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
16.0.14883906304147456.1	x^16 - 2x^15 + 3x^14 - 6x^13 + 4x^12 - 4x^11 + 5x^10 - 4x^9 + 13x^8 - 6x^7 - x^6 + 2x^5 - 2x^4 - 6x^3 + 3x^2 + 1	\( 2^{16}\cdot 17^{6}\cdot 97^{2} \)	16T876	Trivial
16.0.24135629974444521.1	x^16 - 5x^15 + 7x^14 + 2x^13 - 13x^12 + 19x^11 - 19x^10 - 16x^9 + 49x^8 - 16x^7 - 19x^6 + 19x^5 - 13x^4 + 2x^3 + 7x^2 - 5x + 1	\( 3^{12}\cdot 13^{6}\cdot 97^{2} \)	16T876	Trivial
16.0.28114696031640625.1	x^16 + x^14 + 3x^12 + 6x^10 + 3x^8 + 14x^6 - 2x^4 + 4x^2 + 1	\( 5^{8}\cdot 11^{2}\cdot 29^{6} \)	16T876	Trivial
16.4.83879382375390625.1	x^16 - 4x^15 + 3x^14 + 8x^13 - 15x^12 + 2x^11 + 12x^10 - 6x^9 - 3x^8 - 6x^7 + 12x^6 + 2x^5 - 15x^4 + 8x^3 + 3x^2 - 4x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{6} \)	16T876	Trivial
16.4.223291098234765625.1	x^16 - 4x^14 - 5x^13 + 4x^12 + 10x^11 + x^10 - 5x^9 - 5x^8 - 5x^7 + x^6 + 10x^5 + 4x^4 - 5x^3 - 4x^2 + 1	\( 5^{8}\cdot 29^{6}\cdot 31^{2} \)	16T876	Trivial
16.4.390585157266015625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 69x^12 - 50x^11 + 4x^10 + 57x^9 - 129x^8 + 196x^7 - 224x^6 + 193x^5 - 143x^4 + 96x^3 - 46x^2 + 12x - 1	\( 5^{8}\cdot 29^{6}\cdot 41^{2} \)	16T876	Trivial
16.0.1840467002203515625.1	x^16 - x^15 + 9x^14 - 8x^13 + 34x^12 - 19x^11 + 63x^10 - 27x^9 + 99x^8 - 101x^7 + 167x^6 - 158x^5 + 129x^4 - 74x^3 + 31x^2 - 7x + 1	\( 5^{8}\cdot 29^{6}\cdot 89^{2} \)	16T876	Trivial
16.4.3401878219828515625.1	x^16 + 2x^14 - 6x^13 + 2x^12 - 12x^11 + 41x^10 - 7x^9 + 31x^8 - 94x^7 - 36x^6 + 34x^5 + 127x^4 + 2x^3 - 100x^2 + 3x + 1	\( 5^{8}\cdot 11^{4}\cdot 29^{6} \)	16T876	Trivial (GRH)
16.4.3904982718814879744.1	x^16 - 4x^15 + 6x^14 - 15x^12 + 16x^11 + 10x^10 - 24x^9 - 5x^8 + 24x^7 + 10x^6 - 16x^5 - 15x^4 + 6x^2 + 4x + 1	\( 2^{24}\cdot 7^{2}\cdot 41^{6} \)	16T876	Trivial (GRH)
16.4.5158465839656640625.1	x^16 + 5x^14 - 9x^13 + 11x^12 - 31x^11 + 19x^10 - 30x^9 + 39x^8 + 7x^7 + 25x^6 - 5x^5 - 27x^4 - 19x^3 - 14x^2 - 2x + 1	\( 5^{8}\cdot 29^{6}\cdot 149^{2} \)	16T876	Trivial
16.8.7444817979750390625.2	x^16 - 3x^15 + 5x^13 - 6x^12 - 12x^11 + 20x^10 + 27x^9 - 36x^8 + 24x^7 + 72x^6 - 58x^5 - 87x^4 - 13x^3 + 11x^2 + 5x + 1	\( 5^{8}\cdot 29^{6}\cdot 179^{2} \)	16T876	Trivial (GRH)
16.8.15227477017600000000.3	x^16 - 9x^14 + 32x^12 - 56x^10 + 48x^8 - 19x^6 + 8x^4 - 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T876	Trivial (GRH)
16.0.15227477017600000000.7	x^16 + 9x^14 + 32x^12 + 56x^10 + 48x^8 + 19x^6 + 8x^4 + 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{6} \)	16T876	Trivial
16.8.23031428688520413184.1	x^16 - 2x^15 - 5x^14 + 2x^13 + 14x^12 + 8x^11 - 9x^10 - 20x^9 - 3x^8 + 20x^7 - 9x^6 - 8x^5 + 14x^4 - 2x^3 - 5x^2 + 2x + 1	\( 2^{24}\cdot 17^{2}\cdot 41^{6} \)	16T876	Trivial
16.0.30280457037516015625.1	x^16 + 10x^12 + 14x^10 + 43x^8 + 45x^6 + 119x^4 + 26x^2 + 121	\( 5^{8}\cdot 19^{4}\cdot 29^{6} \)	16T876	$[2]$
16.0.49698129096100000000.2	x^16 - 5x^14 + 19x^12 - 84x^10 + 181x^8 - 163x^6 + 143x^4 - 44x^2 + 16	\( 2^{8}\cdot 5^{8}\cdot 89^{6} \)	16T876	Trivial
16.8.80608086462750390625.1	x^16 - 4x^15 + 6x^14 - 3x^13 - 21x^12 + 25x^11 - 8x^10 - 44x^9 + 42x^8 + 133x^7 + 88x^6 - 97x^5 - 88x^4 + 21x^3 + 10x^2 - x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{6}\cdot 31^{2} \)	16T876	Trivial (GRH)
16.0.163266119413359765625.2	x^16 + 15x^14 + 70x^12 + 180x^10 + 287x^8 + 285x^6 + 155x^4 + 30x^2 + 1	\( 5^{8}\cdot 29^{2}\cdot 89^{6} \)	16T876	Trivial
16.8.205744042618125390625.2	x^16 - 4x^15 + 4x^14 - 15x^13 + 30x^12 - 49x^11 + 59x^10 + 86x^9 - 158x^8 + 104x^7 + 134x^6 - 187x^5 - 167x^4 - 32x^3 + 2x + 1	\( 5^{8}\cdot 29^{6}\cdot 941^{2} \)	16T876	Trivial (GRH)
16.0.348725955724781640625.1	x^16 + 5x^14 + 35x^12 + 78x^10 + 155x^8 - 70x^6 + 166x^4 - 40x^2 + 25	\( 5^{8}\cdot 29^{2}\cdot 101^{6} \)	16T876	$[2]$
16.8.424686794052336615424.2	x^16 - 10x^14 + 41x^12 - 98x^10 + 124x^8 - 90x^6 + 65x^4 - 18x^2 + 1	\( 2^{24}\cdot 41^{6}\cdot 73^{2} \)	16T876	Trivial (GRH)
16.12.845468605385858351104.1	x^16 - 8x^15 + 18x^14 + 8x^13 - 78x^12 + 88x^11 - 10x^10 - 74x^9 + 175x^8 - 168x^7 - 62x^6 + 194x^5 - 49x^4 - 74x^3 + 27x^2 + 14x - 1	\( 2^{24}\cdot 41^{6}\cdot 103^{2} \)	16T876	Trivial (GRH)
16.0.1017606619113208152064.1	x^16 - 6x^15 + 27x^14 - 76x^13 + 160x^12 - 214x^11 + 192x^10 - 148x^9 + 329x^8 - 592x^7 + 656x^6 - 440x^5 + 288x^4 - 176x^3 + 104x^2 - 32x + 16	\( 2^{24}\cdot 41^{6}\cdot 113^{2} \)	16T876	$[2]$
16.8.1017606619113208152064.2	x^16 - 6x^14 + 7x^12 + 12x^10 + 17x^8 - 204x^6 + 295x^4 - 34x^2 + 1	\( 2^{24}\cdot 41^{6}\cdot 113^{2} \)	16T876	Trivial
16.8.1495767768355846488064.1	x^16 - 6x^15 + 17x^14 - 28x^13 + 41x^12 - 108x^11 + 113x^10 + 82x^9 - 244x^8 + 238x^7 - 49x^6 + 84x^5 - 215x^4 + 84x^3 + 15x^2 - 10x + 1	\( 2^{24}\cdot 41^{6}\cdot 137^{2} \)	16T876	Trivial (GRH)
16.12.2126173887392822265625.1	x^16 - x^15 - 8x^14 + 7x^13 - 12x^12 + 12x^11 + 172x^10 + 41x^9 - 620x^8 - 253x^7 + 1118x^6 + 167x^5 - 939x^4 + 147x^3 + 268x^2 - 110x + 11	\( 5^{12}\cdot 11^{4}\cdot 29^{6} \)	16T876	Trivial (GRH)
16.0.5896045744261225775104.2	x^16 - 8x^15 + 44x^14 - 168x^13 + 496x^12 - 1156x^11 + 2190x^10 - 3404x^9 + 4449x^8 - 4940x^7 + 4874x^6 - 4300x^5 + 3544x^4 - 2516x^3 + 1530x^2 - 636x + 113	\( 2^{32}\cdot 17^{2}\cdot 41^{6} \)	16T876	$[2]$
16.0.6656082890982399410176.3	x^16 - 2x^15 + 5x^14 - 10x^13 + 64x^12 + 68x^11 + 307x^10 + 292x^9 + 603x^8 + 608x^7 + 669x^6 + 520x^5 + 328x^4 + 114x^3 + 43x^2 + 6x + 1	\( 2^{24}\cdot 17^{4}\cdot 41^{6} \)	16T876	$[4]$
16.0.17941024603692100000000.1	x^16 - x^15 + 5x^14 + 2x^13 - 24x^12 + 24x^11 - 63x^10 - 99x^9 + 159x^8 + 16x^7 + 12x^6 + 624x^5 + 416x^4 - 1088x^3 + 960x^2 - 256x + 256	\( 2^{8}\cdot 5^{8}\cdot 19^{2}\cdot 89^{6} \)	16T876	$[2]$ (GRH)
16.0.29099519213052891015625.1	x^16 - x^15 + 12x^14 + 12x^13 + 74x^12 + 96x^11 + 460x^10 + 670x^9 + 1236x^8 + 1529x^7 + 2882x^6 + 3853x^5 + 4475x^4 + 3423x^3 + 1909x^2 + 627x + 121	\( 5^{8}\cdot 19^{4}\cdot 29^{6}\cdot 31^{2} \)	16T876	$[2, 4]$
16.0.31216831471804594140625.3	x^16 - x^15 + 5x^14 + 9x^13 + 44x^12 + 149x^11 + 430x^10 + 713x^9 + 1056x^8 + 1269x^7 + 1483x^6 + 1512x^5 + 1483x^4 + 1048x^3 + 528x^2 + 136x + 16	\( 5^{8}\cdot 89^{6}\cdot 401^{2} \)	16T876	$[4]$
16.0.191958112137556655079424.1	x^16 - 4x^15 + 16x^14 - 52x^13 + 143x^12 - 316x^11 + 724x^10 - 1252x^9 + 2239x^8 - 3192x^7 + 4490x^6 - 4468x^5 + 5011x^4 - 2840x^3 + 1800x^2 - 932x + 3929	\( 2^{32}\cdot 41^{6}\cdot 97^{2} \)	16T876	$[24]$ (GRH)
16.16.191958112137556655079424.1	x^16 - 4x^15 - 18x^14 + 88x^13 + 86x^12 - 720x^11 + 164x^10 + 2628x^9 - 2335x^8 - 3816x^7 + 5792x^6 + 460x^5 - 4152x^4 + 2060x^3 - 198x^2 - 36x - 1	\( 2^{32}\cdot 41^{6}\cdot 97^{2} \)	16T876	Trivial (GRH)
16.16.222945491014681600000000.2	x^16 - 19x^14 + 124x^12 - 360x^10 + 498x^8 - 351x^6 + 125x^4 - 20x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{6} \)	16T876	Trivial (GRH)