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 39 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.63140689505957347344384.1	x^14 + 20x^12 + 123x^10 + 335x^8 + 445x^6 + 276x^4 + 62x^2 + 1	\( -\,2^{14}\cdot 3^{16}\cdot 547^{4} \)	14T56	$[4, 28]$
14.0.87391712553613254588987.1	x^14 - x^13 + 19x^12 - 52x^11 + 321x^10 - 658x^9 + 1819x^8 - 2372x^7 + 5112x^6 - 5324x^5 + 8835x^4 - 4452x^3 + 5145x^2 + 343x + 2401	\( -\,3^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[203]$
14.0.122288345645958900577483.1	x^14 - 6x^13 + 27x^12 - 88x^11 + 49x^10 + 30x^9 + 1094x^8 + 2216x^7 + 4015x^6 + 7470x^5 + 8603x^4 + 5072x^3 + 7239x^2 - 870x + 2012	\( -\,1987^{7} \)	$D_{7}$ (as 14T2)	$[13, 13]$
14.0.131627295869636184113152.1	x^14 + 16x^12 - 44x^11 - 22x^10 - 316x^9 - 56x^8 + 1628x^7 + 2241x^6 - 9220x^5 + 38232x^4 - 134240x^3 + 292724x^2 - 281808x + 148464	\( -\,2^{21}\cdot 251^{7} \)	$D_{7}$ (as 14T2)	$[13, 26]$ (GRH)
14.0.372085270290075144421376.1	x^14 + 13x^12 - 10x^11 + 103x^10 - 258x^9 + 513x^8 - 1060x^7 + 3590x^6 - 3072x^5 + 4146x^4 - 3444x^3 + 5982x^2 - 2140x + 1454	\( -\,2^{30}\cdot 809^{5} \)	14T42	$[2, 80]$ (GRH)
14.0.418988153029298748294987.1	x^14 + 21x^12 - 42x^11 + 350x^10 - 553x^9 + 2184x^8 - 2696x^7 + 8869x^6 - 8701x^5 + 18151x^4 - 8246x^3 + 17920x^2 - 8148x + 9409	\( -\,3^{7}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[203]$ (GRH)
14.0.742003380228915810271232.1	x^14 - 2x^13 - 9x^12 + 14x^11 + 90x^10 - 104x^9 + 267x^8 + 152x^7 + 2022x^6 - 694x^5 + 10130x^4 - 8292x^3 + 29677x^2 - 7326x + 33251	\( -\,2^{21}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 86]$ (GRH)
14.0.1488341081160300577685504.1	x^14 + 43x^12 + 642x^10 + 4466x^8 + 15508x^6 + 25684x^4 + 16796x^2 + 3236	\( -\,2^{32}\cdot 809^{5} \)	14T42	$[2, 254]$ (GRH)
14.0.4431175254520053739614208.1	x^14 + 33x^12 + 357x^10 + 1717x^8 + 3843x^6 + 3555x^4 + 727x^2 + 7	\( -\,2^{12}\cdot 7^{9}\cdot 173^{6} \)	14T48	$[216]$ (GRH)
14.0.6894849182652903337173011.1	x^14 - 5x^13 + 6x^12 + 11x^11 + 54x^10 - 315x^9 + 1275x^8 - 3203x^7 + 9895x^6 - 18010x^5 + 45292x^4 - 47572x^3 + 108523x^2 - 68096x + 130153	\( -\,11^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 86]$ (GRH)
14.0.8450068952156066122535627.1	x^14 - x^13 + 45x^12 - 46x^11 + 646x^10 - 693x^9 + 3489x^8 - 5970x^7 + 7170x^6 - 27038x^5 + 34790x^4 - 15372x^3 + 128440x^2 - 135147x + 77023	\( -\,7^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 116]$ (GRH)
14.0.16043017139485116019720192.1	x^14 - 4x^13 - 56x^11 + 122x^10 + 672x^9 - 536x^8 - 376x^7 - 14255x^6 + 15828x^5 + 237656x^4 - 710096x^3 + 745620x^2 - 384880x + 270304	\( -\,2^{14}\cdot 997^{7} \)	$D_{7}$ (as 14T2)	$[13, 26]$ (GRH)
14.0.19263103378911619043213312.1	x^14 + 27x^12 + 300x^10 + 1767x^8 + 5900x^6 + 10978x^4 + 10183x^2 + 3323	\( -\,2^{14}\cdot 29^{12}\cdot 3323 \)	$C_2 \wr C_7$ (as 14T29)	$[2, 2, 2, 108]$ (GRH)
14.0.21518098026638558497865728.1	x^14 + 58x^12 + 1160x^10 + 9976x^8 + 36192x^6 + 50112x^4 + 24128x^2 + 3712	\( -\,2^{21}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 86]$ (GRH)
14.0.32908474225670013957008743.1	x^14 - 5x^13 - 13x^12 + 45x^11 + 236x^10 - 82x^9 - 828x^8 - 171x^7 + 6224x^6 + 8174x^5 + 5181x^4 + 3227x^3 + 53608x^2 + 87199x + 85141	\( -\,7^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 2, 2, 14]$ (GRH)
14.0.83801419645740806624509952.1	x^14 - 2x^13 - 21x^12 + 82x^11 + 138x^10 - 1164x^9 + 2063x^8 - 824x^7 + 4950x^6 - 26778x^5 + 57742x^4 - 70268x^3 + 124449x^2 - 210818x + 208427	\( -\,2^{21}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[203]$ (GRH)
14.0.104770985911247257875546875.1	x^14 + 42x^12 - 119x^11 + 553x^10 - 2702x^9 + 6174x^8 - 15735x^7 + 36995x^6 - 61572x^5 + 88655x^4 - 58940x^3 + 2863x^2 - 4557x + 30361	\( -\,5^{7}\cdot 7^{25} \)	$C_{14}$ (as 14T1)	$[254]$ (GRH)
14.0.371695365478652317502799872.1	x^14 - 4x^13 + 12x^12 - 196x^11 + 666x^10 + 196x^9 + 3928x^8 - 20468x^7 - 56679x^6 + 182464x^5 + 35788x^4 + 818984x^3 - 2238836x^2 - 6183696x + 17351728	\( -\,2^{21}\cdot 11^{7}\cdot 71^{7} \)	$D_{7}$ (as 14T2)	$[26, 26]$ (GRH)
14.0.401774962552217617093885952.1	x^14 - 28x^12 - 42x^11 + 371x^10 + 1022x^9 - 791x^8 - 4240x^7 + 8057x^6 + 35938x^5 + 35840x^4 + 6146x^3 + 123060x^2 + 334516x + 420353	\( -\,2^{21}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[953]$ (GRH)
14.0.778700158443122158226851571.1	x^14 - 5x^13 - 6x^12 + 15x^11 + 242x^10 - 7x^9 + 149x^8 - 135x^7 + 11005x^6 + 13904x^5 + 39776x^4 + 35930x^3 + 201521x^2 + 257594x + 376249	\( -\,11^{7}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[743]$ (GRH)
14.0.2235879388560037062539773567.1	x^14 - x^13 + 5x^12 + 53x^11 - 244x^10 - 836x^9 + 2049x^8 + 5527x^7 + 10394x^6 + 4960x^5 - 21241x^4 + 21289x^3 + 157025x^2 + 187457x + 72493	\( -\,127^{13} \)	$C_{14}$ (as 14T1)	$[215]$ (GRH)
14.0.13514079353275555523926235863.1	x^14 - 5x^13 - 37x^12 + 241x^11 + 470x^10 - 5072x^9 + 2206x^8 + 45789x^7 - 85066x^6 - 115656x^5 + 581817x^4 - 1062045x^3 + 1664828x^2 - 2121563x + 2155133	\( -\,7^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[301]$ (GRH)
14.0.21472479964358571500894158848.1	x^14 - 2x^13 - 60x^12 - 64x^11 + 2966x^10 + 948x^9 - 55280x^8 - 117188x^7 + 1093128x^6 - 26052x^5 - 3601860x^4 - 8150904x^3 + 12778236x^2 + 28047240x + 12774708	\( -\,2^{20}\cdot 3^{12}\cdot 7^{11}\cdot 11^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 28]$ (GRH)
14.0.1643129976812137607879885938531.1	x^14 - x^13 + 8x^12 + 58x^11 - 1089x^10 - 1653x^9 + 22837x^8 + 60342x^7 - 23157x^6 - 53486x^5 + 434837x^4 + 473241x^3 - 217661x^2 + 293289x + 715937	\( -\,211^{13} \)	$C_{14}$ (as 14T1)	$[843]$ (GRH)
14.0.8301808522036075428899283574319.1	x^14 - x^13 + 9x^12 + 373x^11 + 170x^10 - 5214x^9 - 4853x^8 + 10839x^7 + 92428x^6 - 33400x^5 - 37491x^4 - 5712x^3 + 452768x^2 + 1090787x + 921317	\( -\,239^{13} \)	$C_{14}$ (as 14T1)	$[4, 4, 60]$ (GRH)
14.0.433976051248557709633933000126464.1	x^14 - 1646412x^7 + 827994062832	\( -\,2^{12}\cdot 3^{13}\cdot 7^{10}\cdot 113^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 2, 84]$ (GRH)
14.0.32433799430259880583578136441745408.1	x^14 - 7x^13 + 35x^12 - 119x^11 + 329x^10 - 721x^9 + 1337x^8 - 1781x^7 + 1750x^6 - 11200x^5 + 25732x^4 + 2716x^3 - 29372x^2 + 7868x + 19268	\( -\,2^{12}\cdot 3^{12}\cdot 7^{15}\cdot 11^{12} \)	$F_7$ (as 14T4)	$[21, 21]$ (GRH)
14.0.786708081482146423456402960489377792.1	x^14 - 7x^13 + 245x^12 - 1379x^11 + 24899x^10 - 112021x^9 + 1365287x^8 - 4803857x^7 + 43689016x^6 - 114741256x^5 + 815970232x^4 - 1444372664x^3 + 8218335496x^2 - 7525686616x + 34364905256	\( -\,2^{12}\cdot 3^{12}\cdot 7^{14}\cdot 127^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 2, 70]$ (GRH)
14.0.31351388821344343113730258484160000000.1	x^14 - 7x^13 + 399x^12 - 2303x^11 + 66941x^10 - 313761x^9 + 6129277x^8 - 22659577x^7 + 330980916x^6 - 914940558x^5 + 10540831434x^4 - 19581358398x^3 + 183205041390x^2 - 173576517366x + 1338931580826	\( -\,2^{12}\cdot 3^{12}\cdot 5^{7}\cdot 7^{14}\cdot 43^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 2, 2, 14]$ (GRH)
14.0.3981828055054226410930351572089280000000.1	x^14 - 7x^13 + 119x^12 - 623x^11 + 5621x^10 - 22561x^9 + 138677x^8 - 425645x^7 + 1940554x^6 - 4496800x^5 + 15613444x^4 - 22376228x^3 + 61475764x^2 - 56224420x + 107616980	\( -\,2^{12}\cdot 3^{12}\cdot 5^{7}\cdot 7^{14}\cdot 11^{13} \)	$F_7 \times C_2$ (as 14T7)	$[7, 84]$ (GRH)
14.2.1199826747425079855646785839045000000000000.1	x^14 - 16820	\( 2^{12}\cdot 5^{13}\cdot 7^{14}\cdot 29^{12} \)	$F_7 \times C_2$ (as 14T7)	$[2, 14, 28]$ (GRH)
14.0.4141665242729086954167903380508891434889216.1	x^14 - 7x^13 + 56x^12 - 245x^11 + 1085x^10 - 3346x^9 + 10157x^8 - 22697x^7 + 49861x^6 - 108598x^5 + 200305x^4 - 9905x^3 - 104972x^2 - 159271x + 169337	\( -\,2^{12}\cdot 3^{12}\cdot 7^{14}\cdot 11^{12}\cdot 19^{7} \)	$F_7 \times C_2$ (as 14T7)	$[7, 21]$ (GRH)
14.2.9594386127500047175735506615189283005353984.1	x^14 - 560802x^7 + 10312500	\( 2^{12}\cdot 3^{13}\cdot 7^{14}\cdot 11^{13}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 42]$ (GRH)
14.2.223287531694546552453480881226223313579147264.1	x^14 - 273x^12 + 31941x^10 - 2076165x^8 - 264x^7 + 80970435x^6 - 216216x^5 - 1894708179x^4 - 14054040x^3 + 24631206327x^2 - 109621512x - 137230989255	\( 2^{20}\cdot 3^{13}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 42]$ (GRH)
14.0.524804219323729928859904125998283000000000000.1	x^14 - 16820x^7 + 282912400	\( -\,2^{12}\cdot 3^{7}\cdot 5^{12}\cdot 7^{14}\cdot 29^{12} \)	$F_7 \times C_2$ (as 14T7)	$[14, 14]$ (GRH)
14.0.9526934685633986238015184265652194712710283264.1	x^14 + 182x^12 + 14196x^10 + 615160x^8 - 264x^7 + 15994160x^6 + 144144x^5 + 249508896x^4 - 6246240x^3 + 2162410432x^2 + 32480448x + 8031827600	\( -\,2^{27}\cdot 3^{12}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 6, 42]$ (GRH)
14.2.9526934685633986238015184265652194712710283264.1	x^14 - 182x^12 + 14196x^10 - 615160x^8 - 264x^7 + 15994160x^6 - 144144x^5 - 249508896x^4 - 6246240x^3 + 2162410432x^2 - 32480448x - 8031792752	\( 2^{27}\cdot 3^{12}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 210]$ (GRH)
14.2.22713982309422460169828377403383719236160000000.1	x^14 - 7x^13 - 91x^12 + 637x^11 + 3731x^10 - 24661x^9 - 91273x^8 + 520087x^7 + 1461292x^6 - 6404692x^5 - 15055796x^4 + 39080692x^3 + 99193108x^2 - 127228444x - 264145324	\( 2^{12}\cdot 3^{12}\cdot 5^{7}\cdot 7^{14}\cdot 11^{12}\cdot 13^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 84]$ (GRH)
14.0.578580738069469566208904832694868803000000000000.1	x^14 - 7x^13 + 98x^12 - 497x^11 + 3731x^10 - 14266x^9 + 73157x^8 - 209793x^7 + 796257x^6 - 2259796x^5 + 6321161x^4 + 1151073x^3 + 1782088x^2 - 26274787x + 30267061	\( -\,2^{12}\cdot 5^{12}\cdot 7^{14}\cdot 11^{12}\cdot 43^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 14, 14]$ (GRH)