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
16.0.15310680244851363610624.2	x^16 + 15x^14 + 86x^12 + 242x^10 + 360x^8 + 281x^6 + 107x^4 + 18x^2 + 1	\( 2^{16}\cdot 483345053^{2} \)	16T1945	$[12]$
16.0.22986704741655040229376.1	x^16 - 31x^12 + 880x^8 - 2511x^4 + 6561	\( 2^{32}\cdot 3^{8}\cdot 13^{8} \)	$C_2^4$ (as 16T3)	$[12]$ (GRH)
16.0.32051921049190634765625.1	x^16 - 2x^15 + 11x^14 + 4x^13 + 38x^12 + 59x^11 + 108x^10 + 326x^9 + 108x^8 + 649x^7 + 983x^6 - 289x^5 + 1773x^4 + 106x^3 + 51x^2 - 3x + 1	\( 3^{8}\cdot 5^{10}\cdot 29^{8} \)	$C_2\times C_2^2.D_4$ (as 16T92)	$[12]$ (GRH)
16.0.45086848686489600000000.1	x^16 + 12x^14 + 114x^12 + 312x^10 + 608x^8 + 624x^6 + 456x^4 + 96x^2 + 16	\( 2^{44}\cdot 3^{8}\cdot 5^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[20]$ (GRH)
16.0.69876989027353600000000.1	x^16 + 15x^14 + 87x^12 + 251x^10 + 384x^8 + 306x^6 + 117x^4 + 19x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 1652141^{2} \)	16T1868	$[12]$
16.0.74247530256000000000000.1	x^16 + 24x^12 + 90x^10 + 206x^8 + 840x^6 + 2049x^4 + 2250x^2 + 961	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 29^{4} \)	$C_2 \times (C_2^2:C_4)$ (as 16T21)	$[2, 8]$
16.0.109009032877825600000000.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 270x^12 - 528x^11 + 811x^10 - 931x^9 + 795x^8 - 542x^7 + 499x^6 - 687x^5 + 1228x^4 - 1480x^3 + 1209x^2 - 561x + 911	\( 2^{12}\cdot 5^{8}\cdot 13^{8}\cdot 17^{4} \)	$(C_2\times D_4):C_2^2$ (as 16T115)	$[12]$
16.0.113799786888217600000000.1	x^16 + 16x^14 + 96x^12 + 282x^10 + 441x^8 + 367x^6 + 151x^4 + 26x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 2108389^{2} \)	16T1868	$[12]$
16.0.114523100106217078515625.3	x^16 - 5x^15 + 23x^14 - 40x^13 + 115x^12 - 42x^11 + 462x^10 + 340x^9 + 1515x^8 + 1563x^7 + 3106x^6 + 2475x^5 + 2795x^4 + 1247x^3 + 922x^2 + 143x + 121	\( 5^{8}\cdot 29^{6}\cdot 149^{4} \)	16T1025	$[2, 8]$ (GRH)
16.0.121029087867608368152576.1	x^16 + 16x^14 + 104x^12 + 352x^10 + 660x^8 + 672x^6 + 336x^4 + 64x^2 + 1	\( 2^{64}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 6]$ (GRH)
16.0.121029087867608368152576.2	x^16 + 6561	\( 2^{64}\cdot 3^{8} \)	$C_8\times C_2$ (as 16T5)	$[3, 6]$ (GRH)
16.0.125439056256992431640625.1	x^16 - x^15 + 6x^14 - 17x^13 + 17x^12 + 49x^11 - 78x^10 + 833x^9 - 2129x^8 + 4998x^7 - 2808x^6 + 10584x^5 + 22032x^4 - 132192x^3 + 279936x^2 - 279936x + 1679616	\( 3^{8}\cdot 5^{12}\cdot 23^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[15]$ (GRH)
16.0.137011437068313600000000.1	x^16 - 4x^14 + 56x^12 - 294x^10 + 1544x^8 - 12936x^6 + 63833x^4 - 109540x^2 + 59536	\( 2^{16}\cdot 3^{8}\cdot 5^{8}\cdot 13^{8} \)	$C_2^4$ (as 16T3)	$[4, 4]$ (GRH)
16.0.138208899689636344140625.2	x^16 - 2x^15 + 3x^14 + 5x^13 + 23x^12 - 15x^11 + 55x^10 + 43x^9 + x^8 - 387x^7 + 401x^6 + 1367x^5 + 5089x^4 + 5471x^3 + 6651x^2 + 3764x + 6091	\( 5^{8}\cdot 29^{12} \)	$C_2^2 : C_4$ (as 16T10)	$[3, 6]$ (GRH)
16.0.140857138691308837890625.2	x^16 - 6x^15 + 31x^14 - 99x^13 + 260x^12 - 480x^11 + 725x^10 - 732x^9 + 857x^8 - 522x^7 + 763x^6 - 60x^5 + 442x^4 + 198x^3 + 216x^2 + 81x + 81	\( 5^{12}\cdot 13^{8}\cdot 29^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[14]$ (GRH)
16.0.154243018307350441230336.1	x^16 + 8x^14 + 100x^12 + 448x^10 + 945x^8 + 896x^6 + 400x^4 + 64x^2 + 16	\( 2^{48}\cdot 3^{8}\cdot 17^{4} \)	$C_2 \times (C_2^2:C_4)$ (as 16T21)	$[2, 12]$
16.0.171992678400000000000000.1	x^16 + 30x^14 + 260x^12 + 1050x^10 + 2270x^8 + 2700x^6 + 1675x^4 + 450x^2 + 25	\( 2^{32}\cdot 3^{8}\cdot 5^{14} \)	$C_2 \times (C_8:C_2)$ (as 16T15)	$[2, 10]$
16.0.173030739841843453515625.1	x^16 - 6x^15 + 31x^14 - 89x^13 + 211x^12 - 330x^11 + 382x^10 - 219x^9 - 49x^8 + 183x^7 - 132x^6 + 10x^5 + 41x^4 - 27x^3 + 14x^2 - 2x + 1	\( 5^{8}\cdot 29^{8}\cdot 941^{2} \)	16T1439	$[20]$
16.0.173030739841843453515625.2	x^16 - 2x^15 + 10x^14 - 24x^13 + 57x^12 - 74x^11 + 170x^10 + 95x^9 + 542x^8 + 626x^7 + 2311x^6 - 4x^5 + 5166x^4 - 985x^3 + 3100x^2 - 375x + 625	\( 5^{8}\cdot 29^{8}\cdot 941^{2} \)	$C_2^4.C_2^3$ (as 16T364)	$[20]$ (GRH)
16.0.191958112137556655079424.1	x^16 - 4x^15 + 16x^14 - 52x^13 + 143x^12 - 316x^11 + 724x^10 - 1252x^9 + 2239x^8 - 3192x^7 + 4490x^6 - 4468x^5 + 5011x^4 - 2840x^3 + 1800x^2 - 932x + 3929	\( 2^{32}\cdot 41^{6}\cdot 97^{2} \)	16T876	$[24]$ (GRH)
16.0.193497104236838597191936.1	x^16 - 3x^15 + 13x^14 - 46x^13 + 117x^12 - 272x^11 + 625x^10 - 1107x^9 + 1821x^8 - 2943x^7 + 4178x^6 - 5032x^5 + 7019x^4 - 8546x^3 + 8581x^2 - 6446x + 3571	\( 2^{8}\cdot 17^{14}\cdot 67^{2} \)	16T817	$[2, 10]$ (GRH)
16.0.196571825135013064605696.1	x^16 - 49x^12 + 2145x^8 - 12544x^4 + 65536	\( 2^{32}\cdot 3^{8}\cdot 17^{8} \)	$C_2^4$ (as 16T3)	$[4, 4]$ (GRH)
16.0.203928109056000000000000.1	x^16 + 8x^14 - 4x^13 + 77x^12 - 224x^11 + 816x^10 - 2152x^9 + 5580x^8 - 10592x^7 + 18568x^6 - 26792x^5 + 32902x^4 - 31104x^3 + 21608x^2 - 8692x + 1681	\( 2^{32}\cdot 3^{4}\cdot 5^{12}\cdot 7^{4} \)	$C_2^3:(C_2\times C_4)$ (as 16T68)	$[2, 6]$ (GRH)
16.0.214134588691231230918656.1	x^16 + 28x^14 + 234x^12 + 876x^10 + 1695x^8 + 1804x^6 + 1066x^4 + 328x^2 + 41	\( 2^{40}\cdot 41^{7} \)	$C_4.D_4:C_4$ (as 16T289)	$[3, 6]$
16.0.229607785695641627262976.1	x^16 + 799x^8 + 6561	\( 2^{48}\cdot 13^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[15]$ (GRH)
16.0.250516897691366976454656.1	x^16 - 13x^14 + 129x^12 - 494x^10 + 1430x^8 - 494x^6 + 129x^4 - 13x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 17^{12} \)	$C_4\times C_2^2$ (as 16T2)	$[20]$ (GRH)
16.0.256992219136000000000000.1	x^16 - 6x^15 + 37x^14 - 128x^13 + 398x^12 - 798x^11 + 1482x^10 - 1784x^9 + 2635x^8 - 2088x^7 + 2818x^6 - 448x^5 + 1016x^4 + 112x^3 + 128x^2 + 16	\( 2^{24}\cdot 5^{12}\cdot 89^{4} \)	$C_2^4.C_2^3$ (as 16T210)	$[14]$ (GRH)
16.0.271737008656000000000000.1	x^16 + 9x^14 + 56x^12 + 279x^10 + 1111x^8 + 6975x^6 + 35000x^4 + 140625x^2 + 390625	\( 2^{16}\cdot 5^{12}\cdot 19^{8} \)	$C_4\times C_2^2$ (as 16T2)	$[2, 8]$ (GRH)
16.0.275347695997472397262848.1	x^16 + 15x^14 + 90x^12 + 277x^10 + 467x^8 + 428x^6 + 200x^4 + 42x^2 + 3	\( 2^{16}\cdot 3^{3}\cdot 19^{4}\cdot 103^{6} \)	16T1879	$[12]$
16.0.287742083309962730143744.3	x^16 - 8x^15 + 32x^14 - 60x^13 - 25x^12 + 384x^11 - 782x^10 + 404x^9 + 1454x^8 - 3616x^7 + 4320x^6 - 2128x^5 - 1220x^4 + 2368x^3 - 184x^2 - 368x + 104	\( 2^{34}\cdot 7^{4}\cdot 17^{8} \)	$C_2\times D_4:D_4$ (as 16T265)	$[2, 6]$ (GRH)
16.0.304624482715110400000000.1	x^16 + 17x^14 + 119x^12 + 444x^10 + 953x^8 + 1180x^6 + 793x^4 + 243x^2 + 19	\( 2^{16}\cdot 5^{8}\cdot 19\cdot 29^{4}\cdot 941^{2} \)	16T1823	$[22]$ (GRH)
16.0.320157704295040000000000.1	x^16 + 27x^14 + 265x^12 + 1179x^10 + 2564x^8 + 2865x^6 + 1615x^4 + 400x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{8} \)	$C_4\wr C_2$ (as 16T42)	$[2, 10]$ (GRH)
16.0.330123790096000000000000.1	x^16 + 2x^14 - 2x^13 + 67x^12 - 108x^11 + 574x^10 - 596x^9 + 2115x^8 - 1864x^7 + 3302x^6 - 2816x^5 + 2647x^4 - 1528x^3 + 522x^2 - 36x + 1	\( 2^{16}\cdot 5^{12}\cdot 379^{4} \)	16T1027	$[2, 6]$ (GRH)
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)
16.0.349384945136768000000000.1	x^16 + 19x^14 + 137x^12 + 489x^10 + 937x^8 + 962x^6 + 486x^4 + 95x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 1652141^{2} \)	16T1885	$[16]$
16.0.349384945136768000000000.2	x^16 + 17x^14 + 108x^12 + 338x^10 + 572x^8 + 531x^6 + 259x^4 + 60x^2 + 5	\( 2^{16}\cdot 5^{9}\cdot 1652141^{2} \)	16T1885	$[16]$
16.0.359634524805529600000000.1	x^16 - 8x^15 + 52x^14 - 224x^13 + 840x^12 - 2492x^11 + 6314x^10 - 13112x^9 + 22557x^8 - 31532x^7 + 34622x^6 - 28952x^5 + 19586x^4 - 11256x^3 + 12652x^2 - 9048x + 14436	\( 2^{32}\cdot 5^{8}\cdot 11^{8} \)	$C_2^4$ (as 16T3)	$[12]$ (GRH)
16.0.383854225736338134765625.1	x^16 - x^15 - 2x^14 + 56x^12 + 45x^11 + 92x^10 - 262x^9 - 19x^8 - 280x^7 + 950x^6 + 375x^5 + 700x^4 - 750x^3 + 625x + 625	\( 5^{12}\cdot 11^{6}\cdot 31^{6} \)	$(C_2\times C_8):C_2^2$ (as 16T75)	$[4, 4]$ (GRH)
16.0.385172627945073865129984.3	x^16 + 24x^14 + 212x^12 + 1024x^10 + 3046x^8 + 5760x^6 + 6728x^4 + 4352x^2 + 1156	\( 2^{62}\cdot 17^{4} \)	$C_2^5.C_2.C_2$ (as 16T257)	$[20]$ (GRH)
16.0.388353313582361600000000.1	x^16 + 19x^14 + 144x^12 + 552x^10 + 1122x^8 + 1176x^6 + 611x^4 + 143x^2 + 11	\( 2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 106759^{2} \)	16T1905	$[18]$
16.0.400821687783040000000000.1	x^16 + 21x^14 + 165x^12 + 628x^10 + 1289x^8 + 1465x^6 + 885x^4 + 250x^2 + 25	\( 2^{16}\cdot 5^{10}\cdot 29^{4}\cdot 941^{2} \)	16T1559	$[20]$
16.0.434911971099673600000000.2	x^16 + 17x^14 + 111x^12 + 356x^10 + 588x^8 + 472x^6 + 154x^4 + 21x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{4}\cdot 29^{6} \)	$C_2^4.C_2^3.C_2$ (as 16T500)	$[16]$ (GRH)
16.0.446012924483368791310336.1	x^16 - 2x^14 + 21x^12 - 50x^10 + 356x^8 + 362x^6 + 1893x^4 + 1274x^2 + 2401	\( 2^{24}\cdot 113^{8} \)	$C_2^2.SD_{16}$ (as 16T163)	$[15]$ (GRH)
16.0.451240001536000000000000.1	x^16 - 4x^15 + 8x^14 - 8x^13 + 38x^12 - 120x^11 + 344x^10 - 664x^9 + 1278x^8 - 1952x^7 + 2736x^6 - 2584x^5 + 2668x^4 - 2064x^3 + 1712x^2 - 704x + 796	\( 2^{40}\cdot 5^{12}\cdot 41^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	$[2, 8]$ (GRH)
16.0.457298012663983220674816.1	x^16 - 5x^15 + 24x^14 - 59x^13 + 128x^12 - 102x^11 + 61x^10 + 320x^9 + 134x^8 - 557x^7 + 2836x^6 - 1360x^5 + 1821x^4 + 4202x^3 + 760x^2 - 654x + 8363	\( 2^{8}\cdot 17^{14}\cdot 103^{2} \)	16T817	$[2, 16]$ (GRH)
16.0.463351970115520828515625.2	x^16 - 5x^15 + 21x^14 - 63x^13 + 125x^12 - 218x^11 + 387x^10 - 336x^9 + 1134x^8 - 314x^7 - 447x^6 - 2461x^5 - 689x^4 + 2225x^3 + 2865x^2 + 1700x + 475	\( 5^{8}\cdot 29^{4}\cdot 109^{6} \)	$C_2^4.C_2^3$ (as 16T392)	$[12]$ (GRH)
16.0.465628562522393600000000.1	x^16 + 17x^14 + 113x^12 + 382x^10 + 713x^8 + 742x^6 + 412x^4 + 110x^2 + 11	\( 2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 29^{4}\cdot 139^{2} \)	16T1823	$[2, 10]$ (GRH)
16.0.478584585616890104119296.1	x^16 - 31x^12 + 336x^8 - 19375x^4 + 390625	\( 2^{32}\cdot 3^{8}\cdot 19^{8} \)	$C_2^4$ (as 16T3)	$[12]$ (GRH)
16.0.490875290811165073997824.1	x^16 + 24x^14 + 224x^12 + 1044x^10 + 2629x^8 + 3612x^6 + 2536x^4 + 712x^2 + 4	\( 2^{46}\cdot 17^{8} \)	$C_2^2.D_4$ (as 16T33)	$[2, 2, 4]$ (GRH)
16.0.490875290811165073997824.3	x^16 - 4x^14 - 2x^12 - 76x^10 + 402x^8 - 476x^6 + 1438x^4 - 980x^2 + 2401	\( 2^{46}\cdot 17^{8} \)	$C_2\times C_2^2.D_4$ (as 16T92)	$[2, 2, 4]$ (GRH)

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