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
16.0.115549174227861504.3	x^16 - 3x^14 + 5x^12 - 4x^10 + 3x^8 - 4x^6 + 6x^4 - 4x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{2} \)	16T1553	Trivial
16.0.115549174227861504.4	x^16 - x^14 + x^12 - 2x^10 + 3x^8 - 4x^6 + 4x^4 - 2x^2 + 1	\( 2^{16}\cdot 3^{8}\cdot 13^{4}\cdot 97^{2} \)	16T1553	Trivial
16.0.239081881600000000.1	x^16 - 2x^15 - x^14 + 6x^13 - 3x^12 - 4x^11 - x^10 + 12x^9 - 4x^8 - 20x^7 + 31x^6 - 24x^5 + 15x^4 - 10x^3 + 6x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 191^{2} \)	16T1553	Trivial
16.0.1612290457600000000.1	x^16 + 4x^14 + 10x^12 + 16x^10 + 20x^8 + 18x^6 + 13x^4 + 6x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 31^{2} \)	16T1553	Trivial
16.4.1612290457600000000.1	x^16 - 4x^14 + 10x^12 - 16x^10 + 20x^8 - 18x^6 + 13x^4 - 6x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 31^{2} \)	16T1553	Trivial
16.4.1612290457600000000.2	x^16 + x^12 - 2x^10 + x^8 + 4x^6 - 3x^4 - 2x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 31^{2} \)	16T1553	Trivial
16.0.2073747458621440000.1	x^16 - 2x^15 - x^14 + 12x^13 - 18x^12 + 2x^11 + 32x^10 - 58x^9 + 65x^8 - 62x^7 + 64x^6 - 62x^5 + 48x^4 - 28x^3 + 21x^2 - 14x + 7	\( 2^{24}\cdot 5^{4}\cdot 7^{6}\cdot 41^{2} \)	16T1553	Trivial
16.0.3802344001600000000.1	x^16 - 2x^14 + 5x^12 - x^10 + 3x^8 - 6x^6 + 3x^2 + 1	\( 2^{12}\cdot 5^{8}\cdot 29^{2}\cdot 41^{4} \)	16T1553	Trivial
16.8.7763680146828515625.1	x^16 - 5x^15 + 6x^14 + 4x^13 - 10x^12 + 7x^11 - 30x^10 + 46x^9 + 32x^8 - 112x^7 + 29x^6 + 85x^5 - 37x^4 - 29x^3 + 10x^2 + 3x - 1	\( 3^{4}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1553	Trivial
16.8.7763680146828515625.2	x^16 - x^15 - 3x^14 + 3x^13 + 7x^12 + 12x^11 - 17x^10 - 40x^9 - 12x^8 + 21x^7 + 58x^6 + 26x^5 - 45x^4 - 25x^3 + 12x^2 + 5x - 1	\( 3^{4}\cdot 5^{8}\cdot 19^{2}\cdot 29^{4}\cdot 31^{2} \)	16T1553	Trivial
16.4.13233297817600000000.1	x^16 - 2x^15 - 6x^14 + 18x^13 + 3x^12 - 50x^11 + 34x^10 + 40x^9 - 50x^8 + 14x^7 + 12x^6 - 10x^5 - x^4 - 6x^3 + 12x^2 - 4x - 1	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 29^{2} \)	16T1553	Trivial
16.4.13233297817600000000.2	x^16 - 4x^15 + 6x^14 - 4x^13 - 7x^12 + 10x^11 - 26x^10 + 2x^9 - 2x^8 - 24x^7 + 2x^6 - 12x^5 - 16x^4 + 6x^3 - 4x^2 - 8x + 1	\( 2^{24}\cdot 5^{8}\cdot 7^{4}\cdot 29^{2} \)	16T1553	Trivial
16.0.13289232793600000000.1	x^16 - 2x^14 + 2x^10 + 5x^8 - 10x^6 + 8x^4 - 4x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 89^{2} \)	16T1553	Trivial
16.0.14580129684520960000.1	x^16 - 6x^15 + 11x^14 + 4x^13 - 37x^12 + 28x^11 + 47x^10 - 86x^9 + 5x^8 + 100x^7 - 70x^6 - 64x^5 + 92x^4 + 16x^3 - 56x^2 + 16	\( 2^{24}\cdot 5^{4}\cdot 7^{4}\cdot 761^{2} \)	16T1553	Trivial
16.0.60837504025600000000.1	x^16 - x^14 - 2x^10 + 3x^8 + 2x^6 + x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 29^{2}\cdot 41^{4} \)	16T1553	Trivial
16.0.157416167833600000000.1	x^16 - 6x^15 + 14x^14 - 10x^13 - 9x^12 + 34x^10 + 14x^9 - 99x^8 + 6x^7 + 130x^6 - 24x^5 - 84x^4 + 36x^3 + 20x^2 - 16x + 4	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 29^{2} \)	16T1553	Trivial
16.4.157416167833600000000.1	x^16 - 4x^15 + 4x^14 + 16x^13 - 59x^12 + 72x^11 + 24x^10 - 124x^9 - 41x^8 + 236x^7 - 38x^6 - 164x^5 - 42x^4 + 100x^3 + 20x^2 - 16x - 4	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 29^{2} \)	16T1553	Trivial
16.0.157416167833600000000.2	x^16 - 2x^15 + 6x^14 - 12x^13 + 5x^12 + 12x^11 - 2x^10 - 74x^9 + 223x^8 - 360x^7 + 432x^6 - 504x^5 + 548x^4 - 464x^3 + 272x^2 - 96x + 16	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 29^{2} \)	16T1553	Trivial
16.4.157416167833600000000.2	x^16 - 8x^15 + 32x^14 - 80x^13 + 137x^12 - 174x^11 + 170x^10 - 62x^9 - 229x^8 + 530x^7 - 438x^6 + 222x^4 - 108x^3 + 12x^2 - 8x + 4	\( 2^{24}\cdot 5^{8}\cdot 13^{4}\cdot 29^{2} \)	16T1553	Trivial
16.0.273390887084557860864.1	x^16 + 8x^14 - 8x^13 + 37x^12 - 60x^11 + 122x^10 - 152x^9 + 185x^8 - 152x^7 + 122x^6 - 60x^5 + 37x^4 - 8x^3 + 8x^2 + 1	\( 2^{32}\cdot 3^{4}\cdot 17^{4}\cdot 97^{2} \)	16T1553	$[2]$
16.8.273390887084557860864.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 70x^12 - 56x^11 + 20x^10 + 32x^9 - 70x^8 + 44x^7 - 6x^6 + 32x^5 - 21x^4 - 40x^3 + 18x^2 + 12x + 1	\( 2^{32}\cdot 3^{4}\cdot 17^{4}\cdot 97^{2} \)	16T1553	Trivial
16.4.1082318753641481109504.1	x^16 - 4x^15 + 6x^14 - 4x^13 - 15x^12 + 52x^11 - 50x^10 + 16x^9 - 73x^8 - 32x^7 - 32x^6 + 196x^5 + 255x^4 + 200x^3 + 56x^2 + 4x - 7	\( 2^{32}\cdot 3^{4}\cdot 17^{4}\cdot 193^{2} \)	16T1553	Trivial
16.4.1082318753641481109504.2	x^16 - 4x^15 + 24x^13 - 35x^12 - 40x^11 + 140x^10 - 52x^9 - 223x^8 + 332x^7 - 22x^6 - 332x^5 + 347x^4 - 196x^3 + 84x^2 - 32x + 1	\( 2^{32}\cdot 3^{4}\cdot 17^{4}\cdot 193^{2} \)	16T1553	Trivial
16.0.1384041365865574170624.1	x^16 - 2x^15 + 3x^14 - 8x^13 + 17x^12 + 8x^11 + 21x^10 + 50x^9 + 16x^8 + 50x^7 + 21x^6 + 8x^5 + 17x^4 - 8x^3 + 3x^2 - 2x + 1	\( 2^{28}\cdot 3^{8}\cdot 17^{4}\cdot 97^{2} \)	16T1553	$[2]$
16.8.1384041365865574170624.1	x^16 - 6x^14 - 4x^13 + 13x^12 - 16x^11 - 32x^10 + 72x^9 - 49x^8 - 80x^7 + 144x^6 - 48x^5 - 72x^4 + 80x^3 - 8x^2 - 16x + 4	\( 2^{28}\cdot 3^{8}\cdot 17^{4}\cdot 97^{2} \)	16T1553	Trivial
16.0.2378302218265600000000.1	x^16 + 7x^14 + 32x^12 + 150x^10 + 490x^8 + 924x^6 + 975x^4 + 539x^2 + 121	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{2} \)	16T1553	Trivial
16.8.2378302218265600000000.1	x^16 - 7x^14 + 32x^12 - 150x^10 + 490x^8 - 924x^6 + 975x^4 - 539x^2 + 121	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{2} \)	16T1553	Trivial (GRH)
16.8.2378302218265600000000.2	x^16 - 14x^14 + 80x^12 - 234x^10 + 385x^8 - 435x^6 + 447x^4 - 352x^2 + 121	\( 2^{16}\cdot 5^{8}\cdot 11^{6}\cdot 229^{2} \)	16T1553	Trivial (GRH)
16.0.2959540814761828515625.1	x^16 + 10x^14 - 9x^13 + 78x^12 - 34x^11 + 291x^10 - 97x^9 + 687x^8 + 865x^7 + 109x^6 + 1686x^5 + 2120x^4 + 1663x^3 + 782x^2 + 2196x + 3721	\( 5^{8}\cdot 11^{2}\cdot 29^{4}\cdot 97^{4} \)	16T1553	Trivial
16.8.5449523800392100000000.1	x^16 - 8x^15 + 29x^14 - 60x^13 + 32x^12 + 266x^11 - 1132x^10 + 2651x^9 - 4267x^8 + 4859x^7 - 3696x^6 + 1425x^5 + 365x^4 - 810x^3 + 412x^2 - 64x - 4	\( 2^{8}\cdot 5^{8}\cdot 11^{4}\cdot 13^{4}\cdot 19^{4} \)	16T1553	Trivial
16.0.18985929775513600000000.1	x^16 + 10x^14 + 20x^12 - 36x^10 - 112x^8 + 40x^6 + 264x^4 + 176x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.12.18985929775513600000000.1	x^16 - 10x^14 + 20x^12 + 36x^10 - 112x^8 - 40x^6 + 264x^4 - 176x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial (GRH)
16.4.18985929775513600000000.1	x^16 - 12x^14 + 60x^12 - 172x^10 + 320x^8 - 424x^6 + 312x^4 - 112x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.8.18985929775513600000000.1	x^16 - 10x^14 + 30x^12 + 8x^10 - 212x^8 + 400x^6 - 264x^4 + 32x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial (GRH)
16.0.18985929775513600000000.2	x^16 + 4x^14 + 4x^12 + 12x^10 + 52x^8 + 56x^6 + 16x^4 + 48x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.12.18985929775513600000000.2	x^16 - 12x^14 + 56x^12 - 140x^10 + 248x^8 - 368x^6 + 360x^4 - 160x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial (GRH)
16.4.18985929775513600000000.2	x^16 + 2x^14 - 12x^12 - 44x^10 - 72x^8 - 88x^6 - 48x^4 + 16x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.8.18985929775513600000000.2	x^16 - 2x^14 - 12x^12 + 44x^10 - 72x^8 + 88x^6 - 48x^4 - 16x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial (GRH)
16.0.18985929775513600000000.3	x^16 + 4x^14 + 10x^12 + 36x^10 + 60x^8 + 8x^6 - 72x^4 + 16x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.4.18985929775513600000000.3	x^16 - 4x^14 + 4x^12 - 12x^10 + 52x^8 - 56x^6 + 16x^4 - 48x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.8.18985929775513600000000.3	x^16 - 6x^14 - 6x^12 + 40x^10 - 12x^8 - 24x^6 + 40x^4 - 80x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial (GRH)
16.0.18985929775513600000000.4	x^16 + 12x^14 + 56x^12 + 140x^10 + 248x^8 + 368x^6 + 360x^4 + 160x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.4.18985929775513600000000.4	x^16 + 10x^14 + 30x^12 - 8x^10 - 212x^8 - 400x^6 - 264x^4 - 32x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.0.18985929775513600000000.5	x^16 + 2x^14 - 4x^12 + 4x^10 - 8x^8 + 8x^6 - 16x^4 + 16x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.4.18985929775513600000000.5	x^16 - 4x^14 + 10x^12 - 36x^10 + 60x^8 - 8x^6 - 72x^4 - 16x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.4.18985929775513600000000.6	x^16 + 6x^14 + 12x^12 + 12x^10 - 12x^8 - 104x^6 - 112x^4 + 32x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.4.18985929775513600000000.7	x^16 - 2x^14 - 4x^12 - 4x^10 - 8x^8 - 8x^6 - 16x^4 - 16x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.4.18985929775513600000000.8	x^16 + 6x^14 - 6x^12 - 40x^10 - 12x^8 + 24x^6 + 40x^4 + 80x^2 + 16	\( 2^{36}\cdot 5^{8}\cdot 29^{4} \)	16T1553	Trivial
16.0.1119809073498348998098944.1	x^16 - 4x^15 + 16x^14 - 28x^13 + 64x^12 - 92x^11 + 192x^10 - 212x^9 + 454x^8 - 940x^7 + 2368x^6 - 3716x^5 + 4192x^4 - 2804x^3 + 944x^2 - 44x + 1	\( 2^{44}\cdot 3^{4}\cdot 17^{4}\cdot 97^{2} \)	16T1553	$[2, 4]$
16.12.1119809073498348998098944.1	x^16 - 20x^14 - 28x^13 + 92x^12 + 248x^11 + 48x^10 - 516x^9 - 752x^8 - 216x^7 + 396x^6 + 324x^5 - 12x^4 - 80x^3 - 16x^2 + 4x + 1	\( 2^{44}\cdot 3^{4}\cdot 17^{4}\cdot 97^{2} \)	16T1553	Trivial