Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 32 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.117310069734811389.1	x^16 - 2x^15 - 2x^13 + 9x^12 - 3x^11 - 2x^10 - 17x^9 + 15x^8 + 4x^7 + 15x^6 - 23x^5 + 5x^4 - 5x^3 + 11x^2 - 6x + 1	\( 3^{8}\cdot 79^{3}\cdot 331^{3} \)	16T1871	Trivial
16.0.180355734956640625.1	x^16 - 5x^15 + 14x^14 - 28x^13 + 46x^12 - 63x^11 + 73x^10 - 72x^9 + 57x^8 - 34x^7 + 23x^6 - 21x^5 + 8x^4 + 8x^3 - 7x^2 + 1	\( 5^{8}\cdot 59^{3}\cdot 131^{3} \)	16T1871	Trivial
16.0.180355734956640625.2	x^16 - 5x^15 + 7x^14 + 2x^13 - 10x^12 + 2x^11 + 7x^10 - 8x^9 + 3x^8 + 10x^7 - 16x^6 + 8x^5 + 5x^4 - 7x^3 + 3x^2 - 2x + 1	\( 5^{8}\cdot 59^{3}\cdot 131^{3} \)	16T1871	Trivial
16.0.9502115648519722509.1	x^16 - 6x^15 + 19x^14 - 48x^13 + 95x^12 - 156x^11 + 220x^10 - 240x^9 + 250x^8 - 216x^7 + 128x^6 - 144x^5 + 86x^4 - 69x^3 + 113x^2 - 21x + 49	\( 3^{12}\cdot 79^{3}\cdot 331^{3} \)	16T1871	Trivial
16.2.960464752179926171875.1	x^16 - 2x^15 + 5x^14 + 9x^13 - 52x^12 + 174x^11 - 380x^10 + 732x^9 - 1104x^8 + 1559x^7 - 1781x^6 + 1850x^5 - 1561x^4 + 1135x^3 - 631x^2 + 268x - 71	\( -\,5^{8}\cdot 71^{3}\cdot 1901^{3} \)	16T1871	Trivial
16.2.1039386538727894921875.1	x^16 - 4x^15 + 11x^14 - 21x^13 + 39x^12 - 96x^11 + 218x^10 - 404x^9 + 576x^8 - 662x^7 + 729x^6 - 763x^5 + 562x^4 - 284x^3 - 436x^2 + 704x - 271	\( -\,5^{8}\cdot 138571^{3} \)	16T1871	Trivial
16.4.7088396383905323828125.1	x^16 - 3x^15 - 9x^14 + 33x^13 + 45x^12 - 160x^11 - 174x^10 + 573x^9 + 563x^8 - 1427x^7 - 1090x^6 + 3124x^5 + 1865x^4 - 4844x^3 - 4267x^2 + 3028x + 1121	\( 5^{8}\cdot 31^{5}\cdot 859^{3} \)	16T1871	Trivial
16.4.7088396383905323828125.2	x^16 - x^15 - 10x^14 + 26x^13 - 2x^12 - 100x^11 + 252x^10 - 220x^9 - 249x^8 + 877x^7 - 810x^6 - 403x^5 + 1622x^4 - 1450x^3 + 151x^2 - 1014x + 971	\( 5^{8}\cdot 31^{5}\cdot 859^{3} \)	16T1871	Trivial (GRH)
16.2.8024490403430400000000.1	x^16 + 12x^10 - 48x^8 + 60x^6 - 29x^4 + 12x^2 - 9	\( -\,2^{32}\cdot 3^{14}\cdot 5^{8} \)	16T1871	Trivial
16.2.8024490403430400000000.2	x^16 - 12x^10 - 48x^8 - 60x^6 - 29x^4 - 12x^2 - 9	\( -\,2^{32}\cdot 3^{14}\cdot 5^{8} \)	16T1871	Trivial
16.10.600290470112453857421875.1	x^16 - 23x^14 - 36x^13 + 121x^12 + 516x^11 + 552x^10 - 1816x^9 - 5965x^8 - 2292x^7 + 11368x^6 + 15544x^5 + 3508x^4 - 5404x^3 - 3857x^2 - 887x - 79	\( -\,5^{12}\cdot 71^{3}\cdot 1901^{3} \)	16T1871	Trivial (GRH)
16.12.632632620311574433203125.1	x^16 - 4x^15 - 20x^14 + 107x^13 + 80x^12 - 1009x^11 + 555x^10 + 4046x^9 - 4331x^8 - 6802x^7 + 8027x^6 + 3835x^5 - 2975x^4 + 220x^3 + 473x^2 - 143x + 11	\( 5^{8}\cdot 11^{3}\cdot 106759^{3} \)	16T1871	Trivial (GRH)
16.10.649616586704934326171875.1	x^16 - 5x^15 - 5x^14 + 45x^13 - 23x^12 - 30x^11 + 250x^10 - 970x^9 - 1236x^8 + 5230x^7 + 2925x^6 - 14365x^5 + 1318x^4 + 18635x^3 - 8670x^2 - 3080x + 1421	\( -\,5^{12}\cdot 138571^{3} \)	16T1871	Trivial (GRH)
16.12.1600567066979512214453125.1	x^16 - 3x^15 - 17x^14 + 27x^13 + 137x^12 + 59x^11 - 550x^10 - 1278x^9 + 811x^8 + 4200x^7 - 73x^6 - 4262x^5 + 1390x^4 + 841x^3 - 4205x^2 - 1748x + 361	\( 5^{8}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	Trivial (GRH)
16.8.1600567066979512214453125.1	x^16 - 2x^15 - 8x^14 + 56x^13 - 78x^12 - 367x^11 + 1159x^10 + 186x^9 - 4516x^8 + 4028x^7 + 5737x^6 - 10608x^5 - 360x^4 + 10892x^3 - 6860x^2 + 50x + 691	\( 5^{8}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	Trivial (GRH)
16.8.1600567066979512214453125.2	x^16 - 6x^15 + 2x^14 + 42x^13 - 53x^12 - 39x^11 - 122x^10 + 415x^9 + 1083x^8 - 3783x^7 + 942x^6 + 6678x^5 - 7195x^4 - 3444x^3 + 5986x^2 - 2467x - 3229	\( 5^{8}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	Trivial (GRH)
16.0.24471271802225000000000000.1	x^16 + 35x^14 + 635x^12 + 6920x^10 + 45510x^8 + 178975x^6 + 408350x^4 + 496450x^2 + 248225	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1871	$[2]$ (GRH)
16.4.24471271802225000000000000.1	x^16 - 5x^15 - 4x^14 + 55x^13 - 43x^12 - 90x^11 - 67x^10 - 335x^9 + 820x^8 - 5325x^7 - 5833x^6 + 35190x^5 + 15777x^4 - 36975x^3 + 131479x^2 + 55160x - 228404	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1871	Trivial (GRH)
16.8.24471271802225000000000000.1	x^16 - 5x^15 + 6x^14 - 163x^12 + 480x^11 - 72x^10 + 455x^9 + 6205x^8 - 5620x^7 - 9803x^6 - 24055x^5 - 136058x^4 - 204260x^3 - 127616x^2 - 32685x - 2869	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1871	Trivial (GRH)
16.0.24471271802225000000000000.2	x^16 - 7x^15 + 31x^14 - 123x^13 + 421x^12 - 1356x^11 + 3794x^10 - 9244x^9 + 22357x^8 - 48379x^7 + 90689x^6 - 154611x^5 + 214936x^4 - 245493x^3 + 265481x^2 - 148567x + 117211	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1871	$[2]$ (GRH)
16.4.24471271802225000000000000.2	x^16 - 5x^15 + 26x^14 - 100x^13 + 387x^12 - 1400x^11 + 4673x^10 - 14075x^9 + 37010x^8 - 84770x^7 + 153177x^6 - 194040x^5 + 125367x^4 + 68785x^3 - 185016x^2 + 79030x + 8231	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1871	Trivial (GRH)
16.8.24471271802225000000000000.2	x^16 - 5x^15 - 19x^14 + 100x^13 + 232x^12 - 1150x^11 - 1852x^10 + 9740x^9 + 3345x^8 - 34435x^7 - 3403x^6 + 57400x^5 + 20427x^4 - 51785x^3 - 24571x^2 + 12530x - 164	\( 2^{12}\cdot 5^{14}\cdot 9929^{3} \)	16T1871	Trivial (GRH)
16.6.44072222439732505600000000.1	x^16 + 6x^14 - 6x^12 + 1737x^10 + 14150x^8 - 14013x^6 - 137064x^4 + 256659x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1871	Trivial (GRH)
16.6.44072222439732505600000000.2	x^16 + 15x^14 - 57x^12 - 830x^10 + 3120x^8 - 6020x^6 - 16154x^4 + 110275x^2 - 119851	\( -\,2^{16}\cdot 5^{8}\cdot 119851^{3} \)	16T1871	Trivial (GRH)
16.4.395395387694734020751953125.1	x^16 + 21x^14 - 55x^13 + 94x^12 - 680x^11 - 138x^10 + 4845x^9 - 19871x^8 + 98025x^7 - 292336x^6 + 665450x^5 - 1310594x^4 + 2014235x^3 - 2972302x^2 + 3560555x - 1714129	\( 5^{12}\cdot 11^{3}\cdot 106759^{3} \)	16T1871	$[2]$ (GRH)
16.4.1000354416862195134033203125.1	x^16 - 5x^15 + 21x^14 - 40x^13 - 106x^12 + 1200x^11 - 5443x^10 + 15945x^9 - 32711x^8 + 19695x^7 + 99934x^6 - 445185x^5 + 977156x^4 - 1528675x^3 + 1183363x^2 - 241270x - 181939	\( 5^{12}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	$[2, 2]$ (GRH)
16.0.41460211404739342054400000000.1	x^16 + 70x^14 + 1877x^12 + 25171x^10 + 185977x^8 + 786626x^6 + 1882680x^4 + 2348698x^2 + 1174349	\( 2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 106759^{3} \)	16T1871	$[2, 3178]$ (GRH)
16.16.41460211404739342054400000000.1	x^16 - 70x^14 + 1877x^12 - 25171x^10 + 185977x^8 - 786626x^6 + 1882680x^4 - 2348698x^2 + 1174349	\( 2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 106759^{3} \)	16T1871	Trivial (GRH)
16.8.41460211404739342054400000000.1	x^16 - 3x^14 - 417x^12 - 1936x^10 + 24684x^8 + 140118x^6 - 267158x^4 - 1174349x^2 + 1174349	\( 2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 106759^{3} \)	16T1871	Trivial (GRH)
16.8.41460211404739342054400000000.2	x^16 + 3x^14 - 417x^12 + 1936x^10 + 24684x^8 - 140118x^6 - 267158x^4 + 1174349x^2 + 1174349	\( 2^{16}\cdot 5^{8}\cdot 11^{3}\cdot 106759^{3} \)	16T1871	$[2]$ (GRH)
16.0.104894763301569312486400000000.1	x^16 + 76x^14 + 2245x^12 + 33403x^10 + 273118x^8 + 1259002x^6 + 3175017x^4 + 3889260x^2 + 1600189	\( 2^{16}\cdot 5^{8}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	$[2, 2, 2564]$ (GRH)
16.16.104894763301569312486400000000.1	x^16 - 76x^14 + 2245x^12 - 33403x^10 + 273118x^8 - 1259002x^6 + 3175017x^4 - 3889260x^2 + 1600189	\( 2^{16}\cdot 5^{8}\cdot 31^{3}\cdot 41^{3}\cdot 1259^{3} \)	16T1871	Trivial (GRH)