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 138)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.80705598398100581643.1	x^14 - 2x^13 + 11x^12 - 6x^11 + 56x^10 - 28x^9 + 169x^8 - 7x^7 + 258x^6 - 117x^5 + 103x^4 - 16x^3 + 11x^2 - x + 1	\( -\,3^{7}\cdot 577^{6} \)	$D_{14}$ (as 14T3)	$[13]$
14.0.179238239738466418688.1	x^14 + 15x^12 + 90x^10 + 276x^8 + 457x^6 + 394x^4 + 153x^2 + 17	\( -\,2^{14}\cdot 17^{3}\cdot 23^{2}\cdot 64879^{2} \)	14T57	$[16]$
14.0.459932348937052094464.1	x^14 + 19x^12 + 120x^10 + 344x^8 + 472x^6 + 284x^4 + 60x^2 + 4	\( -\,2^{30}\cdot 809^{4} \)	14T43	$[18]$
14.0.3023046465831001210880.1	x^14 + 18x^12 + 108x^10 + 300x^8 + 421x^6 + 290x^4 + 82x^2 + 5	\( -\,2^{14}\cdot 5\cdot 577^{6} \)	14T38	$[22]$
14.0.4001610765876182388736.1	x^14 + 16x^12 + 101x^10 + 319x^8 + 528x^6 + 438x^4 + 157x^2 + 16	\( -\,2^{12}\cdot 149^{4}\cdot 211^{4} \)	14T56	$[2, 22]$
14.0.4232265052163401695232.1	x^14 + 22x^12 + 182x^10 + 736x^8 + 1564x^6 + 1740x^4 + 927x^2 + 175	\( -\,2^{14}\cdot 7\cdot 577^{6} \)	14T38	$[36]$
14.0.5796901408038404767744.1	x^14 + 25x^12 + 214x^10 + 767x^8 + 1194x^6 + 686x^4 + 53x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 14]$
14.0.5796901408038404767744.3	x^14 + 16x^12 + 89x^10 + 212x^8 + 236x^6 + 119x^4 + 23x^2 + 1	\( -\,2^{14}\cdot 29^{12} \)	$C_2\times F_8$ (as 14T9)	$[2, 2, 8]$
14.2.5895690467647158497344.1	x^14 + 15x^12 + 80x^10 + 177x^8 + 133x^6 - 7x^4 - 14x^2 - 1	\( 2^{6}\cdot 313^{8} \)	14T35	$[2, 6]$
14.0.7358917582992833511424.1	x^14 + 18x^12 + 114x^10 + 316x^8 + 415x^6 + 254x^4 + 64x^2 + 4	\( -\,2^{34}\cdot 809^{4} \)	14T51	$[2, 24]$
14.0.14717835165985667022848.1	x^14 + 18x^12 + 110x^10 + 304x^8 + 407x^6 + 262x^4 + 76x^2 + 8	\( -\,2^{35}\cdot 809^{4} \)	14T51	$[2, 10]$
14.0.16912693946358557573120.1	x^14 + 25x^12 + 159x^10 + 423x^8 + 527x^6 + 299x^4 + 69x^2 + 5	\( -\,2^{22}\cdot 5\cdot 73^{8} \)	14T44	$[20]$
14.0.22439994995240462987343.1	x^14 - x^13 + 16x^12 - 17x^11 + 66x^10 - 84x^9 + 38x^8 - 315x^7 + 65x^6 - 503x^5 + 1556x^4 + 665x^3 + 2377x^2 - 3516x + 1681	\( -\,3^{7}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 6]$
14.0.22657064019154950467584.1	x^14 - 2x^13 + 22x^12 - 54x^11 + 240x^10 - 648x^9 + 1498x^8 - 4160x^7 + 6684x^6 - 13264x^5 + 20352x^4 - 22164x^3 + 30700x^2 - 15156x + 14300	\( -\,2^{12}\cdot 19^{3}\cdot 73^{8} \)	$C_2\times F_8:C_3$ (as 14T18)	$[18]$
14.2.24385268673304131774761.1	x^14 - 7x^13 + 47x^12 - 191x^11 + 665x^10 - 1741x^9 + 3682x^8 - 6097x^7 + 7180x^6 - 5712x^5 - 237x^4 + 5464x^3 - 8890x^2 + 5836x - 2477	\( 29^{12}\cdot 41^{3} \)	$C_2 \wr C_7$ (as 14T29)	$[2, 6]$
14.0.53009664910029939756127.1	x^14 - x^12 - 3x^11 + 24x^10 - 39x^9 + 106x^8 + 69x^7 + 225x^6 - 123x^5 + 585x^4 - 290x^3 - 421x^2 + 89x + 382	\( -\,7^{11}\cdot 173^{6} \)	$F_7 \times C_2$ (as 14T7)	$[14]$
14.0.54120620628347384233984.1	x^14 + 22x^12 + 188x^10 + 780x^8 + 1584x^6 + 1352x^4 + 288x^2 + 16	\( -\,2^{26}\cdot 73^{8} \)	$C_2\times F_8:C_3$ (as 14T18)	$[48]$
14.0.93021317572518786105344.1	x^14 - 2x^13 + 10x^12 - 24x^11 + 62x^10 - 92x^9 + 242x^8 - 328x^7 + 526x^6 - 84x^5 + 640x^4 - 104x^3 + 688x^2 + 232x + 356	\( -\,2^{28}\cdot 809^{5} \)	$C_2\times \PSL(2,7)$ (as 14T17)	$[2, 32]$
14.0.93021317572518786105344.2	x^14 - 6x^13 + 32x^12 - 144x^11 + 567x^10 - 1958x^9 + 5542x^8 - 13788x^7 + 29425x^6 - 51950x^5 + 73504x^4 - 79680x^3 + 67601x^2 - 35622x + 17902	\( -\,2^{28}\cdot 809^{5} \)	$C_2\times \PSL(2,7)$ (as 14T17)	$[2, 32]$
14.0.140502435866955853458751.1	x^14 - 2x^13 + 41x^12 - 82x^11 + 889x^10 - 2165x^9 + 13716x^8 - 34620x^7 + 136444x^6 - 290952x^5 + 750275x^4 - 1167525x^3 + 1937335x^2 - 1728557x + 1560373	\( -\,107^{5}\cdot 21557^{3} \)	14T54	$[14]$ (GRH)
14.0.168110140833113738264576.1	x^14 + 29x^12 + 290x^10 + 1247x^8 + 2262x^6 + 1566x^4 + 377x^2 + 29	\( -\,2^{14}\cdot 29^{13} \)	$C_{14}$ (as 14T1)	$[2, 2, 2, 6]$ (GRH)
14.0.168110140833113738264576.2	x^14 + 29x^12 + 348x^10 + 2233x^8 + 8236x^6 + 17342x^4 + 19111x^2 + 8381	\( -\,2^{14}\cdot 29^{13} \)	$C_2\times F_8$ (as 14T9)	$[2, 2, 2, 12]$ (GRH)
14.0.291381688005381590432263.1	x^14 - 5x^13 - x^12 + 41x^11 - 266x^9 + 682x^8 - 1271x^7 + 3346x^6 - 5784x^5 + 12267x^4 - 10251x^3 + 20954x^2 - 13581x + 22271	\( -\,7^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	$[2, 2, 14]$ (GRH)
14.0.654698590982350051753984.1	x^14 + 37x^12 + 470x^10 + 2787x^8 + 8570x^6 + 13714x^4 + 10241x^2 + 2401	\( -\,2^{14}\cdot 43^{12} \)	$C_{14}$ (as 14T1)	$[43]$ (GRH)
14.0.1165087474585497590531111.1	x^14 - x^13 + 3x^12 - 11x^11 + 44x^10 + 156x^9 - 250x^8 - 749x^7 + 1560x^6 + 4490x^5 + 3202x^4 + 755x^3 + 4050x^2 + 1750x + 625	\( -\,71^{13} \)	$C_{14}$ (as 14T1)	$[49]$ (GRH)
14.0.1899075109080023031263232.1	x^14 + 26x^12 + 256x^10 + 1188x^8 + 2658x^6 + 2741x^4 + 1081x^2 + 48	\( -\,2^{12}\cdot 3\cdot 7^{8}\cdot 173^{6} \)	14T48	$[30]$ (GRH)
14.0.3138866894939200133545984.1	x^14 + 42x^12 + 623x^10 + 4431x^8 + 16513x^6 + 31906x^4 + 28784x^2 + 9409	\( -\,2^{14}\cdot 7^{24} \)	$C_{14}$ (as 14T1)	$[71]$ (GRH)
14.2.4717811198979405309189241.1	x^14 - 5x^13 + 67x^12 - 227x^11 + 1616x^10 - 3926x^9 + 18994x^8 - 35611x^7 + 117192x^6 - 204216x^5 + 329208x^4 - 841056x^3 + 191744x^2 - 1853568x + 318848	\( 17^{5}\cdot 23^{3}\cdot 64879^{3} \)	14T54	$[4, 16]$ (GRH)
14.0.7979450736541232847417344.1	x^14 - 7x^13 - 7x^12 + 119x^11 - 147x^10 - 147x^9 + 3619x^8 - 3525x^7 - 46746x^6 - 89096x^5 + 122850x^4 + 1088304x^3 + 2562392x^2 + 3225306x + 1986282	\( -\,2^{12}\cdot 7^{15}\cdot 17^{7} \)	$F_7 \times C_2$ (as 14T7)	$[70]$ (GRH)
14.0.17293766349691312351682111.1	x^14 + 28x^12 - 82x^10 + 447x^8 - 553x^6 + 1529x^4 - 470x^2 + 4031	\( -\,29^{7}\cdot 139^{7} \)	$D_{7}$ (as 14T2)	$[12]$ (GRH)
14.0.28033829543340009100599839.1	x^14 - 4x^13 + 12x^12 - 10x^11 - 86x^10 + 63x^9 + 1841x^8 - 11168x^7 + 52503x^6 - 126275x^5 + 250397x^4 + 15948x^3 + 960957x^2 - 2208519x + 1477683	\( -\,7^{7}\cdot 617^{7} \)	$D_{7}$ (as 14T2)	$[12]$ (GRH)
14.0.35887976153781453950585067.1	x^14 - x^13 + 31x^12 + 36x^11 + 643x^10 + 844x^9 + 7385x^8 + 14106x^7 + 58178x^6 + 65124x^5 + 122335x^4 + 9326x^3 + 93727x^2 + 33565x + 18769	\( -\,3^{7}\cdot 71^{12} \)	$C_{14}$ (as 14T1)	$[43]$ (GRH)
14.0.38011043274806994636408671.1	x^14 - 4x^13 + 24x^12 - 17x^11 + 87x^10 - 1171x^9 + 2691x^8 + 3707x^7 + 13199x^6 + 593x^5 + 101717x^4 + 243329x^3 + 487049x^2 - 1106911x + 1351337	\( -\,13^{7}\cdot 347^{7} \)	$D_{7}$ (as 14T2)	$[12]$ (GRH)
14.0.49098849571309452996402359.1	x^14 - 4x^13 - 6x^12 - 21x^11 + 369x^10 + 595x^9 - 3663x^8 - 18667x^7 + 48948x^6 + 192779x^5 - 167580x^4 - 1255412x^3 + 794668x^2 + 5433177x + 3910177	\( -\,4679^{7} \)	$D_{7}$ (as 14T2)	$[13]$ (GRH)
14.0.54638052730056427270720751.1	x^14 - 6x^13 + 7x^12 + 62x^11 - 264x^10 - 117x^9 + 6405x^8 - 5588x^7 - 36573x^6 + 36976x^5 + 251350x^4 - 101850x^3 - 544712x^2 + 132111x + 1331177	\( -\,4751^{7} \)	$D_{7}$ (as 14T2)	$[13]$ (GRH)
14.0.65061924746822370167743991.1	x^14 - 4x^13 - 16x^12 + 128x^11 - 189x^10 - 690x^9 + 3301x^8 - 6162x^7 + 13386x^6 - 37006x^5 + 80953x^4 - 182199x^3 + 322152x^2 - 318951x + 496319	\( -\,4871^{7} \)	$D_{7}$ (as 14T2)	$[13]$ (GRH)
14.0.69684751861829721459380039.1	x^14 + 62x^12 + 1633x^10 + 21314x^8 + 127838x^6 + 206223x^4 - 620741x^2 + 2602151	\( -\,4919^{7} \)	$D_{7}$ (as 14T2)	$[13]$ (GRH)
14.0.151277339258832781070234375.1	x^14 - 38x^12 - 130x^11 + 709x^10 + 3185x^9 - 434x^8 - 35365x^7 - 47811x^6 + 30960x^5 + 562767x^4 + 1094380x^3 + 1667351x^2 + 1089515x + 445655	\( -\,5^{7}\cdot 7^{7}\cdot 157^{7} \)	$D_{7}$ (as 14T2)	$[2, 6]$ (GRH)
14.0.251630624582327009776103424.1	x^14 - 6x^13 + 51x^12 - 96x^11 + 339x^10 + 1134x^9 - 2055x^8 + 12006x^7 + 3813x^6 + 20676x^5 + 106215x^4 - 35742x^3 + 313863x^2 - 43524x + 215205	\( -\,2^{12}\cdot 3^{13}\cdot 7^{11}\cdot 11^{7} \)	$F_7 \times C_2$ (as 14T7)	$[2, 2, 6]$ (GRH)
14.0.312475498577452580635859375.1	x^14 - 4x^13 - 12x^12 + 161x^11 - 449x^10 - 1757x^9 + 11853x^8 + 867x^7 - 57037x^6 + 355203x^5 + 662185x^4 - 562305x^3 + 1085079x^2 + 4992495x + 4158745	\( -\,5^{7}\cdot 23^{7}\cdot 53^{7} \)	$D_{7}$ (as 14T2)	$[2, 6]$ (GRH)
14.0.348598591551339822624996431.1	x^14 + 16x^12 - 23x^11 + 184x^10 - 1422x^9 - 3339x^8 - 3403x^7 + 25724x^6 - 57007x^5 - 298373x^4 + 434497x^3 + 6295270x^2 + 14635125x + 23001625	\( -\,41^{7}\cdot 151^{7} \)	$D_{7}$ (as 14T2)	$[14]$ (GRH)
14.0.377987015999056008227829767.1	x^14 - 4x^13 + 18x^12 + 135x^11 - 819x^10 + 3672x^9 + 318x^8 - 44720x^7 + 262353x^6 - 807128x^5 + 1770111x^4 - 2873985x^3 + 3480188x^2 - 3274534x + 2105941	\( -\,6263^{7} \)	$D_{7}$ (as 14T2)	$[11]$ (GRH)
14.0.479243089919880156320166959.1	x^14 - 4x^13 - 6x^12 + 104x^11 + 214x^10 - 3213x^9 + 10157x^8 + 11487x^7 - 67254x^6 - 371351x^5 + 3860271x^4 - 12829434x^3 + 24569154x^2 - 22475936x + 12295717	\( -\,11^{7}\cdot 19^{7}\cdot 31^{7} \)	$D_{7}$ (as 14T2)	$[2, 6]$ (GRH)
14.0.618204963477212079917000639.1	x^14 - 2x^13 + 74x^11 + 549x^10 - 1392x^9 - 3200x^8 + 11296x^7 + 87904x^6 - 223603x^5 + 203477x^4 - 1200614x^3 + 6395526x^2 - 9406012x + 4742837	\( -\,6719^{7} \)	$D_{7}$ (as 14T2)	$[15]$ (GRH)
14.0.912205534197333179463463487.1	x^14 - 4x^13 - 20x^12 - 28x^11 + 98x^10 + 2492x^9 + 4008x^8 - 14660x^7 - 31723x^6 + 47320x^5 + 149428x^4 - 930864x^3 - 488384x^2 + 2476800x + 6141952	\( -\,7103^{7} \)	$D_{7}$ (as 14T2)	$[11]$ (GRH)
14.0.1025706963691171311737151047.1	x^14 + 32x^12 + 312x^10 - 1426x^8 - 36368x^6 - 65016x^4 + 1347921x^2 + 5265567	\( -\,31^{7}\cdot 233^{7} \)	$D_{7}$ (as 14T2)	$[12]$ (GRH)
14.0.1563017639236784352773715591.1	x^14 + 28x^12 - 172x^11 + 1003x^10 - 3436x^9 + 15553x^8 - 83854x^7 + 224506x^6 - 7434x^5 - 756401x^4 + 1106991x^3 + 1133790x^2 + 439425x + 1726875	\( -\,3^{7}\cdot 2557^{7} \)	$D_{7}$ (as 14T2)	$[12]$ (GRH)
14.0.1911898975188880445832734375.1	x^14 - 2x^13 + 31x^12 - 120x^11 - 192x^10 - 2901x^9 + 1448x^8 + 47705x^7 + 306881x^6 + 1019523x^5 + 2442591x^4 + 4052160x^3 + 4799250x^2 + 3553875x + 1476225	\( -\,5^{7}\cdot 1579^{7} \)	$D_{7}$ (as 14T2)	$[16]$ (GRH)
14.0.2093583355361649269668343808.1	x^14 - 7x^13 + 63x^12 - 287x^11 + 1421x^10 - 4641x^9 + 15757x^8 - 38017x^7 + 94416x^6 - 171234x^5 + 317646x^4 - 341082x^3 + 432810x^2 - 344610x + 299142	\( -\,2^{12}\cdot 3^{12}\cdot 7^{10}\cdot 23^{7} \)	$F_7 \times C_2$ (as 14T7)	$[21]$ (GRH)
14.0.2665908124227273813779851559.1	x^14 - 2x^13 - 17x^12 + 228x^11 - 987x^10 + 21x^9 + 18141x^8 - 102392x^7 + 301240x^6 - 540701x^5 + 872694x^4 - 1497260x^3 + 1333379x^2 - 531483x + 1413721	\( -\,17^{7}\cdot 487^{7} \)	$D_{7}$ (as 14T2)	$[18]$ (GRH)