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 34 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.3006123291015625.1	x^16 - x^15 - 3x^14 + 6x^13 + x^12 - 10x^11 + 8x^10 + 5x^9 - 13x^8 + 5x^7 + 8x^6 - 10x^5 + x^4 + 6x^3 - 3x^2 - x + 1	\( 5^{12}\cdot 11^{4}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.12442705322265625.1	x^16 - 3x^15 + 3x^14 + 3x^13 - 12x^12 + 17x^11 - 11x^10 - 6x^9 + 23x^8 - 28x^7 + 21x^6 - 10x^5 + 3x^4 - x^3 + 2x^2 - 2x + 1	\( 5^{12}\cdot 11^{4}\cdot 59^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.15376000000000000.1	x^16 - 6x^15 + 19x^14 - 44x^13 + 81x^12 - 128x^11 + 181x^10 - 224x^9 + 246x^8 - 244x^7 + 215x^6 - 166x^5 + 107x^4 - 52x^3 + 20x^2 - 6x + 1	\( 2^{16}\cdot 5^{12}\cdot 31^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.20893799072265625.1	x^16 - 2x^15 + 3x^14 - x^13 - 3x^12 + 5x^11 - 3x^10 - 2x^9 + 5x^8 - 2x^7 - 3x^6 + 5x^5 - 3x^4 - x^3 + 3x^2 - 2x + 1	\( 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.26757802978515625.1	x^16 - 2x^15 + x^14 + 3x^13 - 6x^12 + 7x^11 - 3x^10 - 6x^9 + 13x^8 - 8x^7 - 2x^6 + 4x^5 - x^4 - x^3 - x^2 + x + 1	\( 5^{12}\cdot 19^{4}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.62336045166015625.1	x^16 - x^15 - 2x^14 + 4x^13 + 2x^12 - 5x^11 + 2x^10 + 2x^9 - 5x^8 + 2x^7 + 2x^6 - 5x^5 + 2x^4 + 4x^3 - 2x^2 - x + 1	\( 5^{12}\cdot 19^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.290268398681640625.1	x^16 - 3x^15 + 4x^14 - 8x^13 + 16x^12 - 21x^11 + 27x^10 - 39x^9 + 52x^8 - 47x^7 + 23x^6 - 12x^5 + 16x^4 - 19x^3 + 16x^2 - 6x + 1	\( 5^{12}\cdot 29^{4}\cdot 41^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.580191650634765625.1	x^16 - 3x^15 + x^14 + 4x^13 - 13x^11 + 10x^10 + 20x^9 - 19x^8 - 20x^7 + 10x^6 + 13x^5 - 4x^3 + x^2 + 3x + 1	\( 5^{12}\cdot 29^{2}\cdot 41^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.1761468135009765625.1	x^16 + 2x^14 + 15x^12 + 17x^10 + 59x^8 + 28x^6 + 50x^4 + 3x^2 + 1	\( 5^{12}\cdot 29^{4}\cdot 101^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.3833580439697265625.1	x^16 - 2x^15 + 6x^14 - 13x^13 + 23x^12 - 24x^11 + 26x^10 - 14x^9 + 6x^8 + 4x^7 + x^6 + 10x^4 + 2x^3 + 2x^2 + 2x + 1	\( 5^{12}\cdot 29^{4}\cdot 149^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.4.3936256000000000000.1	x^16 - 2x^15 - 2x^14 - 6x^13 + 12x^12 + 30x^11 + 2x^10 - 22x^9 - 90x^8 - 22x^7 + 2x^6 + 30x^5 + 12x^4 - 6x^3 - 2x^2 - 2x + 1	\( 2^{24}\cdot 5^{12}\cdot 31^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.4.3936256000000000000.2	x^16 - 4x^15 + 4x^14 - 10x^13 + 36x^12 - 32x^11 + 20x^10 - 98x^9 + 102x^8 + 6x^7 + 40x^6 - 94x^5 + x^4 + 30x^3 - 4x^2 + 2x + 1	\( 2^{24}\cdot 5^{12}\cdot 31^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial
16.0.19723174912353515625.1	x^16 - 4x^15 + 9x^14 - 10x^13 + 6x^12 - 2x^11 + 100x^10 - 198x^9 + 112x^8 + 131x^7 - 164x^5 + 111x^4 + 80x^3 + 31x^2 + 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{4}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$
16.8.19723174912353515625.1	x^16 - x^15 - 12x^14 + 6x^13 + 62x^12 + x^11 - 167x^10 - 81x^9 + 214x^8 + 205x^7 - 56x^6 - 148x^5 - 87x^4 - 30x^3 + 15x^2 + 18x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{4}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.0.44012651103759765625.1	x^16 - x^15 + 4x^14 + x^12 + 7x^11 + 25x^10 + 3x^9 + 107x^8 - 6x^7 + 100x^6 - 56x^5 + 16x^4 + 256x^2 + 128x + 256	\( 5^{12}\cdot 11^{8}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$
16.8.44012651103759765625.1	x^16 - x^15 - 6x^14 + 16x^13 + 11x^12 - 58x^11 + 11x^10 + 31x^9 - 79x^8 + 131x^7 + 140x^6 - 156x^5 - 118x^4 + 18x^3 + 30x^2 + 9x + 1	\( 5^{12}\cdot 11^{8}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.0.59904939404541015625.1	x^16 - 2x^15 + 9x^14 - 22x^13 + 55x^12 - 70x^11 + 155x^10 - 131x^9 + 212x^8 - 119x^7 + 187x^6 - 245x^5 + 332x^4 - 214x^3 + 119x^2 - 17x + 1	\( 5^{12}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$
16.12.137084215713134765625.1	x^16 - 3x^15 - 10x^14 + 34x^13 + 35x^12 - 142x^11 - 56x^10 + 268x^9 + 66x^8 - 218x^7 - 88x^6 + 32x^5 + 68x^4 + 33x^3 - 16x^2 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.4.137084215713134765625.1	x^16 - 3x^15 + 8x^14 - 24x^13 + 47x^12 - 90x^11 + 117x^10 - 233x^9 + 200x^8 - 278x^7 + 327x^6 - 250x^5 + 407x^4 + 166x^3 + 18x^2 + 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.0.152901339638916015625.2	x^16 - 3x^15 + 7x^14 - 7x^13 + 17x^12 + 48x^10 + 24x^9 + 65x^8 - 24x^7 + 48x^6 + 17x^4 + 7x^3 + 7x^2 + 3x + 1	\( 5^{12}\cdot 29^{4}\cdot 941^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$
16.0.1369296016000000000000.1	x^16 - 9x^14 + 55x^12 - 201x^10 + 464x^8 - 651x^6 + 625x^4 - 374x^2 + 121	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$
16.4.1369296016000000000000.1	x^16 + 5x^14 + 20x^12 + 25x^10 - 25x^8 - 500x^6 - 750x^4 + 625	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.0.1369296016000000000000.2	x^16 + 9x^14 + 55x^12 + 201x^10 + 464x^8 + 651x^6 + 625x^4 + 374x^2 + 121	\( 2^{16}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$
16.12.4085255056000000000000.1	x^16 - 11x^14 + 50x^12 - 129x^10 + 204x^8 - 179x^6 + 80x^4 - 16x^2 + 1	\( 2^{16}\cdot 5^{12}\cdot 19^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.8.4215622865029541015625.1	x^16 - 8x^14 + 40x^12 - 193x^10 + 504x^8 - 1847x^6 + 4390x^4 - 3817x^2 + 961	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.8.4215622865029541015625.2	x^16 - 5x^14 - 6x^12 + 20x^10 + 41x^8 + 20x^6 - 6x^4 - 5x^2 + 1	\( 3^{8}\cdot 5^{12}\cdot 29^{4}\cdot 61^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.0.18652000809482666015625.1	x^16 - 4x^15 + x^14 + 10x^13 + 30x^12 - 166x^11 + 160x^10 + 135x^9 + 136x^8 - 785x^7 - 185x^6 + 2134x^5 + 1300x^4 - 3465x^3 - 1994x^2 + 2416x + 2221	\( 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 61^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2, 2]$
16.0.18652000809482666015625.2	x^16 - 8x^15 + 25x^14 - 34x^13 + 36x^12 - 92x^11 + 126x^10 + 20x^9 + 139x^8 - 240x^7 + 169x^6 + 244x^5 + 111x^4 + 2x^3 - 4x + 1	\( 3^{8}\cdot 5^{12}\cdot 29^{2}\cdot 61^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2, 2]$
16.16.300187334364663585439744.1	x^16 - 8x^15 + 4x^14 + 112x^13 - 214x^12 - 536x^11 + 1496x^10 + 1056x^9 - 4447x^8 - 736x^7 + 6484x^6 + 80x^5 - 4624x^4 - 152x^3 + 1316x^2 + 168x - 31	\( 2^{48}\cdot 17^{4}\cdot 113^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.8.300187334364663585439744.1	x^16 - 8x^14 + 72x^10 - 126x^8 - 136x^6 + 640x^4 - 56x^2 + 1	\( 2^{48}\cdot 17^{4}\cdot 113^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)
16.0.350539780096000000000000.1	x^16 - 4x^15 + 24x^14 - 94x^13 + 314x^12 - 846x^11 + 1828x^10 - 2822x^9 + 3276x^8 - 4370x^7 + 8728x^6 - 16212x^5 + 23099x^4 - 23240x^3 + 15380x^2 - 5962x + 1021	\( 2^{24}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2, 4]$ (GRH)
16.8.350539780096000000000000.1	x^16 - 4x^15 - 12x^14 + 122x^13 - 397x^12 + 540x^11 + 964x^10 - 7154x^9 + 19503x^8 - 32702x^7 + 37036x^6 - 29394x^5 + 16523x^4 - 6344x^3 + 1472x^2 - 154x + 1	\( 2^{24}\cdot 5^{12}\cdot 11^{2}\cdot 29^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2]$ (GRH)
16.0.806950076416000000000000.1	x^16 - 6x^15 + 28x^14 - 96x^13 + 266x^12 - 468x^11 + 820x^10 - 260x^9 - 1004x^8 + 2460x^7 - 960x^6 - 136x^5 + 604x^4 + 104x^3 + 1440x^2 - 1768x + 716	\( 2^{28}\cdot 5^{12}\cdot 11^{4}\cdot 29^{2} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	$[2, 2, 2]$ (GRH)
16.16.3315823592130094569619456.1	x^16 - 4x^15 - 22x^14 + 112x^13 + 97x^12 - 1000x^11 + 486x^10 + 3188x^9 - 2765x^8 - 4904x^7 + 4648x^6 + 4000x^5 - 3264x^4 - 1560x^3 + 936x^2 + 192x - 94	\( 2^{46}\cdot 17^{2}\cdot 113^{4} \)	$C_2^4.C_2^3.C_2$ (as 16T547)	Trivial (GRH)