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 66)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.89145114978091264.1	x^16 - 3x^12 - 4x^10 + 5x^8 + 4x^6 - 3x^4 + 1	\( 2^{8}\cdot 233^{2}\cdot 283^{4} \)	16T1757	Trivial
16.0.131386089973284864.1	x^16 - 6x^15 + 15x^14 - 20x^13 + 8x^12 + 28x^11 - 68x^10 + 80x^9 - 36x^8 - 48x^7 + 127x^6 - 156x^5 + 131x^4 - 78x^3 + 32x^2 - 8x + 1	\( 2^{16}\cdot 3^{6}\cdot 229^{4} \)	16T1757	Trivial
16.0.151571607225696256.2	x^16 - 3x^14 + 5x^12 - 6x^10 + 6x^8 - 4x^6 + 2x^4 - x^2 + 1	\( 2^{16}\cdot 29^{2}\cdot 229^{4} \)	16T1757	Trivial
16.0.262727594844160000.2	x^16 - 5x^14 - 4x^13 + 18x^12 + 14x^11 - 22x^10 - 26x^9 + 26x^7 + 29x^6 + 10x^5 + 3x^4 + 4x^3 + 1	\( 2^{16}\cdot 5^{4}\cdot 283^{4} \)	16T1757	Trivial
16.0.262727594844160000.3	x^16 - 2x^15 + x^14 + 8x^13 - 12x^12 + 8x^11 + 14x^10 - 16x^9 + 34x^8 - 2x^7 - 11x^6 + 44x^5 + 40x^4 + 12x^3 - 4x^2 - 4x + 1	\( 2^{16}\cdot 5^{4}\cdot 283^{4} \)	16T1757	Trivial
16.0.3309409596231975625.1	x^16 - 5x^14 - 6x^13 + 5x^12 + 24x^11 + 32x^10 - 6x^9 - 46x^8 - 44x^7 - 2x^6 + 34x^5 + 41x^4 + 27x^3 + 13x^2 + 4x + 1	\( 5^{4}\cdot 19^{6}\cdot 103^{4} \)	16T1757	Trivial
16.4.8809813357282350625.1	x^16 - 5x^15 + 11x^14 - 8x^13 - 16x^12 + 40x^11 - 23x^10 - 37x^9 + 50x^8 + 37x^7 - 158x^6 + 185x^5 - 115x^4 + 31x^3 + x^2 - 4x + 1	\( 5^{4}\cdot 19^{4}\cdot 31^{2}\cdot 103^{4} \)	16T1757	Trivial
16.4.15336535719789789184.1	x^16 - x^14 - 7x^12 - x^10 + 11x^8 + 17x^6 + 16x^4 + 6x^2 + 1	\( 2^{16}\cdot 37^{2}\cdot 643^{4} \)	16T1757	Trivial
16.4.16257540100096000000.1	x^16 - 5x^15 + 13x^14 - 17x^13 + x^12 + 40x^11 - 88x^10 + 114x^9 - 113x^8 + 83x^7 - 21x^6 - 37x^5 + 44x^4 - 15x^3 - 5x^2 + 5x - 1	\( 2^{18}\cdot 5^{6}\cdot 251^{4} \)	16T1757	Trivial (GRH)
16.4.16257540100096000000.2	x^16 - 5x^15 + 15x^14 - 33x^13 + 58x^12 - 91x^11 + 133x^10 - 185x^9 + 215x^8 - 212x^7 + 202x^6 - 192x^5 + 165x^4 - 109x^3 + 47x^2 - 11x + 1	\( 2^{18}\cdot 5^{6}\cdot 251^{4} \)	16T1757	Trivial
16.4.29784686366087780625.1	x^16 - x^15 - 6x^14 + 8x^13 - 5x^11 + 7x^10 - 8x^9 + 83x^8 - 96x^7 - 19x^6 - 23x^5 + 30x^4 - 9x^3 + 3x^2 - 9x + 1	\( 3^{2}\cdot 5^{4}\cdot 19^{6}\cdot 103^{4} \)	16T1757	Trivial (GRH)
16.8.31911509153693925625.1	x^16 - 9x^14 - 5x^13 + 21x^12 + 19x^11 + x^10 + 6x^9 - 6x^8 + x^7 + 23x^6 - 25x^5 - 43x^4 - 5x^3 - 6x^2 - 9x - 1	\( 5^{4}\cdot 19^{4}\cdot 59^{2}\cdot 103^{4} \)	16T1757	Trivial
16.4.34111670658114075625.1	x^16 - 2x^15 + 2x^14 - 3x^13 + 18x^11 - 40x^10 + 48x^9 - 92x^8 + 181x^7 - 185x^6 + 102x^5 - 64x^4 + 35x^3 + 26x^2 - 35x + 9	\( 5^{4}\cdot 19^{4}\cdot 61^{2}\cdot 103^{4} \)	16T1757	Trivial
16.4.46212558932424900625.1	x^16 - 7x^15 + 24x^14 - 51x^13 + 70x^12 - 58x^11 + 18x^10 + 8x^9 + 21x^8 - 88x^7 + 120x^6 - 56x^5 - 52x^4 + 85x^3 - 38x^2 + x + 1	\( 5^{4}\cdot 19^{4}\cdot 71^{2}\cdot 103^{4} \)	16T1757	Trivial
16.4.72614496985466700625.1	x^16 - 6x^15 + 14x^14 - 11x^13 - 29x^12 + 104x^11 - 129x^10 + 63x^9 - 10x^8 - 7x^7 + 25x^6 - 22x^5 + 13x^4 + 21x^3 - 4x^2 - 6x - 1	\( 5^{4}\cdot 19^{4}\cdot 89^{2}\cdot 103^{4} \)	16T1757	Trivial
16.0.93516031277458125625.1	x^16 + 8x^14 - 6x^13 + 42x^12 - 44x^11 + 121x^10 - 123x^9 + 209x^8 - 189x^7 + 211x^6 - 144x^5 + 103x^4 - 44x^3 + 19x^2 - 4x + 1	\( 5^{4}\cdot 19^{4}\cdot 101^{2}\cdot 103^{4} \)	16T1757	Trivial
16.4.93516031277458125625.1	x^16 - x^15 - 3x^14 + 2x^13 + 14x^12 + 40x^11 + 36x^10 + 38x^9 - 22x^8 - 36x^7 - 71x^6 - 72x^5 - 48x^4 - 45x^3 - 12x^2 - 9x - 1	\( 5^{4}\cdot 19^{4}\cdot 101^{2}\cdot 103^{4} \)	16T1757	Trivial
16.8.113439755125911784761.1	x^16 - 2x^15 - 2x^14 - 2x^13 + 11x^12 + 2x^11 - 15x^10 + 28x^9 - 48x^8 - 34x^7 + 124x^6 + 8x^5 - 87x^4 + 2x^3 + 16x^2 - 4x - 1	\( 3^{6}\cdot 19^{4}\cdot 103^{6} \)	16T1757	Trivial
16.8.113439755125911784761.2	x^16 - 7x^15 + 13x^14 + 17x^13 - 82x^12 + 42x^11 + 143x^10 - 165x^9 - 83x^8 + 178x^7 + 4x^6 - 81x^5 - 2x^4 + 18x^3 + 9x^2 - 3x - 3	\( 3^{6}\cdot 19^{4}\cdot 103^{6} \)	16T1757	Trivial
16.4.157320714905642475625.1	x^16 - 3x^15 + 4x^14 - 5x^13 + 8x^12 - 9x^11 - 10x^10 + 15x^9 - 17x^8 + 76x^7 - 152x^6 + 219x^5 - 308x^4 + 402x^3 - 375x^2 + 226x - 73	\( 5^{4}\cdot 19^{4}\cdot 103^{4}\cdot 131^{2} \)	16T1757	Trivial
16.8.177122168445423825625.1	x^16 - 2x^15 + x^14 + 2x^13 - 7x^12 - 10x^11 + 12x^10 + 58x^9 - 45x^8 - 29x^7 - 15x^6 - 26x^5 + 106x^4 - 14x^3 - 40x^2 + 8x + 1	\( 5^{4}\cdot 19^{4}\cdot 103^{4}\cdot 139^{2} \)	16T1757	Trivial
16.4.203524106498465625625.1	x^16 - x^15 - x^14 + 3x^13 - 18x^12 + 5x^10 - 4x^9 + 27x^8 + 51x^7 + 19x^6 - 130x^5 - 9x^4 + 60x^3 + 10x^2 - 11x - 3	\( 5^{4}\cdot 19^{4}\cdot 103^{4}\cdot 149^{2} \)	16T1757	Trivial
16.0.209024510259516000625.1	x^16 - 3x^15 + 13x^14 - 24x^13 + 53x^12 - 68x^11 + 104x^10 - 93x^9 + 116x^8 - 61x^7 + 86x^6 - 32x^5 + 59x^4 - 24x^3 + 23x^2 - 7x + 1	\( 5^{4}\cdot 19^{4}\cdot 103^{4}\cdot 151^{2} \)	16T1757	Trivial
16.0.273010140219158102016.1	x^16 - 4x^15 + 11x^14 - 20x^13 + 32x^12 - 52x^11 + 82x^10 - 112x^9 + 117x^8 - 92x^7 + 53x^6 - 22x^5 + 9x^4 - 2x^3 - x^2 + 1	\( 2^{16}\cdot 3^{6}\cdot 83^{4}\cdot 347^{2} \)	16T1757	$[2]$
16.4.363035815568926500625.1	x^16 - 6x^15 + 14x^14 - 15x^13 + 8x^12 + 2x^11 - 17x^10 + 8x^9 + 6x^8 + 33x^7 + 11x^6 - 50x^5 - 36x^4 - 25x^3 + 8x - 1	\( 5^{4}\cdot 19^{4}\cdot 103^{4}\cdot 199^{2} \)	16T1757	Trivial
16.0.512712094832608149504.1	x^16 + 6x^14 + 19x^12 + 48x^10 + 84x^8 + 108x^6 + 98x^4 + 48x^2 + 9	\( 2^{32}\cdot 3^{2}\cdot 41^{2}\cdot 53^{4} \)	16T1757	Trivial
16.8.512712094832608149504.1	x^16 - 6x^14 + 19x^12 - 48x^10 + 84x^8 - 108x^6 + 98x^4 - 48x^2 + 9	\( 2^{32}\cdot 3^{2}\cdot 41^{2}\cdot 53^{4} \)	16T1757	Trivial (GRH)
16.0.600790768140328960000.3	x^16 - 2x^15 + 7x^14 - 8x^13 + 12x^12 - 14x^11 + 45x^10 - 104x^9 + 187x^8 - 260x^7 + 235x^6 - 326x^5 + 420x^4 - 386x^3 + 269x^2 - 76x + 19	\( 2^{16}\cdot 5^{4}\cdot 19^{4}\cdot 103^{4} \)	16T1757	Trivial
16.0.600790768140328960000.4	x^16 - 8x^15 + 40x^14 - 130x^13 + 323x^12 - 608x^11 + 927x^10 - 1132x^9 + 1175x^8 - 1054x^7 + 858x^6 - 644x^5 + 401x^4 - 204x^3 + 71x^2 - 10x + 1	\( 2^{16}\cdot 5^{4}\cdot 19^{4}\cdot 103^{4} \)	16T1757	Trivial
16.0.630532439264025000000.1	x^16 - 4x^15 + 9x^14 - 13x^13 + 21x^12 - 42x^11 + 71x^10 - 125x^9 + 195x^8 - 281x^7 + 318x^6 - 270x^5 + 227x^4 - 125x^3 + 84x^2 - 44x + 24	\( 2^{6}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4} \)	16T1757	$[4]$
16.4.1835790061181274525625.1	x^16 - 3x^15 - 2x^14 + 5x^13 + 2x^12 - 5x^11 - 3x^10 - 4x^9 + 18x^8 + 10x^7 - 13x^6 - 3x^5 - 3x^4 - 4x^3 - 4x^2 + 4x + 1	\( 5^{4}\cdot 491^{4}\cdot 7109^{2} \)	16T1757	Trivial (GRH)
16.0.3193653193464934540729.1	x^16 - 4x^15 + 13x^14 - 22x^13 + 26x^12 - 8x^11 - 17x^10 + 40x^9 - 14x^8 + 10x^7 + 11x^6 - 12x^5 + 3x^4 - 7x^3 + 5x^2 + 5x + 1	\( 17^{6}\cdot 43^{4}\cdot 6221^{2} \)	16T1757	Trivial
16.0.14572785094099128765625.1	x^16 - 4x^15 - 4x^14 + 25x^13 + 16x^12 - 64x^11 - 9x^10 + 137x^9 + 48x^8 - 140x^7 - 20x^6 + 77x^5 + 28x^4 - 40x^3 + 3x^2 + 6x + 1	\( 5^{6}\cdot 251^{4}\cdot 15329^{2} \)	16T1757	Trivial
16.0.25036744363448352178176.1	x^16 - 2x^14 - 2x^12 + 34x^10 - 37x^8 - 3x^6 + 139x^4 + 72x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial
16.8.25036744363448352178176.1	x^16 + 2x^14 - 2x^12 - 34x^10 - 37x^8 + 3x^6 + 139x^4 - 72x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial (GRH)
16.0.25036744363448352178176.2	x^16 + 12x^14 + 42x^12 + 77x^10 + 102x^8 + 93x^6 + 62x^4 + 33x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial
16.8.25036744363448352178176.2	x^16 - 12x^14 + 42x^12 - 77x^10 + 102x^8 - 93x^6 + 62x^4 - 33x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial (GRH)
16.0.25036744363448352178176.3	x^16 + 11x^14 + 54x^12 + 153x^10 + 264x^8 + 274x^6 + 166x^4 + 57x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial
16.8.25036744363448352178176.3	x^16 - 11x^14 + 54x^12 - 153x^10 + 264x^8 - 274x^6 + 166x^4 - 57x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial (GRH)
16.0.25036744363448352178176.4	x^16 + 3x^14 + 6x^12 + 5x^10 + 111x^8 + 264x^6 + 224x^4 + 78x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial
16.8.25036744363448352178176.4	x^16 - 3x^14 + 6x^12 - 5x^10 + 111x^8 - 264x^6 + 224x^4 - 78x^2 + 9	\( 2^{16}\cdot 3^{6}\cdot 13^{2}\cdot 1327^{4} \)	16T1757	Trivial (GRH)
16.12.33011788718388998569984.1	x^16 - 6x^15 + 3x^14 + 40x^13 - 50x^12 - 110x^11 + 120x^10 + 318x^9 - 271x^8 - 506x^7 + 394x^6 + 358x^5 - 236x^4 - 108x^3 + 39x^2 + 14x + 1	\( 2^{28}\cdot 223^{6} \)	16T1757	Trivial (GRH)
16.4.33011788718388998569984.3	x^16 + 8x^14 - 10x^12 - 24x^10 + 49x^8 - 48x^6 - 40x^4 + 64x^2 + 16	\( 2^{28}\cdot 223^{6} \)	16T1757	$[2]$
16.8.53647541928200825550625.1	x^16 - x^15 - 17x^14 + 19x^13 + 105x^12 - 142x^11 - 254x^10 + 388x^9 + 300x^8 - 485x^7 - 212x^6 + 292x^5 + 110x^4 - 69x^3 - 30x^2 + x + 1	\( 5^{4}\cdot 29^{2}\cdot 283^{4}\cdot 3989^{2} \)	16T1757	Trivial (GRH)
16.0.135091395493847885676544.1	x^16 - 4x^14 + 38x^12 - 100x^10 + 385x^8 - 608x^6 + 928x^4 - 640x^2 + 256	\( 2^{24}\cdot 389^{4}\cdot 593^{2} \)	16T1757	$[8]$ (GRH)
16.0.135884508726577661476864.1	x^16 - 4x^15 + 2x^14 + 6x^13 - 5x^12 - 18x^11 + 48x^10 + 28x^9 - 36x^8 - 40x^7 + 58x^6 - 2x^5 + 3x^4 - 30x^3 + 6x^2 + 4x + 1	\( 2^{24}\cdot 43^{4}\cdot 48673^{2} \)	16T1757	Trivial (GRH)
16.0.153802436643924213760000.1	x^16 - 6x^15 + 28x^14 - 90x^13 + 254x^12 - 456x^11 + 662x^10 - 438x^9 - 49x^8 + 772x^7 - 462x^6 - 210x^5 + 1466x^4 - 1334x^3 + 954x^2 - 316x + 81	\( 2^{24}\cdot 5^{4}\cdot 19^{4}\cdot 103^{4} \)	16T1757	$[2]$ (GRH)
16.12.153802436643924213760000.1	x^16 - 6x^15 - 6x^14 + 110x^13 - 195x^12 - 260x^11 + 958x^10 - 106x^9 - 1577x^8 + 354x^7 + 1962x^6 - 464x^5 - 1451x^4 + 216x^3 + 438x^2 + 70x + 3	\( 2^{24}\cdot 5^{4}\cdot 19^{4}\cdot 103^{4} \)	16T1757	Trivial (GRH)
16.0.216885467298658754560000.1	x^16 - 4x^14 - 10x^13 + 27x^12 + 12x^11 + 25x^10 - 102x^9 + 18x^8 + 56x^7 + 482x^6 - 218x^5 - 50x^4 + 112x^3 + 655x^2 - 434x + 471	\( 2^{16}\cdot 5^{4}\cdot 19^{6}\cdot 103^{4} \)	16T1757	$[6]$ (GRH)
16.12.216885467298658754560000.1	x^16 - 6x^15 + 15x^14 - 2x^13 - 144x^12 + 478x^11 - 514x^10 - 370x^9 + 1424x^8 - 1046x^7 - 491x^6 + 1120x^5 - 409x^4 - 154x^3 + 118x^2 - 20x + 1	\( 2^{16}\cdot 5^{4}\cdot 19^{6}\cdot 103^{4} \)	16T1757	Trivial (GRH)