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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.5575888916015625.1	x^16 - 5x^15 + 15x^14 - 30x^13 + 49x^12 - 70x^11 + 90x^10 - 105x^9 + 111x^8 - 105x^7 + 90x^6 - 70x^5 + 49x^4 - 30x^3 + 15x^2 - 5x + 1	\( 3^{8}\cdot 5^{12}\cdot 59^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.5960322509765625.1	x^16 - 5x^15 + 11x^14 - 10x^13 - 10x^12 + 45x^11 - 56x^10 - 10x^9 + 159x^8 - 315x^7 + 374x^6 - 300x^5 + 160x^4 - 50x^3 + 6x^2 + 1	\( 3^{8}\cdot 5^{12}\cdot 61^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.26896000000000000.1	x^16 - 6x^15 + 16x^14 - 24x^13 + 21x^12 - 12x^11 + 28x^10 - 102x^9 + 232x^8 - 354x^7 + 392x^6 - 326x^5 + 206x^4 - 98x^3 + 34x^2 - 8x + 1	\( 2^{16}\cdot 5^{12}\cdot 41^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.38483404541015625.1	x^16 - 8x^15 + 26x^14 - 37x^13 - 4x^12 + 96x^11 - 126x^10 - 26x^9 + 312x^8 - 541x^7 + 579x^6 - 444x^5 + 256x^4 - 112x^3 + 36x^2 - 8x + 1	\( 3^{8}\cdot 5^{14}\cdot 31^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.52476787353515625.1	x^16 - 7x^15 + 23x^14 - 45x^13 + 60x^12 - 68x^11 + 89x^10 - 130x^9 + 164x^8 - 160x^7 + 116x^6 - 61x^5 + 25x^4 - 10x^3 + 2x^2 + x + 1	\( 3^{8}\cdot 5^{12}\cdot 181^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.67315924072265625.1	x^16 - x^15 - x^14 + 4x^13 + x^12 - 8x^11 + 11x^10 + 7x^9 - 13x^8 + 13x^7 + 11x^6 - 7x^5 + 6x^4 + 6x^3 - x^2 + x + 1	\( 3^{8}\cdot 5^{14}\cdot 41^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.163216000000000000.1	x^16 - x^14 + 5x^12 + x^10 + 9x^8 + 11x^6 + 10x^4 + 4x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 101^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.889042730712890625.1	x^16 - x^15 + x^14 - 14x^13 + 13x^12 + 34x^11 - 41x^10 + 3x^9 - 37x^8 + 9x^7 + 126x^6 - 82x^5 - 57x^4 + 38x^3 + 9x^2 - 2x + 1	\( 3^{8}\cdot 5^{14}\cdot 149^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.1669788916259765625.1	x^16 + 16x^14 + 90x^12 + 239x^10 + 329x^8 + 239x^6 + 90x^4 + 16x^2 + 1	\( 3^{8}\cdot 5^{12}\cdot 1021^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.20106256000000000000.1	x^16 - 8x^15 + 27x^14 - 46x^13 + 28x^12 + 36x^11 - 66x^10 - 28x^9 + 153x^8 - 56x^7 - 264x^6 + 288x^5 + 448x^4 - 1472x^3 + 1728x^2 - 1024x + 256	\( 2^{16}\cdot 5^{12}\cdot 19^{2}\cdot 59^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.12.365421456000000000000.2	x^16 - 2x^14 - 5x^12 - 7x^10 + 69x^8 - 98x^6 + 55x^4 - 13x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.4.365421456000000000000.2	x^16 - 6x^12 - 15x^10 - 19x^8 - 15x^6 - 6x^4 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 59^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.8.390615696000000000000.1	x^16 - 5x^14 + 9x^12 - 20x^10 + 36x^8 - 50x^6 + 44x^4 - 15x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 61^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.12.671846400000000000000.1	x^16 - 2x^15 - 16x^14 + 8x^13 + 113x^12 + 108x^11 - 294x^10 - 776x^9 - 297x^8 + 1148x^7 + 1764x^6 + 894x^5 + 13x^4 - 124x^3 - 24x^2 + 4x + 1	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.4.671846400000000000000.1	x^16 - 2x^15 + 4x^14 - 12x^13 + 28x^12 - 12x^11 - 104x^10 + 204x^9 - 192x^8 - 302x^7 + 284x^6 - 136x^5 - 737x^4 - 794x^3 - 664x^2 - 326x - 59	\( 2^{24}\cdot 3^{8}\cdot 5^{14} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.1007681536000000000000.1	x^16 + 12x^14 + 70x^12 + 222x^10 + 399x^8 + 378x^6 + 170x^4 + 18x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 31^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.0.1007681536000000000000.2	x^16 + 6x^14 + 25x^12 + 74x^10 + 194x^8 + 374x^6 + 500x^4 + 386x^2 + 121	\( 2^{32}\cdot 5^{12}\cdot 31^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial
16.8.1762656256000000000000.3	x^16 - 8x^14 + 35x^12 - 88x^10 + 109x^8 - 72x^6 + 35x^4 - 12x^2 + 1	\( 2^{32}\cdot 5^{12}\cdot 41^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.8.3439118736000000000000.1	x^16 - 10x^14 + 39x^12 - 95x^10 + 161x^8 - 110x^6 - 21x^4 - 25x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 5^{12}\cdot 181^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.0.171144380416000000000000.1	x^16 + 12x^14 + 70x^12 + 252x^10 + 579x^8 + 708x^6 + 1890x^4 + 2128x^2 + 1681	\( 2^{36}\cdot 5^{12}\cdot 101^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	$[10]$ (GRH)
16.16.171144380416000000000000.1	x^16 - 24x^14 + 220x^12 - 976x^10 + 2204x^8 - 2416x^6 + 1120x^4 - 224x^2 + 16	\( 2^{36}\cdot 5^{12}\cdot 101^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)
16.8.171144380416000000000000.1	x^16 - 8x^14 - 6x^12 + 8x^10 + 291x^8 - 480x^6 + 290x^4 - 600x^2 + 25	\( 2^{36}\cdot 5^{12}\cdot 101^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (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)
16.16.451240001536000000000000.1	x^16 - 4x^15 - 16x^14 + 76x^13 + 44x^12 - 416x^11 + 108x^10 + 888x^9 - 509x^8 - 800x^7 + 628x^6 + 248x^5 - 296x^4 + 20x^3 + 40x^2 - 12x + 1	\( 2^{40}\cdot 5^{12}\cdot 41^{2} \)	$C_2\times C_2\wr C_4$ (as 16T261)	Trivial (GRH)