306640625.1	x^16 - x^15 - 31x^14 + 42x^13 + 355x^12 - 612x^11 - 1789x^10 + 3881x^9 + 3512x^8 - 10771x^7 - 1053x^6 + 12235x^5 - 1575x^4 - 6082x^3 + 490x^2 + 1218x + 179	\( 3^{4}\cdot 5^{10}\cdot 29^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.0.35465739761106676596342784.1	x^16 + 32x^14 + 378x^12 + 2088x^10 + 5778x^8 + 8432x^6 + 6426x^4 + 2312x^2 + 289	\( 2^{44}\cdot 17^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2, 4, 8]$ (GRH)
16.16.35465739761106676596342784.1	x^16 - 32x^14 + 378x^12 - 2088x^10 + 5778x^8 - 8432x^6 + 6426x^4 - 2312x^2 + 289	\( 2^{44}\cdot 17^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.35465739761106676596342784.1	x^16 + 8x^14 - 134x^12 + 80x^10 + 1426x^8 - 1496x^6 - 2278x^4 + 289	\( 2^{44}\cdot 17^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.35465739761106676596342784.2	x^16 - 8x^14 - 134x^12 - 80x^10 + 1426x^8 + 1496x^6 - 2278x^4 + 289	\( 2^{44}\cdot 17^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.81925410828566900634765625.3	x^16 - 6x^15 - 7x^14 + 128x^13 - 289x^12 - 276x^11 + 2240x^10 - 3291x^9 - 1401x^8 + 10758x^7 - 13600x^6 + 2377x^5 + 12566x^4 - 16359x^3 + 10412x^2 - 3423x + 441	\( 5^{14}\cdot 41^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.1078732544346879404306640625.13	x^16 - 2x^15 - 20x^14 + 76x^13 + 56x^12 - 766x^11 - 647x^10 - 1839x^9 - 5348x^8 + 12084x^7 + 16544x^6 - 8586x^5 - 10198x^4 - 7155x^3 - 3956x^2 + 5340x + 2845	\( 5^{10}\cdot 101^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.4353899607317398687744140625.2	x^16 - 27x^14 - 20x^13 + 273x^12 + 400x^11 - 1334x^10 - 2180x^9 + 470x^8 + 4600x^7 + 16361x^6 + 14670x^5 - 19337x^4 - 31470x^3 - 10577x^2 - 2590x - 2404	\( 5^{14}\cdot 61^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.24109722907876309716269637601.7	x^16 - 4x^15 - 7x^14 + 55x^13 + x^12 + 397x^11 - 3039x^10 + 4906x^9 - 20627x^8 + 57243x^7 + 41440x^6 - 196260x^5 + 17648x^4 + 80707x^3 + 25989x^2 + 7020x - 1223	\( 13^{10}\cdot 53^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.98340377973019428085802419249.5	x^16 - 4x^15 + 8x^14 + 48x^13 - 551x^12 + 1068x^11 + 1380x^10 - 14445x^9 + 18636x^8 + 80410x^7 - 15842x^6 - 336095x^5 - 145654x^4 + 452112x^3 + 86423x^2 + 27755x - 19825	\( 13^{10}\cdot 61^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.1656482725689092973620649257089.3	x^16 - x^15 - 37x^14 - 42x^13 + 578x^12 + 1705x^11 - 4367x^10 - 18627x^9 + 7346x^8 + 117118x^7 - 7647x^6 - 352485x^5 - 65817x^4 + 901634x^3 - 732188x^2 + 138288x + 16448	\( 13^{14}\cdot 29^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.326340530003540716649666265244140625.4	x^16 + 13x^14 - 982x^12 - 2398x^11 - 10549x^10 - 42946x^9 - 123966x^8 - 45344x^7 + 1825173x^6 + 23045434x^5 + 129529688x^4 + 12770440x^3 - 1155728032x^2 - 1620521312x + 187726144	\( 5^{10}\cdot 109^{14} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.25934622137786186512293731859285256849.13	x^16 - 6x^15 - 51x^14 + 491x^13 - 2046x^12 - 3267x^11 + 86127x^10 - 208356x^9 - 5272x^8 + 382749x^7 - 4535462x^6 + 7629119x^5 - 56895286x^4 + 361128255x^3 - 875529162x^2 + 1153732464x - 497848761	\( 37^{10}\cdot 149^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[4]$ (GRH)
16.8.25960186080802016874638962845712890625.1	x^16 - 131x^14 + 4947x^12 + 731x^10 - 150192x^9 - 3584998x^8 + 9918036x^7 + 62552122x^6 - 180375228x^5 - 63289201x^4 + 638329410x^3 - 5561915004x^2 + 3661444944x - 620598976	\( 5^{10}\cdot 149^{14} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.35826423586415848519139534914245144961.3	x^16 - 6x^15 + 129x^14 - 671x^13 + 6058x^12 - 26624x^11 + 64298x^10 - 280059x^9 - 2350140x^8 + 5714488x^7 - 31636488x^6 + 58581679x^5 + 775454875x^4 - 127242000x^3 - 2543361055x^2 + 290985398x + 1902420484	\( 13^{14}\cdot 157^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.43753597243831965200444502399484946401.17	x^16 - 4x^15 - 109x^14 + 323x^13 + 1718x^12 + 15156x^11 - 137850x^10 - 967355x^9 + 19130705x^8 - 30590271x^7 - 338054405x^6 + 461570699x^5 + 158786487x^4 + 1377467087x^3 - 3831224257x^2 - 7371959x + 2749255547	\( 37^{10}\cdot 157^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.52039206599103315275932373479504463569.3	x^16 - 2x^15 - 67x^14 + 143x^13 - 88x^12 - 3848x^11 + 25904x^10 + 173397x^9 + 1683238x^8 - 8854192x^7 - 34531314x^6 + 138673151x^5 - 89105387x^4 - 105159148x^3 + 35679363x^2 + 90002488x + 31776832	\( 29^{14}\cdot 53^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.1576096602835514136235637969229632141761.1	x^16 - 3x^15 - 120x^14 + 536x^13 - 963x^12 + 17814x^11 + 323635x^10 - 4574878x^9 + 10029551x^8 + 93173012x^7 - 652229481x^6 + 1679761614x^5 - 1689125860x^4 - 494535179x^3 + 1977927713x^2 - 423649600x - 605912492	\( 37^{14}\cdot 53^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.42446930611030025911778708127377056380611209.3	x^16 - 7x^15 + 55x^14 + 2673x^13 - 13589x^12 - 373907x^11 - 1807538x^10 + 32057398x^9 + 235889409x^8 - 1022153529x^7 - 12091496560x^6 + 8803629494x^5 + 301450266691x^4 + 119599276971x^3 - 3126568524328x^2 - 1974895242930x + 6612908543775	\( 61^{14}\cdot 73^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.43029097861869577828178499597148046196454969.1	x^16 - 4x^15 - 337x^14 + 1992x^13 + 17170x^12 - 206720x^11 + 1442572x^10 + 1229215x^9 - 25307029x^8 + 612567235x^7 - 4410149877x^6 - 16828496949x^5 + 11289021552x^4 - 92952384657x^3 - 1781065804040x^2 + 6211470910074x - 4334460464259	\( 53^{14}\cdot 89^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.55273437382717328226723918791876367935996449.2	x^16 - 8x^15 + 38x^14 - 126x^13 - 863x^12 + 5644x^11 - 21897x^10 + 80208x^9 + 139258x^8 - 1294348x^7 + 5356541x^6 - 14124804x^5 + 15506419x^4 + 77391304x^3 - 719056917x^2 + 902653490x - 180997979	\( 37^{10}\cdot 101^{14} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)
16.8.101760566745940911333128943658372964904935881.2	x^16 - x^15 - 103x^14 + 432x^13 - 41565x^12 - 480761x^11 + 827806x^10 + 64766322x^9 + 609769156x^8 + 1508236734x^7 - 13311677332x^6 - 106391518916x^5 - 340510468007x^4 - 190307136710x^3 + 2958573104934x^2 + 8392420893314x + 5550170605771	\( 53^{14}\cdot 97^{10} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	Trivial (GRH)
16.8.1118375737550090727607450849340740343042175601.1	x^16 - 3x^15 - 423x^14 + 4064x^13 + 44342x^12 - 1061325x^11 + 1797989x^10 + 56558428x^9 - 321324127x^8 + 1969112717x^7 - 30081227003x^6 + 24714866448x^5 + 1610473646654x^4 - 6363865443214x^3 - 6076638595078x^2 + 47996844987430x - 25067773199375	\( 29^{10}\cdot 149^{14} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[10]$ (GRH)
16.8.9049517470391542347782977198790354514633273409.4	x^16 - 3x^15 - 786x^14 + 2345x^13 + 227127x^12 - 877763x^11 - 29621345x^10 + 175767416x^9 + 1582675217x^8 - 17659077219x^7 + 3690014449x^6 + 756003618333x^5 - 3545496769300x^4 - 5114937956805x^3 + 89221420987155x^2 - 274349832137406x + 284965015118076	\( 29^{10}\cdot 173^{14} \)	$(C_2\times OD_{16}).C_2$ (as 16T123)	$[2]$ (GRH)