Global number field search results

Further refine search

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 267)

Label	Polynomial	Discriminant	Galois group	Class group
14.14.1776478047975643577.1	x^14 - 6x^13 + 3x^12 + 39x^11 - 51x^10 - 90x^9 + 150x^8 + 91x^7 - 175x^6 - 42x^5 + 89x^4 + 7x^3 - 18x^2 + 1	\( 1697\cdot 32354821^{2} \)	14T57	Trivial
14.14.10260628712958602189.1	x^14 - x^13 - 13x^12 + 12x^11 + 66x^10 - 55x^9 - 165x^8 + 120x^7 + 210x^6 - 126x^5 - 126x^4 + 56x^3 + 28x^2 - 7x - 1	\( 29^{13} \)	$C_{14}$ (as 14T1)	Trivial
14.14.19195235171446953125.1	x^14 - x^13 - 21x^12 + 22x^11 + 145x^10 - 138x^9 - 433x^8 + 371x^7 + 560x^6 - 449x^5 - 244x^4 + 194x^3 + 4x^2 - 11x + 1	\( 5^{7}\cdot 13^{2}\cdot 1205753^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial (GRH)
14.14.19852344578500703125.1	x^14 - 3x^13 - 10x^12 + 30x^11 + 37x^10 - 107x^9 - 63x^8 + 172x^7 + 46x^6 - 130x^5 - 7x^4 + 43x^3 - 4x^2 - 5x + 1	\( 5^{7}\cdot 89\cdot 2371\cdot 1204204411 \)	14T61	Trivial (GRH)
14.14.21292697885552828353.1	x^14 - 2x^13 - 25x^12 + 69x^11 + 161x^10 - 632x^9 - 147x^8 + 2146x^7 - 1171x^6 - 2669x^5 + 2682x^4 + 667x^3 - 1466x^2 + 336x + 49	\( 577^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.14.31671389178003828125.1	x^14 - x^13 - 19x^12 + 14x^11 + 107x^10 - 53x^9 - 240x^8 + 87x^7 + 241x^6 - 66x^5 - 108x^4 + 22x^3 + 19x^2 - 2x - 1	\( 5^{7}\cdot 71^{2}\cdot 283583^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial (GRH)
14.14.45782583872342265625.1	x^14 - 2x^13 - 12x^12 + 21x^11 + 56x^10 - 84x^9 - 127x^8 + 161x^7 + 142x^6 - 153x^5 - 69x^4 + 67x^3 + 9x^2 - 10x + 1	\( 5^{7}\cdot 15749\cdot 37209795769 \)	14T61	Trivial (GRH)
14.14.46493802010200358912.1	x^14 - 15x^12 + 83x^10 - 214x^8 + 278x^6 - 183x^4 + 58x^2 - 7	\( 2^{14}\cdot 7\cdot 71^{2}\cdot 283583^{2} \)	14T57	Trivial (GRH)
14.14.50123987618145255424.1	x^14 - 13x^12 + 62x^10 - 136x^8 + 142x^6 - 68x^4 + 14x^2 - 1	\( 2^{14}\cdot 313^{2}\cdot 176713^{2} \)	14T55	Trivial (GRH)
14.14.59253507863224160256.1	x^14 - 14x^12 + 74x^10 - 186x^8 + 234x^6 - 145x^4 + 41x^2 - 4	\( 2^{12}\cdot 3^{6}\cdot 61^{2}\cdot 103^{2}\cdot 709^{2} \)	14T55	Trivial
14.14.103445227318228025344.1	x^14 - 17x^12 + 106x^10 - 304x^8 + 419x^6 - 259x^4 + 59x^2 - 1	\( 2^{18}\cdot 4457^{4} \)	14T34	Trivial
14.14.152387536786230345728.1	x^14 - 18x^12 + 114x^10 - 320x^8 + 425x^6 - 266x^4 + 76x^2 - 8	\( 2^{19}\cdot 4129^{4} \)	14T51	Trivial
14.14.155466135854662578125.1	x^14 - 7x^13 + 3x^12 + 72x^11 - 114x^10 - 223x^9 + 438x^8 + 377x^7 - 659x^6 - 448x^5 + 383x^4 + 290x^3 - 20x^2 - 31x - 1	\( 5^{7}\cdot 6679^{4} \)	$A_7\times C_2$ (as 14T47)	Trivial (GRH)
14.14.275168988624452583424.1	x^14 - 17x^12 + 104x^10 - 296x^8 + 408x^6 - 252x^4 + 60x^2 - 4	\( 2^{26}\cdot 1423^{4} \)	14T34	Trivial
14.14.519372213204121812992.1	x^14 - 17x^12 + 102x^10 - 273x^8 + 360x^6 - 236x^4 + 72x^2 - 8	\( 2^{21}\cdot 3967^{4} \)	14T51	Trivial
14.14.919864697874104188928.1	x^14 - 24x^12 + 219x^10 - 978x^8 + 2263x^6 - 2628x^4 + 1357x^2 - 242	\( 2^{31}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.14.919864697874104188928.2	x^14 - 20x^12 + 144x^10 - 466x^8 + 740x^6 - 568x^4 + 176x^2 - 8	\( 2^{31}\cdot 809^{4} \)	$\GL(3,2) \times C_2$ (as 14T19)	Trivial
14.14.1064726745878753869969.1	x^14 - 4x^13 - 28x^12 + 91x^11 + 271x^10 - 620x^9 - 1144x^8 + 1365x^7 + 2396x^6 - 620x^5 - 1817x^4 - 337x^3 + 266x^2 + 70x + 1	\( 1009^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.14.1714445270973235712000.1	x^14 - 27x^12 - 12x^11 + 248x^10 + 154x^9 - 1008x^8 - 698x^7 + 1858x^6 + 1328x^5 - 1406x^4 - 954x^3 + 317x^2 + 138x - 28	\( 2^{12}\cdot 5^{3}\cdot 7607^{4} \)	14T43	Trivial
14.14.2633084517175978360832.1	x^14 - 6x^13 - 5x^12 + 88x^11 - 80x^10 - 412x^9 + 638x^8 + 744x^7 - 1558x^6 - 496x^5 + 1504x^4 + 116x^3 - 491x^2 - 58x - 1	\( 2^{21}\cdot 107881^{3} \)	$D_7 \wr C_2$ (as 14T20)	Trivial (GRH)
14.14.2883001771765710078125.1	x^14 - 3x^13 - 22x^12 + 67x^11 + 147x^10 - 474x^9 - 335x^8 + 1305x^7 + 304x^6 - 1649x^5 - 118x^4 + 948x^3 + 64x^2 - 193x - 41	\( 5^{7}\cdot 577^{6} \)	$D_{14}$ (as 14T3)	Trivial (GRH)
14.14.3023046465831001210880.1	x^14 - 18x^12 + 108x^10 - 300x^8 + 421x^6 - 290x^4 + 82x^2 - 5	\( 2^{14}\cdot 5\cdot 577^{6} \)	14T38	Trivial (GRH)
14.14.3679458791496416755712.1	x^14 - 20x^12 + 136x^10 - 428x^8 + 684x^6 - 560x^4 + 220x^2 - 32	\( 2^{33}\cdot 809^{4} \)	14T43	Trivial
14.14.4001610765876182388736.1	x^14 - 16x^12 + 101x^10 - 319x^8 + 528x^6 - 438x^4 + 157x^2 - 16	\( 2^{12}\cdot 149^{4}\cdot 211^{4} \)	14T53	Trivial (GRH)
14.14.4232265052163401695232.1	x^14 - 22x^12 + 182x^10 - 736x^8 + 1564x^6 - 1740x^4 + 927x^2 - 175	\( 2^{14}\cdot 7\cdot 577^{6} \)	14T38	Trivial (GRH)
14.14.5586931326989478175797.1	x^14 - 5x^13 - 5x^12 + 55x^11 - 18x^10 - 232x^9 + 171x^8 + 461x^7 - 426x^6 - 414x^5 + 442x^4 + 112x^3 - 164x^2 + 18x + 3	\( 3\cdot 53\cdot 647\cdot 7283^{2}\cdot 9049\cdot 113149 \)	14T63	Trivial (GRH)
14.14.5796901408038404767744.1	x^14 - 16x^12 + 89x^10 - 212x^8 + 236x^6 - 119x^4 + 23x^2 - 1	\( 2^{14}\cdot 29^{12} \)	$F_8$ (as 14T6)	Trivial (GRH)
14.14.6517333038313561346048.1	x^14 - 7x^13 + 4x^12 + 67x^11 - 121x^10 - 176x^9 + 509x^8 + 43x^7 - 749x^6 + 320x^5 + 325x^4 - 261x^3 + 38x^2 + 7x - 1	\( 2^{12}\cdot 73^{8}\cdot 1973 \)	14T44	Trivial
14.14.6606521072796311552000.1	x^14 - 2x^13 - 21x^12 + 38x^11 + 175x^10 - 278x^9 - 733x^8 + 974x^7 + 1599x^6 - 1640x^5 - 1661x^4 + 1150x^3 + 597x^2 - 258x - 47	\( 2^{16}\cdot 5^{3}\cdot 73^{8} \)	$C_2\times F_8:C_3$ (as 14T18)	Trivial
14.14.6620494548366593622016.1	x^14 - 16x^12 + 97x^10 - 277x^8 + 379x^6 - 230x^4 + 51x^2 - 1	\( 2^{24}\cdot 4457^{4} \)	14T50	Trivial (GRH)
14.14.7358917582992833511424.1	x^14 - 18x^12 + 114x^10 - 316x^8 + 415x^6 - 254x^4 + 64x^2 - 4	\( 2^{34}\cdot 809^{4} \)	14T50	Trivial (GRH)
14.14.7706506831416897425408.1	x^14 - 5x^13 - 14x^12 + 127x^11 - 165x^10 - 484x^9 + 1495x^8 - 691x^7 - 2185x^6 + 3510x^5 - 1891x^4 + 209x^3 + 120x^2 - 29x + 1	\( 2^{12}\cdot 73^{8}\cdot 2333 \)	14T44	Trivial
14.14.13107708723619561567601.1	x^14 - 3x^13 - 13x^12 + 39x^11 + 69x^10 - 197x^9 - 193x^8 + 487x^7 + 301x^6 - 609x^5 - 251x^4 + 357x^3 + 98x^2 - 74x - 11	\( 13107708723619561567601 \)	14T63	Trivial (GRH)
14.14.15115232329155006054400.1	x^14 - 20x^12 + 128x^10 - 381x^8 + 588x^6 - 472x^4 + 180x^2 - 25	\( 2^{14}\cdot 5^{2}\cdot 577^{6} \)	14T28	Trivial (GRH)
14.14.15115232329155006054400.2	x^14 - 24x^12 + 165x^10 - 515x^8 + 821x^6 - 664x^4 + 240x^2 - 25	\( 2^{14}\cdot 5^{2}\cdot 577^{6} \)	14T28	Trivial (GRH)
14.14.15432833226052183785472.1	x^14 - 23x^12 + 189x^10 - 723x^8 + 1363x^6 - 1241x^4 + 511x^2 - 73	\( 2^{18}\cdot 73^{9} \)	$C_2\times F_8:C_3$ (as 14T18)	Trivial (GRH)
14.14.19662754355948284297216.1	x^14 - 6x^13 - 15x^12 + 104x^11 + 104x^10 - 598x^9 - 502x^8 + 1280x^7 + 1280x^6 - 672x^5 - 908x^4 - 8x^3 + 152x^2 + 8x - 8	\( 2^{14}\cdot 4129^{5} \)	$C_2\times \PSL(2,7)$ (as 14T17)	Trivial
14.14.19662754355948284297216.2	x^14 - 30x^12 - 14x^11 + 261x^10 + 108x^9 - 890x^8 - 150x^7 + 1283x^6 - 78x^5 - 660x^4 + 76x^3 + 120x^2 - 12x - 4	\( 2^{14}\cdot 4129^{5} \)	$C_2\times \PSL(2,7)$ (as 14T17)	Trivial (GRH)
14.14.23255329393129696526336.1	x^14 - 33x^12 - 12x^11 + 347x^10 + 268x^9 - 1307x^8 - 1596x^7 + 1210x^6 + 2592x^5 + 962x^4 - 232x^3 - 174x^2 - 16x + 2	\( 2^{26}\cdot 809^{5} \)	14T42	Trivial
14.14.26736653147041339876997.1	x^14 - 22x^12 - 3x^11 + 162x^10 + 12x^9 - 485x^8 + 81x^7 + 591x^6 - 246x^5 - 219x^4 + 145x^3 - 10x^2 - 7x + 1	\( 7^{8}\cdot 173^{7} \)	$F_7$ (as 14T4)	Trivial (GRH)
14.14.26961206542479413771201.1	x^14 - 4x^13 - 36x^12 + 153x^11 + 406x^10 - 2005x^9 - 1624x^8 + 11863x^7 - 455x^6 - 32213x^5 + 16953x^4 + 32032x^3 - 27733x^2 - 102x + 2601	\( 1601^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.14.27641779937927268828125.1	x^14 - 5x^13 - 22x^12 + 131x^11 + 90x^10 - 1019x^9 + 223x^8 + 3253x^7 - 1853x^6 - 4170x^5 + 2916x^4 + 1404x^3 - 781x^2 - 168x + 41	\( 5^{7}\cdot 29^{12} \)	$C_{14}$ (as 14T1)	Trivial (GRH)
14.14.33032605363981557760000.1	x^14 - 4x^13 - 26x^12 + 54x^11 + 254x^10 - 244x^9 - 1166x^8 + 388x^7 + 2612x^6 - 66x^5 - 2796x^4 - 162x^3 + 1398x^2 + 52x - 254	\( 2^{16}\cdot 5^{4}\cdot 73^{8} \)	$F_8:C_3$ (as 14T11)	Trivial (GRH)
14.14.52518884338097360421921.1	x^14 - 4x^13 - 38x^12 + 169x^11 + 383x^10 - 2243x^9 - 473x^8 + 11399x^7 - 7862x^6 - 18489x^5 + 22026x^4 + 3042x^3 - 9774x^2 + 1215x + 729	\( 3^{7}\cdot 587^{7} \)	$D_{7}$ (as 14T2)	Trivial (GRH)
14.14.54120620628347384233984.1	x^14 - 22x^12 + 188x^10 - 780x^8 + 1584x^6 - 1352x^4 + 288x^2 - 16	\( 2^{26}\cdot 73^{8} \)	$F_8:C_3$ (as 14T11)	Trivial (GRH)
14.14.63140689505957347344384.1	x^14 - 23x^12 + 162x^10 - 452x^8 + 535x^6 - 276x^4 + 53x^2 - 1	\( 2^{14}\cdot 3^{16}\cdot 547^{4} \)	14T53	Trivial (GRH)
14.14.76324668233417175078125.1	x^14 - 3x^13 - 22x^12 + 65x^11 + 160x^10 - 475x^9 - 423x^8 + 1351x^7 + 329x^6 - 1444x^5 - 76x^4 + 608x^3 - 20x^2 - 81x + 11	\( 5^{7}\cdot 149^{4}\cdot 211^{4} \)	$A_7\times C_2$ (as 14T47)	Trivial (GRH)
14.14.77389989525273630998528.1	x^14 - 4x^13 - 24x^12 + 96x^11 + 183x^10 - 772x^9 - 458x^8 + 2486x^7 + 275x^6 - 3370x^5 + 60x^4 + 1886x^3 + x^2 - 310x - 25	\( 2^{21}\cdot 577^{6} \)	$D_{14}$ (as 14T3)	Trivial (GRH)
14.14.95943073544227445938801.1	x^14 - x^13 - 28x^12 + 19x^11 + 277x^10 - 124x^9 - 1186x^8 + 395x^7 + 2198x^6 - 662x^5 - 1425x^4 + 457x^3 + 170x^2 - 35x - 7	\( 7^{4}\cdot 43^{12} \)	$F_8$ (as 14T6)	Trivial
14.14.101886286793711667200000.1	x^14 - 19x^12 + 116x^10 - 307x^8 + 382x^6 - 218x^4 + 55x^2 - 5	\( 2^{14}\cdot 5^{5}\cdot 6679^{4} \)	14T56	Trivial (GRH)