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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.24109135612084224.1	x^16 - 4x^15 + 10x^14 - 22x^13 + 44x^12 - 82x^11 + 136x^10 - 200x^9 + 259x^8 - 282x^7 + 256x^6 - 192x^5 + 118x^4 - 58x^3 + 22x^2 - 6x + 1	\( 2^{28}\cdot 3^{12}\cdot 13^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial
16.0.38430445773775104.1	x^16 - 7x^15 + 25x^14 - 59x^13 + 95x^12 - 94x^11 + 35x^10 + 25x^9 - 14x^8 - 26x^7 + 11x^6 + 26x^5 - 13x^4 - 14x^3 + 4x^2 + 5x + 1	\( 2^{8}\cdot 3^{12}\cdot 7^{10} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial
16.4.50024641296100000000.1	x^16 - 7x^14 - 5x^12 - x^10 + 8x^8 - x^6 - 5x^4 - 7x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.8.2321651418902203515625.1	x^16 - 2x^15 - 8x^14 + 5x^13 - 14x^12 + 68x^11 - 9x^10 - 7x^9 - 32x^8 - 173x^7 + 51x^6 + 151x^5 + 82x^4 - 38x^3 - 58x^2 - 17x - 1	\( 5^{8}\cdot 29^{8}\cdot 109^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.0.2426812655987815612416.1	x^16 - 8x^15 + 24x^14 - 16x^13 - 91x^12 + 268x^11 - 204x^10 - 408x^9 + 1130x^8 - 816x^7 - 816x^6 + 2144x^5 - 1456x^4 - 512x^3 + 1536x^2 - 1024x + 256	\( 2^{32}\cdot 3^{4}\cdot 17^{8} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial
16.0.2426812655987815612416.2	x^16 + 4x^14 - 16x^13 + 24x^12 - 60x^11 + 144x^10 - 252x^9 + 430x^8 - 604x^7 + 902x^6 - 1332x^5 + 1385x^4 - 1152x^3 + 1116x^2 - 944x + 356	\( 2^{32}\cdot 3^{4}\cdot 17^{8} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial
16.4.3775492556570109765625.1	x^16 - 2x^14 - 9x^12 - 27x^10 - 81x^8 - 252x^6 + 6x^4 - 37x^2 + 1	\( 5^{8}\cdot 29^{8}\cdot 139^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.8.4338269771151234765625.1	x^16 - 4x^15 - 5x^14 + 31x^13 - 9x^12 - 61x^11 + 77x^10 - 5x^9 - 107x^8 + 115x^7 + 133x^6 - 93x^5 - 39x^4 + 7x^3 - 15x^2 - 2x + 1	\( 5^{8}\cdot 29^{8}\cdot 149^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.12.12806308171801600000000.1	x^16 - 5x^14 - 12x^12 + 85x^10 - 97x^8 + 5x^6 + 38x^4 - 15x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{8} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.12.14453792694473893871616.1	x^16 - 14x^14 - 6x^13 + 56x^12 + 102x^11 - 116x^10 - 228x^9 - 212x^8 + 102x^7 + 968x^6 + 186x^5 - 919x^4 - 252x^3 + 248x^2 + 96x + 4	\( 2^{20}\cdot 3^{12}\cdot 11^{10} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.0.14832394327221826748416.1	x^16 - 6x^15 + 19x^14 - 46x^13 + 89x^12 - 172x^11 + 506x^10 - 1480x^9 + 3757x^8 - 7354x^7 + 11715x^6 - 14394x^5 + 14093x^4 - 10292x^3 + 5788x^2 - 1904x + 392	\( 2^{28}\cdot 17^{8}\cdot 89^{2} \)	$C_2^4.C_2^3$ (as 16T364)	$[2]$
16.0.66183076013297341825024.1	x^16 - 10x^14 + 57x^12 - 174x^10 + 288x^8 + 102x^6 + 393x^4 - 686x^2 + 2401	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	$C_2^4.C_2^3$ (as 16T364)	$[2]$
16.0.66183076013297341825024.2	x^16 - 2x^15 + 9x^14 - 4x^13 + 24x^12 + 8x^11 + 192x^10 - 384x^9 + 1460x^8 - 1368x^7 + 2548x^6 - 272x^5 + 3088x^4 + 544x^3 + 1168x^2 - 64x + 64	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.0.66183076013297341825024.3	x^16 + 6x^14 + x^12 + 26x^10 + 32x^8 + 78x^6 + 481x^4 + 50x^2 + 1	\( 2^{32}\cdot 17^{8}\cdot 47^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial
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)
16.8.199287737842427385348096.1	x^16 - 12x^14 + 36x^12 - 108x^10 + 954x^8 - 1836x^6 + 324x^4 - 972x^2 + 81	\( 2^{46}\cdot 3^{12}\cdot 73^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.16.797150951369709541392384.1	x^16 - 32x^14 - 16x^13 + 316x^12 + 288x^11 - 1196x^10 - 1608x^9 + 1402x^8 + 3016x^7 + 304x^6 - 1792x^5 - 1000x^4 - 16x^3 + 88x^2 + 8x - 2	\( 2^{48}\cdot 3^{12}\cdot 73^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.8.966526094481948100000000.1	x^16 - x^14 + 40x^12 - 337x^10 + 981x^8 - 1812x^6 + 2664x^4 - 1920x^2 + 400	\( 2^{8}\cdot 5^{8}\cdot 29^{8}\cdot 139^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.0.1058929216212757469200384.1	x^16 - 12x^14 + 76x^12 - 328x^10 + 776x^8 + 240x^6 + 1072x^4 - 17248x^2 + 38416	\( 2^{36}\cdot 17^{8}\cdot 47^{2} \)	$C_2^4.C_2^3$ (as 16T364)	$[2, 2]$ (GRH)
16.0.1058929216212757469200384.2	x^16 - 24x^13 + 13x^12 + 160x^10 - 112x^9 + 88x^8 - 1280x^7 + 800x^6 + 128x^5 + 16420x^4 - 14336x^3 + 8704x^2 - 1280x + 64	\( 2^{36}\cdot 17^{8}\cdot 47^{2} \)	$C_2^4.C_2^3$ (as 16T364)	$[2]$ (GRH)
16.16.2944392860546173636706304.1	x^16 - 30x^14 - 18x^13 + 298x^12 + 258x^11 - 1254x^10 - 1188x^9 + 2427x^8 + 2322x^7 - 2058x^6 - 1908x^5 + 622x^4 + 498x^3 - 60x^2 - 18x + 1	\( 2^{20}\cdot 3^{12}\cdot 11^{8}\cdot 157^{2} \)	$C_2^4.C_2^3$ (as 16T364)	Trivial (GRH)
16.0.14800683719141267324534784.1	x^16 + 34x^14 + 412x^12 + 2344x^10 + 6865x^8 + 10714x^6 + 8734x^4 + 3388x^2 + 484	\( 2^{30}\cdot 3^{12}\cdot 11^{10} \)	$C_2^4.C_2^3$ (as 16T364)	$[2, 4, 8]$ (GRH)