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
16.0.76196774280167424.2	x^16 - 10x^12 - 8x^10 + 51x^8 + 112x^6 + 78x^4 + 16x^2 + 1	\( 2^{36}\cdot 3^{8}\cdot 13^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.0.76196774280167424.3	x^16 - 8x^14 + 18x^12 + 4x^10 - 45x^8 + 4x^6 + 50x^4 - 12x^2 + 1	\( 2^{36}\cdot 3^{8}\cdot 13^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.0.510138777600000000.1	x^16 - 2x^15 + x^14 + 6x^13 + x^12 - 14x^11 + 16x^10 + 12x^9 - 19x^8 - 14x^7 + 34x^6 - 8x^5 - 14x^4 + 8x^3 + 4x^2 - 4x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 31^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.4.510138777600000000.1	x^16 - 2x^15 + x^14 + 2x^13 - 12x^12 + 12x^11 - x^10 - 12x^9 + 21x^8 - 12x^7 - x^6 + 12x^5 - 12x^4 + 2x^3 + x^2 - 2x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 31^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.4.892344729600000000.1	x^16 - 2x^15 - x^14 + 2x^13 + 6x^12 - 20x^11 + 17x^10 - 8x^9 + 21x^8 - 36x^7 + 23x^6 - 4x^4 - 6x^3 + 11x^2 - 6x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 41^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.4.892344729600000000.2	x^16 - 4x^15 + 8x^14 - 12x^13 + 15x^12 - 8x^11 - 18x^10 + 44x^9 - 53x^8 + 44x^7 - 18x^6 - 8x^5 + 15x^4 - 12x^3 + 8x^2 - 4x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 41^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.0.2675972505600000000.1	x^16 - 4x^15 + 12x^14 - 30x^13 + 59x^12 - 88x^11 + 105x^10 - 100x^9 + 80x^8 - 60x^7 + 35x^6 - 16x^5 + 9x^4 + 3x^2 + 2x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 71^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.4.2675972505600000000.1	x^16 - 2x^15 - 3x^14 + 8x^13 - x^12 - 8x^11 + 3x^10 + 2x^9 - 16x^8 + 2x^7 + 3x^6 - 8x^5 - x^4 + 8x^3 - 3x^2 - 2x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 71^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.8.12103719321600000000.1	x^16 - 4x^15 + 2x^14 + 10x^13 - 31x^12 + 52x^11 - 55x^10 + 40x^9 + 10x^8 - 60x^7 + 75x^6 - 36x^5 - 21x^4 + 20x^3 - 7x^2 + 2x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 151^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.8.15264603491297918976.1	x^16 - 8x^14 - 4x^13 + 18x^12 + 12x^11 - 8x^10 + 8x^9 - 4x^8 - 40x^7 - 8x^6 + 8x^5 + 4x^4 + 24x^3 + 8x^2 - 8x - 2	\( 2^{42}\cdot 3^{8}\cdot 23^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.4.20882706457600000000.4	x^16 - 4x^14 + x^12 + 2x^10 - 4x^8 + 2x^6 + x^4 - 4x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{8} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.0.30831810969600000000.1	x^16 - 4x^15 + 10x^14 - 16x^13 + 28x^12 - 32x^11 + 42x^10 - 26x^9 + 43x^8 + 8x^7 + 58x^6 + 34x^5 + 43x^4 - 2x^3 + 5x^2 - 2x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 241^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.8.30831810969600000000.1	x^16 - 6x^15 + 7x^14 + 10x^13 - 26x^12 + 20x^11 - 5x^10 - 4x^9 + 5x^8 - 4x^7 - 5x^6 + 20x^5 - 26x^4 + 10x^3 + 7x^2 - 6x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 241^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.4.179877452185600000000.1	x^16 - 6x^15 + 13x^14 - 14x^13 + 4x^12 + 16x^11 - 23x^10 - 16x^9 + 9x^8 + 16x^7 - 23x^6 - 16x^5 + 4x^4 + 14x^3 + 13x^2 + 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 31^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.0.228440250777600000000.1	x^16 - 4x^15 + 8x^14 + 14x^12 - 60x^11 + 232x^10 - 428x^9 + 676x^8 - 836x^7 + 928x^6 - 820x^5 + 539x^4 - 240x^3 + 72x^2 - 12x + 1	\( 2^{32}\cdot 3^{4}\cdot 5^{8}\cdot 41^{2} \)	$C_2^6.C_2^2$ (as 16T528)	$[2]$
16.8.228440250777600000000.1	x^16 - 8x^15 + 40x^14 - 140x^13 + 318x^12 - 452x^11 + 300x^10 + 260x^9 - 822x^8 + 760x^7 - 170x^6 - 272x^5 + 277x^4 - 108x^3 + 12x^2 + 4x - 1	\( 2^{32}\cdot 3^{4}\cdot 5^{8}\cdot 41^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.8.314645158297600000000.2	x^16 - 2x^15 - 5x^14 - 4x^13 + 5x^12 + 24x^11 + 43x^10 + 68x^9 + 44x^8 - 44x^7 - 143x^6 - 188x^5 - 125x^4 - 38x^3 + 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.8.314645158297600000000.3	x^16 - 2x^15 - x^14 + 4x^13 - 9x^12 + 4x^11 - 31x^10 - 2x^9 + 96x^8 + 2x^7 - 31x^6 - 4x^5 - 9x^4 - 4x^3 - x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.0.490243365273600000000.1	x^16 - 2x^15 + 5x^14 - 10x^13 + 14x^12 + 5x^10 - 32x^9 + 29x^8 + 32x^7 + 5x^6 + 14x^4 + 10x^3 + 5x^2 + 2x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 31^{4} \)	$C_2^6.C_2^2$ (as 16T528)	$[2]$
16.8.2471977847294525440000.1	x^16 - 2x^15 - 5x^14 + 12x^13 + x^12 - 20x^11 + 3x^10 + 48x^9 - 48x^8 - 76x^7 + 249x^6 - 288x^5 + 149x^4 + 66x^3 - 178x^2 + 104x - 17	\( 2^{24}\cdot 5^{4}\cdot 13^{8}\cdot 17^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.8.2471977847294525440000.2	x^16 - 2x^15 - 9x^14 + 18x^13 + 13x^12 - 30x^11 + 52x^10 - 72x^9 - 211x^8 + 346x^7 + 198x^6 - 536x^5 + 284x^4 + 116x^3 - 276x^2 + 84x - 1	\( 2^{24}\cdot 5^{4}\cdot 13^{8}\cdot 17^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial
16.12.4267831204249600000000.1	x^16 - 6x^15 + 3x^14 + 48x^13 - 146x^12 + 258x^11 - 286x^10 - 246x^9 + 1199x^8 - 938x^7 - 606x^6 + 1102x^5 - 276x^4 - 196x^3 + 97x^2 - 6x - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 151^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.12.4267831204249600000000.2	x^16 - 6x^15 + 3x^14 + 58x^13 - 201x^12 + 338x^11 - 216x^10 - 716x^9 + 2539x^8 - 3618x^7 + 2414x^6 - 228x^5 - 706x^4 + 364x^3 - 8x^2 - 16x - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 151^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.0.5345972853145600000000.4	x^16 + 7x^14 + 7x^12 + 13x^10 + 8x^8 + 13x^6 + 7x^4 + 7x^2 + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{8} \)	$C_2^6.C_2^2$ (as 16T528)	$[2]$
16.16.108398345460121600000000.1	x^16 - 26x^14 - 8x^13 + 234x^12 + 116x^11 - 952x^10 - 562x^9 + 1899x^8 + 1160x^7 - 1844x^6 - 1010x^5 + 805x^4 + 282x^3 - 133x^2 + 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 761^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.16.108398345460121600000000.2	x^16 - 2x^15 - 25x^14 + 30x^13 + 172x^12 - 152x^11 - 513x^10 + 368x^9 + 753x^8 - 456x^7 - 547x^6 + 276x^5 + 182x^4 - 70x^3 - 25x^2 + 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 761^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.0.528918511098265600000000.5	x^16 - 2x^15 + 17x^14 - 28x^13 + 175x^12 - 292x^11 + 987x^10 - 1390x^9 + 3413x^8 - 3988x^7 + 7202x^6 - 6816x^5 + 10040x^4 - 7536x^3 + 7344x^2 - 2592x + 1296	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{4} \)	$C_2^6.C_2^2$ (as 16T528)	$[2, 2, 4]$ (GRH)
16.0.528918511098265600000000.6	x^16 + 10x^14 - 20x^13 + 85x^12 - 232x^11 + 614x^10 - 1412x^9 + 3129x^8 - 6760x^7 + 9196x^6 - 17464x^5 + 16031x^4 - 2808x^3 + 28404x^2 + 35236x + 17639	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 41^{4} \)	$C_2^6.C_2^2$ (as 16T528)	$[2, 10]$ (GRH)
16.0.632826328907398512640000.1	x^16 + 12x^14 + 28x^12 - 86x^10 - 142x^8 + 468x^6 - 335x^4 + 334x^2 + 289	\( 2^{32}\cdot 5^{4}\cdot 13^{8}\cdot 17^{2} \)	$C_2^6.C_2^2$ (as 16T528)	$[2]$ (GRH)
16.0.632826328907398512640000.2	x^16 + 4x^14 + 88x^12 + 250x^10 + 366x^8 + 320x^6 + 141x^4 + 22x^2 + 1	\( 2^{32}\cdot 5^{4}\cdot 13^{8}\cdot 17^{2} \)	$C_2^6.C_2^2$ (as 16T528)	$[4]$ (GRH)
16.0.2020593563703705600000000.1	x^16 + 18x^14 + 129x^12 + 480x^10 + 1001x^8 + 1164x^6 + 693x^4 + 162x^2 + 1	\( 2^{40}\cdot 3^{4}\cdot 5^{8}\cdot 241^{2} \)	$C_2^6.C_2^2$ (as 16T528)	$[24]$ (GRH)
16.0.3333974497696153600000000.5	x^16 - 4x^15 + 32x^14 - 92x^13 + 362x^12 - 764x^11 + 1772x^10 - 2606x^9 + 3751x^8 - 3676x^7 + 2818x^6 - 830x^5 + 579x^4 - 394x^3 + 211x^2 + 270x + 89	\( 2^{24}\cdot 5^{8}\cdot 37^{4}\cdot 521^{2} \)	$C_2^6.C_2^2$ (as 16T528)	Trivial (GRH)
16.0.40291974979216000000000000.1	x^16 - x^14 + 54x^12 + 163x^10 + 234x^8 - 3229x^6 + 16021x^4 - 26208x^2 + 20736	\( 2^{16}\cdot 5^{12}\cdot 17^{8}\cdot 19^{2} \)	$C_2^6.C_2^2$ (as 16T528)	$[2, 16]$ (GRH)
16.0.644671599667456000000000000.1	x^16 - 4x^15 + 4x^14 + 16x^13 - 27x^12 + 42x^11 - 276x^10 + 518x^9 - 219x^8 - 882x^7 + 4044x^6 - 15830x^5 + 55825x^4 - 109846x^3 + 109408x^2 - 59964x + 32661	\( 2^{20}\cdot 5^{12}\cdot 17^{8}\cdot 19^{2} \)	$C_2^6.C_2^2$ (as 16T528)	$[2, 2, 26]$ (GRH)