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 all 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.394070062500000000.1	x^16 - 6x^15 + 23x^14 - 64x^13 + 127x^12 - 184x^11 + 198x^10 - 146x^9 + 69x^8 - 46x^6 + 22x^5 - 2x^4 + 10x^3 + 20x^2 + 8x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2} \)	16T1102	Trivial
16.0.394070062500000000.2	x^16 - 4x^15 + 7x^14 + 2x^13 - 20x^12 + 6x^11 + 123x^10 - 357x^9 + 570x^8 - 573x^7 + 389x^6 - 153x^5 + 29x^4 + 11x^3 - 4x^2 + 3x + 1	\( 2^{8}\cdot 3^{8}\cdot 5^{12}\cdot 31^{2} \)	16T1102	Trivial
16.12.365421456000000000000.1	x^16 - 2x^15 - 10x^14 + 32x^13 + 4x^12 - 146x^11 + 189x^10 + 144x^9 - 439x^8 + 152x^7 + 251x^6 - 202x^5 - 16x^4 + 56x^3 - 10x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.4.365421456000000000000.1	x^16 - 8x^15 + 34x^14 - 90x^13 + 167x^12 - 224x^11 + 224x^10 - 168x^9 + 67x^8 + 100x^7 - 349x^6 + 602x^5 - 675x^4 + 482x^3 - 189x^2 + 26x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial
16.8.365421456000000000000.1	x^16 - 2x^15 - 5x^14 + 22x^12 + 6x^11 + 60x^10 - 170x^9 - 41x^8 + 108x^7 + 132x^6 - 78x^5 - 42x^4 + 8x^3 - 7x^2 + 8x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial
16.8.365421456000000000000.2	x^16 - 8x^15 + 22x^14 - 14x^13 - 56x^12 + 154x^11 - 156x^10 - 12x^9 + 223x^8 - 270x^7 + 130x^6 + 30x^5 - 73x^4 + 34x^3 - x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial
16.12.390615696000000000000.1	x^16 - 3x^14 - 4x^13 - 27x^12 + 34x^11 + 85x^10 + 10x^9 - 79x^8 - 324x^7 + 335x^6 + 268x^5 - 490x^4 + 230x^3 - 32x^2 - 4x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2} \)	16T1102	Trivial (GRH)
16.4.390615696000000000000.1	x^16 - 8x^15 + 33x^14 - 84x^13 + 140x^12 - 138x^11 + 22x^10 + 184x^9 - 370x^8 + 424x^7 - 339x^6 + 246x^5 - 216x^4 + 172x^3 - 81x^2 + 14x + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2} \)	16T1102	Trivial
16.12.6879707136000000000000.1	x^16 - 8x^14 + 20x^12 - 8x^10 - 36x^8 + 48x^6 - 15x^4 - 2x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{12} \)	16T1102	Trivial (GRH)
16.4.6879707136000000000000.1	x^16 + 8x^14 + 20x^12 + 8x^10 - 36x^8 - 48x^6 - 15x^4 + 2x^2 + 1	\( 2^{32}\cdot 3^{8}\cdot 5^{12} \)	16T1102	Trivial
16.8.85977968400000000000000.1	x^16 - 8x^15 + 40x^14 - 140x^13 + 330x^12 - 524x^11 + 412x^10 + 360x^9 - 1395x^8 + 1660x^7 - 628x^6 - 836x^5 + 960x^4 - 80x^3 - 200x^2 + 48x + 16	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 181^{2} \)	16T1102	Trivial (GRH)
16.8.85977968400000000000000.2	x^16 - 2x^15 - 5x^14 + 20x^13 - 60x^12 - 16x^11 + 307x^10 - 170x^9 + 105x^8 + 40x^7 - 613x^6 + 486x^5 + 1010x^4 - 1090x^3 - 565x^2 + 432x - 59	\( 2^{16}\cdot 3^{8}\cdot 5^{14}\cdot 181^{2} \)	16T1102	Trivial (GRH)
16.0.832444563456000000000000.1	x^16 + 16x^14 + 132x^12 + 808x^10 + 3540x^8 + 9052x^6 + 10097x^4 + 1254x^2 + 121	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T1102	$[2]$
16.0.832444563456000000000000.2	x^16 + 18x^14 + 125x^12 + 428x^10 + 789x^8 + 842x^6 + 615x^4 + 242x^2 + 121	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 11^{2} \)	16T1102	$[2]$
16.12.1453481004816000000000000.1	x^16 - 4x^15 - 11x^14 + 42x^13 + 82x^12 - 150x^11 - 517x^10 + 134x^9 + 1859x^8 + 576x^7 - 3026x^6 - 2156x^5 + 1548x^4 + 2918x^3 + 364x^2 - 1360x - 239	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{4} \)	16T1102	Trivial (GRH)
16.4.1453481004816000000000000.1	x^16 - 2x^15 + 5x^14 + 20x^13 - 37x^12 + 142x^11 - 61x^10 + 140x^9 + 649x^8 - 526x^7 + 1863x^6 - 2014x^5 + 1472x^4 - 1684x^3 - 3832x^2 + 2724x - 4799	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{4} \)	16T1102	$[2]$
16.0.23948260540416000000000000.1	x^16 + 32x^14 + 390x^12 + 2472x^10 + 9054x^8 + 19658x^6 + 24455x^4 + 15458x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	$[2, 122]$ (GRH)
16.12.23948260540416000000000000.1	x^16 - 14x^14 + 15x^12 + 354x^10 - 1266x^8 + 124x^6 + 5270x^4 - 8024x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.16.23948260540416000000000000.1	x^16 - 36x^14 + 527x^12 - 4038x^10 + 17390x^8 - 42102x^6 + 53962x^4 - 30444x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.4.23948260540416000000000000.1	x^16 + 14x^14 - 23x^12 - 738x^10 - 1910x^8 + 2848x^6 + 14562x^4 + 13806x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	$[2]$ (GRH)
16.8.23948260540416000000000000.1	x^16 - 6x^14 - 70x^12 + 366x^10 + 1094x^8 - 3954x^6 - 2015x^4 + 5664x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.0.23948260540416000000000000.2	x^16 + 36x^14 + 527x^12 + 4038x^10 + 17390x^8 + 42102x^6 + 53962x^4 + 30444x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	$[2, 106]$ (GRH)
16.12.23948260540416000000000000.2	x^16 - 32x^14 + 393x^12 - 2214x^10 + 4395x^8 + 9256x^6 - 52837x^4 + 60298x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.16.23948260540416000000000000.2	x^16 - 32x^14 + 390x^12 - 2472x^10 + 9054x^8 - 19658x^6 + 24455x^4 - 15458x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.4.23948260540416000000000000.2	x^16 + 28x^14 + 265x^12 + 918x^10 + 334x^8 - 4018x^6 - 5670x^4 + 1062x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	$[2]$ (GRH)
16.8.23948260540416000000000000.2	x^16 + 16x^14 + 35x^12 - 356x^10 - 756x^8 + 2994x^6 + 2820x^4 - 9794x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.8.23948260540416000000000000.3	x^16 - 6x^14 - 80x^12 + 186x^10 + 1469x^8 - 1374x^6 - 7660x^4 - 1416x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.8.23948260540416000000000000.4	x^16 + 6x^14 - 75x^12 - 506x^10 + 514x^8 + 4164x^6 - 5870x^4 - 1534x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.8.23948260540416000000000000.5	x^16 + 12x^14 - 90x^12 - 1048x^10 + 694x^8 + 14958x^6 - 4385x^4 - 35282x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.8.23948260540416000000000000.6	x^16 - 14x^14 - 53x^12 + 1128x^10 - 365x^8 - 15838x^6 - 12183x^4 + 19824x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.8.23948260540416000000000000.7	x^16 - 14x^14 - 13x^12 + 838x^10 - 2610x^8 - 3948x^6 + 13062x^4 + 17464x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)
16.8.23948260540416000000000000.8	x^16 - 18x^14 - 22x^12 + 1134x^10 + 1190x^8 - 12786x^6 - 24167x^4 - 7788x^2 + 3481	\( 2^{32}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	16T1102	Trivial (GRH)