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
16.0.7380528100000000.1	x^16 + 2x^14 + 2x^12 + 4x^6 + 5x^4 + 4x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 71^{2} \)	16T1728	Trivial
16.0.15615001600000000.1	x^16 - 2x^15 + 5x^14 - 10x^13 + 12x^12 - 16x^11 + 15x^10 - 8x^9 + 3x^8 + 4x^7 - 4x^6 - 2x^5 + 6x^4 - 8x^3 + 6x^2 - 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{2}\cdot 71^{2} \)	16T1728	Trivial
16.0.56801432950182144.1	x^16 - 4x^14 + 4x^12 + 8x^10 - 17x^8 + 2x^6 + 13x^4 - 7x^2 + 1	\( 2^{8}\cdot 3^{14}\cdot 7^{4}\cdot 139^{2} \)	16T1728	Trivial
16.0.265373802305224704.1	x^16 - 2x^15 + 2x^14 + 8x^13 - 6x^12 + 4x^11 + 32x^10 - 6x^9 + 13x^8 + 42x^7 + 14x^6 + 16x^5 + 21x^4 + 8x^3 + 5x^2 + 4x + 1	\( 2^{16}\cdot 3^{10}\cdot 7^{4}\cdot 13^{4} \)	16T1728	Trivial
16.0.315214873600000000.4	x^16 - x^12 + x^10 + x^8 + 2x^6 + 3x^4 + x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial
16.0.315214873600000000.5	x^16 + 3x^14 + 5x^12 + 5x^10 + 3x^8 + x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial
16.0.315214873600000000.6	x^16 - x^12 - x^10 + x^8 - 2x^6 + 3x^4 - x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial
16.0.315214873600000000.7	x^16 - 3x^14 + 5x^12 - 5x^10 + 3x^8 - x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial
16.0.790022102016015625.1	x^16 - 7x^15 + 28x^14 - 74x^13 + 147x^12 - 222x^11 + 269x^10 - 262x^9 + 224x^8 - 171x^7 + 131x^6 - 84x^5 + 47x^4 - 12x^3 + 2x^2 + x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 89^{2} \)	16T1728	Trivial
16.4.790022102016015625.1	x^16 - x^15 - x^14 + x^13 - 5x^12 + 12x^11 - 13x^10 - 8x^9 + 54x^8 - 72x^7 + 31x^6 + 51x^5 - 106x^4 + 92x^3 - 47x^2 + 9x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 89^{2} \)	16T1728	Trivial
16.4.1304712217600000000.2	x^16 + 3x^14 + x^12 - 7x^10 - 11x^8 - 7x^6 - 4x^4 - 2x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 59^{2} \)	16T1728	Trivial
16.4.1304712217600000000.3	x^16 - 5x^14 + 9x^12 - 5x^10 - 3x^8 + 6x^4 - 5x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 59^{2} \)	16T1728	Trivial
16.4.1889415193600000000.2	x^16 - 2x^15 - 2x^14 + 4x^12 + 4x^11 + x^10 - 2x^9 - 7x^8 - 2x^7 + x^6 + 4x^5 + 4x^4 - 2x^2 - 2x + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 71^{2} \)	16T1728	Trivial
16.4.2103078227250390625.1	x^16 - 5x^15 + 14x^14 - 31x^13 + 51x^12 - 72x^11 + 85x^10 - 94x^9 + 78x^8 - 47x^7 + 2x^6 + 23x^5 - 26x^4 + 12x^3 - x^2 - 2x + 1	\( 5^{8}\cdot 29^{4}\cdot 31^{2}\cdot 89^{2} \)	16T1728	Trivial
16.4.2403160732922265625.1	x^16 - 4x^15 + 6x^14 - 5x^13 - 6x^12 + 24x^11 - 22x^10 + 12x^9 + 24x^8 - 44x^7 + 14x^6 - 16x^5 - 33x^4 - 16x^2 + 3x + 1	\( 5^{8}\cdot 29^{2}\cdot 31^{4}\cdot 89^{2} \)	16T1728	Trivial
16.4.3052847617600000000.1	x^16 - 2x^14 - x^13 + x^12 + 5x^11 + 2x^10 - 4x^9 - 8x^8 - 4x^7 + 2x^6 + 5x^5 + x^4 - x^3 - 2x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 11^{4}\cdot 19^{4} \)	16T1728	Trivial (GRH)
16.0.3802344001600000000.2	x^16 + 4x^14 + 7x^12 + 9x^10 + 15x^8 + 18x^6 + 18x^4 + 7x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 29^{2}\cdot 41^{4} \)	16T1728	Trivial
16.0.3802344001600000000.3	x^16 - x^14 + 5x^12 - 6x^10 + 6x^8 + 2x^6 + 5x^4 + 3x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 29^{2}\cdot 41^{4} \)	16T1728	Trivial
16.4.5296626073600000000.1	x^16 - 2x^15 - 6x^14 + 18x^13 + 10x^12 - 58x^11 + 6x^10 + 90x^9 - 40x^8 - 62x^7 + 46x^6 - 18x^5 - 18x^4 + 26x^3 - 14x^2 + 6x - 1	\( 2^{24}\cdot 5^{8}\cdot 29^{2}\cdot 31^{2} \)	16T1728	Trivial (GRH)
16.0.7440862152281640625.1	x^16 + 4x^14 - 4x^13 + 18x^12 - 15x^11 + 43x^10 - 37x^9 + 57x^8 - 41x^7 + 52x^6 - 25x^5 + 23x^4 - 17x^3 + 16x^2 - 5x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{2}\cdot 89^{4} \)	16T1728	Trivial
16.4.7440862152281640625.1	x^16 - 7x^15 + 21x^14 - 34x^13 + 26x^12 + 6x^11 - 14x^10 - 53x^9 + 131x^8 - 114x^7 + 4x^6 + 92x^5 - 94x^4 + 38x^3 - x^2 - 4x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{2}\cdot 89^{4} \)	16T1728	Trivial
16.4.9264961945600000000.1	x^16 - 6x^15 + 16x^14 - 22x^13 + 11x^12 + 6x^11 - 20x^9 - 10x^8 + 58x^7 - 16x^6 - 34x^5 + 15x^4 + 22x^3 - 4x - 1	\( 2^{24}\cdot 5^{8}\cdot 29^{2}\cdot 41^{2} \)	16T1728	Trivial (GRH)
16.4.9264961945600000000.2	x^16 - 4x^15 + 8x^14 - 16x^13 + 24x^12 - 38x^11 + 58x^10 - 92x^9 + 122x^8 - 80x^7 + 46x^6 + 34x^5 - 43x^4 + 46x^3 + 8x^2 - 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 29^{2}\cdot 41^{2} \)	16T1728	Trivial (GRH)
16.0.19655390233600000000.1	x^16 + 3x^14 - 2x^12 - 6x^10 + 13x^8 + 33x^6 + 27x^4 + 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{2} \)	16T1728	Trivial
16.8.19655390233600000000.1	x^16 - 3x^14 - 2x^12 + 6x^10 + 13x^8 - 33x^6 + 27x^4 - 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 11^{4}\cdot 229^{2} \)	16T1728	Trivial (GRH)
16.4.37555593608578515625.1	x^16 - x^15 - 7x^12 + 6x^11 - 8x^10 + 25x^9 - 12x^8 + 25x^7 - 17x^6 - 3x^5 - 13x^4 - 36x^3 + 15x^2 + 5x + 1	\( 5^{8}\cdot 29^{4}\cdot 89^{2}\cdot 131^{2} \)	16T1728	Trivial
16.8.37555593608578515625.1	x^16 - 3x^15 + 6x^14 - 19x^13 + 38x^12 - 55x^11 + 80x^10 - 91x^9 + 63x^8 + 20x^7 - 116x^6 + 141x^5 - 76x^4 - 28x^3 + 57x^2 - 20x + 1	\( 5^{8}\cdot 29^{4}\cdot 89^{2}\cdot 131^{2} \)	16T1728	Trivial
16.0.44172757950699995136.1	x^16 + 3x^14 + 2x^12 + 13x^8 + 39x^6 + 37x^4 + 11x^2 + 1	\( 2^{16}\cdot 3^{4}\cdot 13^{8}\cdot 101^{2} \)	16T1728	Trivial
16.8.44172757950699995136.1	x^16 - 3x^14 + 2x^12 + 13x^8 - 39x^6 + 37x^4 - 11x^2 + 1	\( 2^{16}\cdot 3^{4}\cdot 13^{8}\cdot 101^{2} \)	16T1728	Trivial (GRH)
16.0.48585265060547265625.1	x^16 - x^15 + 3x^14 - 4x^13 + 8x^12 + 5x^11 - 3x^10 + 19x^9 - 20x^8 + 5x^7 + 15x^6 - 40x^5 + 73x^4 - 77x^3 + 62x^2 - 38x + 11	\( 5^{8}\cdot 29^{4}\cdot 89^{2}\cdot 149^{2} \)	16T1728	Trivial
16.4.48585265060547265625.1	x^16 - 7x^15 + 21x^14 - 31x^13 + 18x^12 + 22x^10 - 55x^9 + 11x^8 + 80x^7 - 87x^6 + 10x^5 + 28x^4 - 8x^3 - 6x^2 + x + 1	\( 5^{8}\cdot 29^{4}\cdot 89^{2}\cdot 149^{2} \)	16T1728	Trivial
16.8.184689982165435285504.1	x^16 - 2x^14 - x^12 - 18x^10 + 25x^8 + 56x^6 - 16x^4 - 24x^2 + 4	\( 2^{38}\cdot 7^{4}\cdot 23^{4} \)	16T1728	Trivial
16.8.184703321113600000000.1	x^16 - 8x^15 + 23x^14 - 18x^13 - 47x^12 + 100x^11 + 16x^10 - 166x^9 + 3x^8 + 204x^7 + 28x^6 - 156x^5 - 40x^4 + 44x^3 + 18x^2 - 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 101^{2} \)	16T1728	Trivial (GRH)
16.0.184703321113600000000.2	x^16 - 4x^15 + 13x^14 - 24x^13 + 56x^12 - 86x^11 + 144x^10 - 144x^9 + 147x^8 - 34x^7 - x^6 + 90x^5 - 55x^4 + 34x^3 + 3x^2 - 12x + 11	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 101^{2} \)	16T1728	Trivial
16.8.310723820569600000000.1	x^16 - 2x^14 - 4x^12 + 6x^10 + 7x^8 - 3x^6 - 6x^4 - x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{4}\cdot 131^{2} \)	16T1728	Trivial (GRH)
16.0.457602716462062890625.1	x^16 - 2x^15 + 7x^14 - 4x^13 + 29x^12 - 26x^11 + 77x^10 - 11x^9 + 75x^8 - 15x^7 + 85x^6 + 8x^5 + 76x^4 + 20x^3 + 31x^2 + 6x + 4	\( 5^{8}\cdot 29^{2}\cdot 89^{4}\cdot 149^{2} \)	16T1728	Trivial
16.4.457602716462062890625.1	x^16 - x^15 - 4x^14 + x^13 + 7x^12 - 2x^11 - 21x^10 + 2x^9 + 5x^8 + 2x^7 - 21x^6 - 2x^5 + 7x^4 + x^3 - 4x^2 - x + 1	\( 5^{8}\cdot 29^{2}\cdot 89^{4}\cdot 149^{2} \)	16T1728	Trivial (GRH)
16.4.1291120122265600000000.1	x^16 - 2x^15 - 6x^14 + 16x^13 - 2x^12 - 50x^11 + 54x^10 + 58x^9 - 77x^8 + 18x^7 + 70x^6 - 10x^5 - 100x^4 - 4x^3 + 172x^2 + 42x - 49	\( 2^{28}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial (GRH)
16.8.1291120122265600000000.1	x^16 - 4x^14 - 30x^12 + 96x^10 - 9x^8 - 72x^6 + 10x^4 + 12x^2 + 1	\( 2^{28}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial (GRH)
16.8.1291120122265600000000.2	x^16 - 6x^15 + 16x^14 - 20x^13 - 2x^12 + 46x^11 - 92x^10 + 62x^9 + 113x^8 - 122x^7 - 172x^6 + 238x^5 - 26x^4 - 52x^3 + 16x^2 + 2x - 1	\( 2^{28}\cdot 5^{8}\cdot 11^{4}\cdot 29^{2} \)	16T1728	Trivial (GRH)
16.0.2240378809369600000000.1	x^16 - 8x^15 + 37x^14 - 116x^13 + 276x^12 - 498x^11 + 684x^10 - 696x^9 + 540x^8 - 332x^7 + 109x^6 + 42x^5 - 26x^4 - 56x^3 + 69x^2 - 30x + 5	\( 2^{16}\cdot 5^{8}\cdot 29^{2}\cdot 101^{4} \)	16T1728	Trivial
16.8.2240378809369600000000.1	x^16 - 8x^15 + 25x^14 - 28x^13 - 74x^12 + 420x^11 - 1037x^10 + 1648x^9 - 1745x^8 + 1082x^7 - 45x^6 - 714x^5 + 874x^4 - 604x^3 + 251x^2 - 40x - 5	\( 2^{16}\cdot 5^{8}\cdot 29^{2}\cdot 101^{4} \)	16T1728	Trivial (GRH)
16.4.6257765070068859765625.1	x^16 + 7x^14 - 8x^12 - 46x^10 + 24x^8 + 56x^6 - 23x^4 + 33x^2 + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 89^{4} \)	16T1728	$[4]$ (GRH)
16.8.6257765070068859765625.1	x^16 - 2x^15 + 2x^14 + 9x^13 - 37x^12 + 46x^11 - 74x^10 + 82x^9 + 12x^8 - 4x^7 + 19x^6 - 88x^5 - 32x^4 + 37x^3 + 23x^2 + 6x + 1	\( 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 89^{4} \)	16T1728	$[2]$ (GRH)
16.12.6281488174105600000000.1	x^16 - 6x^14 + 5x^12 + 31x^10 - 70x^8 + 38x^6 + 8x^4 - 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1728	Trivial (GRH)
16.4.6281488174105600000000.1	x^16 + 6x^14 + 5x^12 - 31x^10 - 70x^8 - 38x^6 + 8x^4 + 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1728	Trivial (GRH)
16.12.6281488174105600000000.2	x^16 - 3x^14 - 9x^12 + 39x^10 - 33x^8 - 12x^6 + 24x^4 - 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1728	Trivial (GRH)
16.4.6281488174105600000000.2	x^16 + 3x^14 - 9x^12 - 39x^10 - 33x^8 + 12x^6 + 24x^4 + 9x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1728	Trivial (GRH)
16.0.11859656630330062890625.1	x^16 - x^15 - 4x^14 + 10x^13 + 17x^12 - 69x^11 + 62x^10 - 41x^9 + 261x^8 - 364x^7 + 92x^6 + 93x^5 + 2x^4 + 221x^3 + 135x^2 + 25x + 59	\( 5^{8}\cdot 19^{2}\cdot 29^{2}\cdot 31^{2}\cdot 101^{4} \)	16T1728	Trivial
16.0.11859656630330062890625.2	x^16 - x^15 + 6x^14 - 16x^13 + 24x^12 - 68x^11 + 140x^10 - 202x^9 + 391x^8 - 577x^7 + 625x^6 - 847x^5 + 760x^4 - 247x^3 + 126x^2 - 169x + 59	\( 5^{8}\cdot 19^{2}\cdot 29^{2}\cdot 31^{2}\cdot 101^{4} \)	16T1728	Trivial