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 matches 1-50 of 80)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.36560480908034304.1	x^16 - 7x^15 + 29x^14 - 87x^13 + 204x^12 - 389x^11 + 628x^10 - 871x^9 + 1039x^8 - 1062x^7 + 927x^6 - 676x^5 + 393x^4 - 171x^3 + 52x^2 - 10x + 1	\( 2^{8}\cdot 3^{12}\cdot 13^{4}\cdot 97^{2} \)	16T1772	Trivial
16.0.76280509548861696.1	x^16 - 2x^15 + 4x^14 - 5x^13 - x^12 + 19x^11 - 31x^10 + 47x^9 - 42x^8 + 5x^7 + 87x^6 - 145x^5 + 138x^4 - 82x^3 + 33x^2 - 8x + 1	\( 2^{8}\cdot 3^{8}\cdot 13^{6}\cdot 97^{2} \)	16T1772	Trivial
16.4.118893936100000000.1	x^16 + 3x^14 + x^12 - 6x^10 - 7x^8 - 2x^6 + 4x^4 + 4x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{4}\cdot 41^{2} \)	16T1772	Trivial
16.4.188981478400000000.1	x^16 - 2x^15 + 3x^14 - 7x^12 + 10x^11 + 4x^10 - 22x^9 + 17x^8 + 20x^7 - 36x^6 + 28x^4 - 8x^3 - 10x^2 + 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 13^{2}\cdot 19^{2} \)	16T1772	Trivial
16.4.232322192503515625.1	x^16 - 3x^15 + 2x^14 + 7x^13 - 15x^12 + 12x^11 - 6x^10 + 16x^9 - 24x^8 - 5x^7 + 67x^6 - 114x^5 + 110x^4 - 70x^3 + 30x^2 - 8x + 1	\( 5^{8}\cdot 7^{2}\cdot 29^{4}\cdot 131^{2} \)	16T1772	Trivial
16.4.433764662316015625.1	x^16 - x^15 + x^14 - 2x^13 - 7x^12 + x^11 - 7x^10 - 10x^9 - x^8 - 10x^7 - 7x^6 + x^5 - 7x^4 - 2x^3 + x^2 - x + 1	\( 5^{8}\cdot 7^{2}\cdot 29^{4}\cdot 179^{2} \)	16T1772	Trivial
16.0.513114342400000000.1	x^16 - 4x^13 + 7x^12 - 8x^11 + 8x^10 - 20x^9 + 49x^8 - 36x^7 - 28x^6 + 44x^5 + 5x^4 - 20x^3 - 2x^2 + 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{2} \)	16T1772	Trivial
16.4.513114342400000000.2	x^16 - 4x^15 + 6x^14 - 12x^13 + 25x^12 - 10x^11 - 15x^10 - 36x^9 + 83x^8 + 2x^7 - 81x^6 + 32x^5 + 20x^4 - 12x^3 + 3x^2 - 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 37^{2} \)	16T1772	Trivial
16.4.2821923320128515625.1	x^16 - 4x^15 + 3x^14 + 5x^13 - 5x^12 - 3x^11 + 2x^10 - 5x^9 + 22x^8 - 8x^7 - 71x^6 + 157x^5 - 165x^4 + 96x^3 - 32x^2 + 7x - 1	\( 5^{8}\cdot 11^{4}\cdot 97^{2}\cdot 229^{2} \)	16T1772	Trivial
16.0.2845689369749094400.1	x^16 + 6x^14 - 2x^13 + 26x^12 - 14x^11 + 59x^10 - 26x^9 + 75x^8 - 26x^7 + 59x^6 - 14x^5 + 26x^4 - 2x^3 + 6x^2 + 1	\( 2^{24}\cdot 5^{2}\cdot 7^{4}\cdot 41^{4} \)	16T1772	Trivial
16.4.2845689369749094400.1	x^16 - 4x^15 + 4x^14 + 2x^13 - 5x^12 + 4x^11 - x^10 - 2x^9 - 7x^8 + 23x^6 - 4x^5 - 20x^4 + 6x^3 + 7x^2 - 2x - 1	\( 2^{24}\cdot 5^{2}\cdot 7^{4}\cdot 41^{4} \)	16T1772	Trivial
16.0.2885780971334926336.1	x^16 + 4x^14 - 4x^13 + 7x^12 - 20x^11 + 8x^10 - 36x^9 + 45x^8 + 16x^7 + 74x^6 - 20x^5 + 13x^4 + 36x^2 + 12x + 1	\( 2^{32}\cdot 7^{4}\cdot 23^{4} \)	16T1772	Trivial
16.4.2885780971334926336.3	x^16 - 2x^14 - 8x^13 - 2x^12 + 4x^11 + 12x^10 - 8x^9 + 19x^8 + 52x^7 - 8x^6 - 80x^5 - 18x^4 + 12x^3 + 18x^2 + 8x + 1	\( 2^{32}\cdot 7^{4}\cdot 23^{4} \)	16T1772	Trivial
16.4.2972348402500000000.1	x^16 - 3x^15 + 5x^14 - 16x^13 + 21x^12 - 28x^11 + 43x^10 - 49x^9 + 68x^8 - 49x^7 + 43x^6 - 28x^5 + 21x^4 - 16x^3 + 5x^2 - 3x + 1	\( 2^{8}\cdot 5^{10}\cdot 29^{4}\cdot 41^{2} \)	16T1772	Trivial
16.4.3059980518400000000.2	x^16 - 6x^15 + 17x^14 - 34x^13 + 58x^12 - 94x^11 + 135x^10 - 152x^9 + 145x^8 - 114x^7 + 35x^6 + 42x^5 - 66x^4 + 50x^3 - 25x^2 + 8x - 1	\( 2^{16}\cdot 5^{8}\cdot 13^{2}\cdot 29^{4} \)	16T1772	Trivial
16.4.3059980518400000000.3	x^16 - 4x^15 + 3x^14 + 12x^13 - 24x^12 + 16x^11 - 17x^10 + 18x^9 - 11x^8 + 18x^7 - 17x^6 + 16x^5 - 24x^4 + 12x^3 + 3x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 13^{2}\cdot 29^{4} \)	16T1772	Trivial
16.4.16198295614987890625.1	x^16 - 6x^15 + 12x^14 - 11x^13 + 10x^12 - 14x^11 + 17x^10 - 11x^9 + 5x^8 - 11x^7 + 17x^6 - 14x^5 + 10x^4 - 11x^3 + 12x^2 - 6x + 1	\( 5^{8}\cdot 13^{2}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial
16.8.16198295614987890625.1	x^16 - 3x^15 + 2x^14 + 2x^13 + 2x^12 - 14x^11 - 5x^10 + 45x^9 - 24x^8 - 63x^7 + 58x^6 + 73x^5 - 97x^4 + 3x^3 + 32x^2 - 12x + 1	\( 5^{8}\cdot 13^{2}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial
16.4.62086835430400000000.1	x^16 - 6x^15 + 14x^14 - 10x^13 - 23x^12 + 46x^11 + 23x^10 - 160x^9 + 182x^8 + 16x^7 - 235x^6 + 236x^5 - 117x^4 + 16x^3 + 15x^2 - 8x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{2} \)	16T1772	Trivial (GRH)
16.0.62086835430400000000.3	x^16 - 4x^15 + 14x^14 - 34x^13 + 80x^12 - 148x^11 + 237x^10 - 306x^9 + 356x^8 - 330x^7 + 203x^6 - 88x^5 + 37x^4 - 26x^3 + 26x^2 - 8x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{2} \)	16T1772	Trivial
16.0.62086835430400000000.4	x^16 - 2x^15 + 4x^14 + 4x^13 + 5x^12 + 26x^11 + 36x^10 + 76x^9 + 87x^8 + 120x^7 + 170x^6 + 150x^5 + 167x^4 + 176x^3 + 154x^2 + 66x + 11	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{2} \)	16T1772	Trivial
16.0.62086835430400000000.5	x^16 - 4x^15 + 11x^14 - 24x^13 + 59x^12 - 106x^11 + 140x^10 - 208x^9 + 263x^8 - 208x^7 + 140x^6 - 106x^5 + 59x^4 - 24x^3 + 11x^2 - 4x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 37^{2} \)	16T1772	Trivial
16.4.102796887654400000000.1	x^16 - 5x^14 + 14x^12 - x^10 - 20x^8 + 3x^6 + 21x^4 - 18x^2 + 4	\( 2^{22}\cdot 5^{8}\cdot 89^{4} \)	16T1772	Trivial
16.0.126513454752400000000.1	x^16 - x^15 + 8x^14 - 2x^13 + 21x^12 + 14x^11 + 28x^10 + 37x^9 + 44x^8 + 37x^7 + 28x^6 + 14x^5 + 21x^4 - 2x^3 + 8x^2 - x + 1	\( 2^{10}\cdot 5^{8}\cdot 71^{2}\cdot 89^{4} \)	16T1772	Trivial
16.8.227126601318400000000.1	x^16 - 2x^15 + 2x^14 - 8x^13 + 13x^12 - 58x^11 + 148x^10 - 118x^9 + 8x^8 + 80x^7 - 2x^6 - 194x^5 + 98x^4 + 60x^3 - 18x^2 - 10x - 1	\( 2^{24}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4} \)	16T1772	Trivial (GRH)
16.8.227126601318400000000.2	x^16 - 2x^15 - 4x^14 - 4x^13 + 25x^12 + 42x^11 - 44x^10 - 122x^9 - 66x^8 + 68x^7 + 46x^6 + 18x^5 + 48x^4 - 36x^3 - 20x^2 + 10x - 1	\( 2^{24}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4} \)	16T1772	Trivial (GRH)
16.4.341452721735550390625.1	x^16 - x^15 - 10x^14 + 6x^13 + 22x^12 - x^11 + 61x^10 - 64x^9 - 387x^8 + 367x^7 + 225x^6 + 37x^5 - 300x^4 - 17x^3 + 22x^2 + 9x + 1	\( 5^{8}\cdot 11^{6}\cdot 97^{2}\cdot 229^{2} \)	16T1772	Trivial (GRH)
16.8.783355012710400000000.1	x^16 - 2x^15 - 8x^14 - 6x^13 + 46x^12 + 68x^11 - 38x^10 - 182x^9 - 177x^8 + 104x^7 + 290x^6 + 54x^5 - 138x^4 - 38x^3 + 38x^2 + 16x + 1	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{4} \)	16T1772	Trivial (GRH)
16.8.783355012710400000000.2	x^16 - 2x^15 - 8x^14 + 42x^13 - 94x^12 + 112x^11 - 52x^10 - 34x^9 + 74x^8 - 28x^7 + 36x^6 - 234x^5 + 393x^4 - 304x^3 + 116x^2 - 16x - 1	\( 2^{24}\cdot 5^{8}\cdot 13^{2}\cdot 29^{4} \)	16T1772	Trivial (GRH)
16.4.5193406022784100000000.1	x^16 - x^15 - 3x^14 - x^12 - 5x^10 + x^9 + x^7 - 5x^6 - x^4 - 3x^2 - x + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{2}\cdot 19^{2}\cdot 29^{4}\cdot 41^{2} \)	16T1772	$[2]$ (GRH)
16.8.6281488174105600000000.1	x^16 - 15x^12 + 3x^10 + 43x^8 + 15x^6 - 14x^4 - 3x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial (GRH)
16.8.6281488174105600000000.2	x^16 + 6x^14 - x^12 - 35x^10 + 13x^8 + 44x^6 - 35x^4 + 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial (GRH)
16.12.6281488174105600000000.3	x^16 - 7x^14 + 11x^12 + 25x^10 - 92x^8 + 82x^6 - 5x^4 - 15x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial (GRH)
16.4.6281488174105600000000.3	x^16 + 7x^14 + 11x^12 - 25x^10 - 92x^8 - 82x^6 - 5x^4 + 15x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial (GRH)
16.12.6281488174105600000000.4	x^16 - 10x^14 + 27x^12 + 3x^10 - 77x^8 + 78x^6 - 22x^4 - 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial (GRH)
16.0.11984260029569459814400.1	x^16 + 10x^14 + 53x^12 + 210x^10 + 352x^8 + 10x^6 - 199x^4 + 10x^2 + 25	\( 2^{36}\cdot 5^{2}\cdot 17^{8} \)	16T1772	Trivial
16.8.11984260029569459814400.1	x^16 - 10x^14 + 53x^12 - 210x^10 + 352x^8 - 10x^6 - 199x^4 - 10x^2 + 25	\( 2^{36}\cdot 5^{2}\cdot 17^{8} \)	16T1772	Trivial (GRH)
16.8.11984260029569459814400.2	x^16 - 10x^14 - 2x^13 + 51x^12 + 6x^11 - 254x^10 - 246x^9 + 327x^8 + 508x^7 - 12x^6 - 240x^5 - 92x^4 - 4x^3 + 20x^2 + 12x + 2	\( 2^{36}\cdot 5^{2}\cdot 17^{8} \)	16T1772	Trivial (GRH)
16.0.39499622723814400000000.1	x^16 + 18x^14 + 136x^12 + 559x^10 + 1350x^8 + 1921x^6 + 1514x^4 + 553x^2 + 49	\( 2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4}\cdot 211^{2} \)	16T1772	$[5]$
16.12.39499622723814400000000.1	x^16 - 18x^14 + 136x^12 - 559x^10 + 1350x^8 - 1921x^6 + 1514x^4 - 553x^2 + 49	\( 2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4}\cdot 211^{2} \)	16T1772	Trivial (GRH)
16.0.421056051832422400000000.1	x^16 + 16x^14 + 70x^12 + 142x^10 + 187x^8 + 210x^6 + 162x^4 + 52x^2 + 4	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1772	$[2]$ (GRH)
16.8.421056051832422400000000.1	x^16 - 2x^14 - 25x^12 - 16x^10 - 43x^8 - 130x^6 + 258x^4 - 76x^2 + 4	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1772	Trivial (GRH)
16.12.421056051832422400000000.2	x^16 - 14x^14 + 63x^12 - 98x^10 + 45x^8 - 2x^6 + 22x^4 - 20x^2 + 4	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1772	Trivial (GRH)
16.4.421056051832422400000000.2	x^16 + 2x^14 - 25x^12 + 16x^10 - 43x^8 + 130x^6 + 258x^4 + 76x^2 + 4	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1772	Trivial (GRH)
16.8.421056051832422400000000.2	x^16 + 2x^14 - 43x^12 + 106x^10 - 115x^8 + 46x^6 + 18x^4 - 20x^2 + 4	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1772	Trivial (GRH)
16.4.421056051832422400000000.3	x^16 - 2x^14 - 43x^12 - 106x^10 - 115x^8 - 46x^6 + 18x^4 + 20x^2 + 4	\( 2^{34}\cdot 5^{8}\cdot 89^{4} \)	16T1772	Trivial (GRH)
16.4.462639521059669144140625.1	x^16 - 7x^15 + 35x^14 - 117x^13 + 284x^12 - 527x^11 + 597x^10 - 506x^9 + 199x^8 - 1274x^7 + 4103x^6 - 4864x^5 - 2121x^4 + 18249x^3 - 26578x^2 + 16326x - 3631	\( 5^{8}\cdot 13^{6}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	$[2]$ (GRH)
16.8.462639521059669144140625.1	x^16 - x^15 - 34x^13 - 27x^12 + 85x^11 + 289x^10 + 762x^9 - 717x^8 - 910x^7 - 2553x^6 - 48x^5 + 3235x^4 - 436x^3 + 3761x^2 - 4957x + 1381	\( 5^{8}\cdot 13^{6}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1772	Trivial (GRH)
16.4.814254147110502400000000.1	x^16 - 3x^14 - 33x^12 + 100x^10 + 262x^8 - 604x^6 - 684x^4 - 32x^2 + 64	\( 2^{22}\cdot 5^{8}\cdot 89^{6} \)	16T1772	Trivial (GRH)
16.8.814254147110502400000000.1	x^16 - 13x^14 + 32x^12 - 55x^10 + 122x^8 - 29x^6 - 139x^4 + 58x^2 + 4	\( 2^{22}\cdot 5^{8}\cdot 89^{6} \)	16T1772	Trivial (GRH)