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
16.0.13857126676869888.1	x^16 + 7x^14 + 22x^12 + 41x^10 + 49x^8 + 39x^6 + 22x^4 + 9x^2 + 3	\( 2^{8}\cdot 3^{9}\cdot 229^{4} \)	16T1759	Trivial
16.0.97944847357902848.1	x^16 - 2x^15 - x^14 + 4x^13 + 11x^12 - 40x^11 + 40x^10 + 10x^9 - 52x^8 + 16x^7 + 81x^6 - 150x^5 + 141x^4 - 84x^3 + 33x^2 - 8x + 1	\( 2^{16}\cdot 233\cdot 283^{4} \)	16T1759	Trivial
16.2.122484747687109375.1	x^16 - 2x^15 - x^14 + 3x^13 - 2x^10 - 6x^9 + 7x^8 + 6x^7 - 5x^6 + 2x^5 - 3x^3 - 1	\( -\,5^{8}\cdot 79\cdot 251^{4} \)	16T1759	Trivial
16.0.124714140091828992.1	x^16 - 7x^15 + 22x^14 - 43x^13 + 57x^12 - 49x^11 + 31x^10 - 49x^9 + 146x^8 - 313x^7 + 463x^6 - 492x^5 + 388x^4 - 218x^3 + 77x^2 - 14x + 1	\( 2^{8}\cdot 3^{11}\cdot 229^{4} \)	16T1759	Trivial
16.0.170941269965602816.1	x^16 - 2x^15 + 10x^13 - 15x^12 - 2x^11 + 29x^10 - 28x^9 - 4x^8 + 28x^7 - 20x^6 - 8x^5 + 30x^4 - 32x^3 + 19x^2 - 6x + 1	\( 2^{16}\cdot 17\cdot 53\cdot 61\cdot 83^{4} \)	16T1759	Trivial
16.2.641424792100000000.1	x^16 - 2x^14 - 8x^12 + 16x^10 + 11x^8 - 18x^6 + 3x^4 - x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 283^{4} \)	16T1759	Trivial
16.6.6350601601600000000.1	x^16 - x^14 + 3x^12 - 13x^8 - 13x^6 + 4x^4 + 4x^2 - 1	\( -\,2^{12}\cdot 5^{8}\cdot 251^{4} \)	16T1759	Trivial
16.6.6350601601600000000.2	x^16 - 7x^14 + 25x^12 - 47x^10 + 43x^8 + 3x^6 - 27x^4 + 11x^2 - 1	\( -\,2^{12}\cdot 5^{8}\cdot 251^{4} \)	16T1759	Trivial
16.0.7404240787764450048.1	x^16 - 4x^14 + 18x^12 - 40x^10 + 64x^8 - 66x^6 + 45x^4 - 18x^2 + 3	\( 2^{8}\cdot 3^{13}\cdot 367^{4} \)	16T1759	Trivial
16.0.7404240787764450048.2	x^16 + 5x^14 + 12x^12 + 14x^10 + 10x^8 + 3x^6 + 6x^4 - 6x^2 + 3	\( 2^{8}\cdot 3^{13}\cdot 367^{4} \)	16T1759	Trivial
16.4.21242863936361005056.1	x^16 - 6x^15 + 17x^14 - 34x^13 + 57x^12 - 86x^11 + 116x^10 - 134x^9 + 139x^8 - 134x^7 + 116x^6 - 86x^5 + 57x^4 - 34x^3 + 17x^2 - 6x + 1	\( 2^{16}\cdot 3^{9}\cdot 83^{4}\cdot 347 \)	16T1759	Trivial (GRH)
16.4.23766692370831640625.1	x^16 - x^15 - 8x^14 + 14x^13 + 21x^12 - 51x^11 - 29x^10 + 122x^9 - 7x^8 - 155x^7 + 75x^6 + 80x^5 - 74x^4 + 20x^2 - 8x + 1	\( 5^{8}\cdot 251^{4}\cdot 15329 \)	16T1759	Trivial
16.6.108862157770788671875.1	x^16 - 2x^15 - 7x^14 + 15x^13 + 8x^12 - 20x^11 - 10x^10 + 12x^9 + 7x^8 + 12x^7 - 10x^6 - 20x^5 + 8x^4 + 15x^3 - 7x^2 - 2x + 1	\( -\,5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial
16.4.126859426136835751936.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 72x^12 - 68x^11 + 58x^10 - 48x^9 + 34x^8 - 24x^7 + 20x^6 - 12x^5 - 3x^4 + 12x^3 - 6x^2 + 1	\( 2^{32}\cdot 29^{4}\cdot 41761 \)	16T1759	Trivial
16.4.148362927650115107261.1	x^16 - 8x^15 + 29x^14 - 63x^13 + 92x^12 - 97x^11 + 85x^10 - 84x^9 + 91x^8 - 69x^7 + 13x^6 + 34x^5 - 36x^4 + 13x^3 + 3x^2 - 4x + 1	\( 17^{8}\cdot 43^{4}\cdot 6221 \)	16T1759	Trivial
16.6.157633109816006250000.1	x^16 - 4x^15 + x^14 + 11x^13 - 26x^12 + 24x^11 - 33x^9 + 48x^8 - 33x^7 + 24x^5 - 26x^4 + 11x^3 + x^2 - 4x + 1	\( -\,2^{4}\cdot 3^{12}\cdot 5^{8}\cdot 83^{4} \)	16T1759	Trivial (GRH)
16.4.161396650476620703125.1	x^16 - 3x^15 + 3x^14 + 4x^13 - 17x^12 + 22x^11 - 12x^10 + 4x^9 - 14x^8 + 46x^7 - 111x^6 + 212x^5 - 304x^4 + 267x^3 - 102x^2 + 2x + 1	\( 5^{8}\cdot 491^{4}\cdot 7109 \)	16T1759	Trivial
16.10.177617204783918359375.1	x^16 - 7x^15 + 16x^14 - 6x^13 - 37x^12 + 100x^11 - 141x^10 + 6x^9 + 314x^8 - 377x^7 + 31x^6 + 222x^5 - 167x^4 + 42x^3 + 12x^2 - 9x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 31\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.289846333495781640625.1	x^16 - 2x^15 + x^13 - 15x^12 + 18x^11 - 21x^10 - x^9 + 63x^8 - 43x^7 - 5x^6 + 23x^5 - 5x^4 - 6x^3 - 17x^2 + 9x - 1	\( 5^{8}\cdot 29\cdot 283^{4}\cdot 3989 \)	16T1759	Trivial (GRH)
16.10.338045647814554296875.1	x^16 - 4x^15 - 4x^14 + 29x^13 - 7x^12 - 59x^11 + 28x^10 + 27x^9 + 26x^8 - 15x^7 - 81x^6 + 42x^5 + 54x^4 - 16x^3 - 18x^2 - 5x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 59\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.349504822316742578125.1	x^16 - 8x^15 + 24x^14 - 24x^13 - 36x^12 + 113x^11 - 81x^10 + 20x^9 - 97x^8 - 9x^7 + 458x^6 - 471x^5 - 107x^4 + 320x^3 - 64x^2 - 56x + 16	\( 5^{8}\cdot 19^{4}\cdot 61\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.6.406800694827683984375.1	x^16 - 2x^15 - 6x^14 + 19x^13 - 23x^12 - 4x^11 + 59x^10 - 61x^9 - 96x^8 + 19x^7 + 123x^6 + 60x^5 - 45x^4 - 37x^3 + 2x^2 + 6x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 71\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.509933265347378515625.1	x^16 - 7x^15 + 10x^14 + 26x^13 - 55x^12 - 72x^11 + 155x^10 + 120x^9 - 223x^8 - 88x^7 + 216x^6 + 11x^5 - 122x^4 + 35x^3 + 17x^2 - 9x + 1	\( 5^{8}\cdot 19^{4}\cdot 89\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.578688312360508203125.1	x^16 - 7x^15 + 12x^14 + 21x^13 - 107x^12 + 157x^11 - 42x^10 - 196x^9 + 323x^8 - 196x^7 - 42x^6 + 157x^5 - 107x^4 + 21x^3 + 12x^2 - 7x + 1	\( 5^{8}\cdot 19^{4}\cdot 101\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.578688312360508203125.2	x^16 - 2x^15 - 7x^14 + 16x^13 + 10x^12 - 29x^11 - 17x^10 + 13x^9 + 82x^8 - 61x^7 - 29x^6 + 84x^5 - 124x^4 - 30x^3 + 85x^2 + 25x - 1	\( 5^{8}\cdot 19^{4}\cdot 101\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.10.750575929893332421875.1	x^16 - 3x^15 - 8x^14 + 22x^13 + 14x^12 - 60x^11 + 28x^10 + 69x^9 - 124x^8 - 8x^7 + 152x^6 - 55x^5 - 66x^4 + 41x^3 + 3x^2 - 6x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 103^{4}\cdot 131 \)	16T1759	Trivial (GRH)
16.10.796412627902085546875.1	x^16 - 8x^15 + 24x^14 - 25x^13 - 39x^12 + 137x^11 - 56x^10 - 231x^9 + 207x^8 + 200x^7 - 232x^6 - 84x^5 + 118x^4 + 14x^3 - 24x^2 - 2x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 103^{4}\cdot 139 \)	16T1759	Trivial (GRH)
16.8.853708500413026953125.1	x^16 - 4x^15 - 3x^14 + 42x^13 - 70x^12 - 27x^11 + 147x^10 - 38x^9 - 135x^8 + 204x^7 - 247x^6 + 252x^5 - 132x^4 - 3x^3 + 32x^2 - 11x + 1	\( 5^{8}\cdot 19^{4}\cdot 103^{4}\cdot 149 \)	16T1759	Trivial (GRH)
16.6.865167674915215234375.1	x^16 - 2x^15 - 9x^14 + 11x^13 + 57x^12 - 21x^11 - 235x^10 + 14x^9 + 498x^8 + 68x^7 - 473x^6 - 178x^5 + 215x^4 + 111x^3 - 73x^2 - 19x + 19	\( -\,5^{8}\cdot 19^{4}\cdot 103^{4}\cdot 151 \)	16T1759	Trivial (GRH)
16.10.979759419937098046875.1	x^16 - 3x^15 - 8x^14 + 27x^13 + 7x^12 - 69x^11 + 62x^10 + 52x^9 - 119x^8 + 52x^7 + 62x^6 - 69x^5 + 7x^4 + 27x^3 - 8x^2 - 3x + 1	\( -\,3^{2}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.4.1130736087846675808256.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 262x^12 - 480x^11 + 696x^10 - 796x^9 + 689x^8 - 400x^7 + 60x^6 + 172x^5 - 236x^4 + 176x^3 - 84x^2 + 24x - 2	\( 2^{40}\cdot 11^{4}\cdot 70241 \)	16T1759	Trivial
16.10.1140187862967733984375.1	x^16 - 5x^14 - 9x^13 - 34x^12 + 33x^11 + 172x^10 - 73x^9 - 224x^8 + 103x^7 + 62x^6 - 77x^5 + 51x^4 + 28x^3 - 24x^2 - 4x + 1	\( -\,5^{8}\cdot 19^{4}\cdot 103^{4}\cdot 199 \)	16T1759	Trivial (GRH)
16.2.1466774336280100000000.1	x^16 - x^15 - 5x^14 + 3x^13 + 17x^12 - 8x^11 - 40x^10 + 4x^9 + 88x^8 + 8x^7 - 160x^6 - 64x^5 + 272x^4 + 96x^3 - 320x^2 - 128x + 256	\( -\,2^{8}\cdot 5^{8}\cdot 19^{4}\cdot 103^{4} \)	16T1759	Trivial
16.6.1466774336280100000000.1	x^16 - 32x^12 + 2x^10 + 260x^8 + 8x^6 - 223x^4 - 76x^2 - 1	\( -\,2^{8}\cdot 5^{8}\cdot 19^{4}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.0.1594001002001600000000.1	x^16 - x^14 - 30x^12 + 11x^10 + 309x^8 + 236x^6 - 455x^4 - 251x^2 + 251	\( 2^{12}\cdot 5^{8}\cdot 251^{5} \)	16T1759	Trivial
16.8.1594001002001600000000.1	x^16 - 20x^14 + 157x^12 - 660x^10 + 1658x^8 - 2575x^6 + 2427x^4 - 1255x^2 + 251	\( 2^{12}\cdot 5^{8}\cdot 251^{5} \)	16T1759	Trivial (GRH)
16.14.2368558831812663574528.1	x^16 - 4x^15 - 8x^14 + 48x^13 + 4x^12 - 208x^11 + 106x^10 + 400x^9 - 290x^8 - 348x^7 + 202x^6 + 192x^5 + 33x^4 - 152x^3 - 2x^2 + 28x - 1	\( -\,2^{32}\cdot 223^{5} \)	16T1759	Trivial (GRH)
16.6.2368558831812663574528.1	x^16 - 4x^15 + 12x^13 - 2x^12 - 8x^11 - 58x^10 + 160x^9 - 135x^8 + 32x^7 - 50x^6 + 36x^4 + 28x^3 + 34x^2 - 4x - 1	\( -\,2^{32}\cdot 223^{5} \)	16T1759	Trivial
16.0.3201324299442626494464.1	x^16 + 8x^14 - 4x^13 + 32x^12 - 24x^11 + 56x^10 - 84x^9 + 39x^8 - 112x^7 - 4x^6 - 100x^5 + 186x^4 + 184x^3 + 116x^2 - 40x + 17	\( 2^{40}\cdot 3^{2}\cdot 41\cdot 53^{4} \)	16T1759	Trivial (GRH)
16.2.27868712389321900000000.1	x^16 - x^15 - 4x^14 + 13x^13 + 16x^12 - 39x^11 - 16x^10 + 94x^9 + 49x^8 - 52x^7 + 8x^6 + 89x^5 + 137x^4 - 51x^3 - 165x^2 - 189x - 101	\( -\,2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	$[2]$ (GRH)
16.12.27868712389321900000000.1	x^16 - x^14 - 23x^12 + 47x^10 + 94x^8 - 359x^6 + 373x^4 - 152x^2 + 19	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.4.27868712389321900000000.1	x^16 + 14x^14 + 72x^12 + 160x^10 + 103x^8 - 146x^6 - 225x^4 - 57x^2 + 19	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.27868712389321900000000.1	x^16 - x^14 - 45x^12 - 77x^10 + 300x^8 + 881x^6 + 451x^4 - 228x^2 + 19	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.12.27868712389321900000000.2	x^16 - x^15 - 21x^14 + 24x^13 + 154x^12 - 181x^11 - 518x^10 + 602x^9 + 859x^8 - 977x^7 - 663x^6 + 749x^5 + 137x^4 - 154x^3 - 20x^2 + 7x + 1	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.27868712389321900000000.2	x^16 - 8x^15 + 21x^14 - 3x^13 - 97x^12 + 210x^11 - 113x^10 - 175x^9 + 262x^8 - 99x^7 - 53x^6 + 37x^5 - 19x^4 + 86x^3 + 23x^2 - 13x + 1	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.12.27868712389321900000000.3	x^16 - 5x^15 + 3x^14 + 15x^13 - 15x^12 + 46x^11 - 162x^10 - 126x^9 + 631x^8 - 128x^7 - 606x^6 + 271x^5 + 184x^4 - 113x^3 - 6x^2 + 10x - 1	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.8.27868712389321900000000.3	x^16 - 6x^15 + 11x^14 + 11x^13 - 46x^12 - 25x^11 + 78x^10 + 231x^9 - 587x^8 + 357x^7 + 271x^6 - 564x^5 + 439x^4 - 186x^3 - 90x^2 + 127x - 31	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.12.27868712389321900000000.4	x^16 - 2x^15 - 12x^14 + 15x^13 + 67x^12 - 11x^11 - 281x^10 + 33x^9 + 392x^8 + 89x^7 - 199x^6 - 249x^5 + 64x^4 + 100x^3 - 5x^2 - 10x - 1	\( 2^{8}\cdot 5^{8}\cdot 19^{5}\cdot 103^{4} \)	16T1759	Trivial (GRH)
16.4.156767236777186781640625.1	x^16 - 8x^15 + 36x^14 - 112x^13 + 254x^12 - 432x^11 + 528x^10 - 396x^9 - 10x^8 + 524x^7 - 854x^6 + 832x^5 - 546x^4 + 238x^3 - 60x^2 + 5x + 1	\( 5^{8}\cdot 19^{4}\cdot 103^{4}\cdot 27361 \)	16T1759	Trivial (GRH)
16.14.170690133797345543359375.1	x^16 - 2x^15 - 19x^14 + 26x^13 + 130x^12 - 67x^11 - 463x^10 - 207x^9 + 1033x^8 + 924x^7 - 1394x^6 - 803x^5 + 937x^4 + 5x^3 - 100x^2 + 19x - 1	\( -\,5^{8}\cdot 19^{4}\cdot 31^{3}\cdot 103^{4} \)	16T1759	Trivial (GRH)