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 62)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.161956496702767104.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 29x^12 + 8x^11 - 27x^10 + 14x^9 + 6x^8 - 20x^7 + 21x^6 - 4x^5 - 8x^4 + 4x^3 + 1	\( 2^{16}\cdot 3^{8}\cdot 13\cdot 73^{2}\cdot 5437 \)	16T1769	Trivial
16.0.171163247133589504.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 158x^12 - 220x^11 + 224x^10 - 152x^9 + 44x^8 + 32x^7 - 34x^6 - 12x^5 + 51x^4 - 52x^3 + 28x^2 - 8x + 1	\( 2^{32}\cdot 113^{2}\cdot 3121 \)	16T1769	Trivial
16.2.1612290457600000000.3	x^16 + 6x^14 + 15x^12 + 22x^10 + 32x^8 + 30x^6 + 17x^4 + 2x^2 - 1	\( -\,2^{32}\cdot 5^{8}\cdot 31^{2} \)	16T1769	Trivial
16.2.2104170905600000000.1	x^16 - 6x^15 + 19x^14 - 38x^13 + 51x^12 - 46x^11 + 22x^10 + 8x^9 - 29x^8 + 30x^7 - 20x^6 + 16x^5 - 4x^4 - 8x^3 + 4x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 41^{2}\cdot 191 \)	16T1769	Trivial
16.0.4792785305600000000.1	x^16 - 2x^15 + 5x^14 - 8x^13 + 10x^12 - 12x^11 + 6x^10 + 2x^9 - 7x^8 + 16x^7 - 11x^6 + 6x^5 + 5x^4 - 14x^3 + 10x^2 - 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 31^{2}\cdot 761 \)	16T1769	Trivial
16.4.9802357145600000000.1	x^16 - 2x^15 - x^14 + 12x^13 - 34x^12 + 50x^11 - 22x^10 - 50x^9 + 91x^8 - 50x^7 - 22x^6 + 50x^5 - 34x^4 + 12x^3 - x^2 - 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 41\cdot 191^{2} \)	16T1769	Trivial
16.2.10470660505600000000.1	x^16 + 2x^14 - x^12 - 6x^10 - 2x^8 - 10x^6 + 3x^4 - 2x^2 - 1	\( -\,2^{32}\cdot 5^{8}\cdot 79^{2} \)	16T1769	Trivial
16.6.13314398617600000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 80x^12 - 116x^11 + 178x^10 - 208x^9 + 130x^8 + 24x^7 - 116x^6 + 84x^5 - 11x^4 - 20x^3 + 10x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 31 \)	16T1769	Trivial
16.4.25140926873600000000.1	x^16 - 2x^15 - x^14 + 6x^13 - 6x^12 + 16x^11 - 17x^10 - 20x^9 + 29x^8 + 14x^7 + 13x^6 - 80x^5 + 45x^4 + 22x^3 - 44x^2 + 24x - 9	\( 2^{24}\cdot 5^{8}\cdot 71^{2}\cdot 761 \)	16T1769	Trivial
16.0.31125674393600000000.1	x^16 - 4x^15 + 8x^14 - 10x^13 + 18x^11 - 3x^10 - 22x^9 + 5x^8 + 16x^7 + 5x^6 - 26x^5 + x^4 + 24x^3 - 8x^2 - 8x + 4	\( 2^{24}\cdot 5^{8}\cdot 79^{2}\cdot 761 \)	16T1769	Trivial
16.6.33930241638400000000.1	x^16 - 8x^15 + 32x^14 - 76x^13 + 96x^12 + 12x^11 - 332x^10 + 760x^9 - 997x^8 + 844x^7 - 448x^6 + 160x^5 - 86x^4 + 76x^3 - 44x^2 + 12x - 1	\( -\,2^{40}\cdot 5^{8}\cdot 79 \)	16T1769	Trivial
16.0.39504320921600000000.1	x^16 - 4x^15 + 10x^14 - 12x^13 + 10x^12 - 2x^11 + 12x^10 - 26x^9 + 49x^8 - 38x^7 + 33x^6 - 14x^5 + 20x^4 - 6x^3 + 5x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{2}\cdot 761 \)	16T1769	Trivial
16.0.39504320921600000000.2	x^16 - 2x^15 + 5x^14 - 14x^13 + 28x^12 - 54x^11 + 79x^10 - 90x^9 + 87x^8 - 50x^7 + 6x^6 + 22x^5 - 32x^4 + 8x^3 + 10x^2 - 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 89^{2}\cdot 761 \)	16T1769	Trivial
16.6.42733397606400000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 25x^12 + 32x^11 - 79x^10 + 54x^9 + 25x^8 - 72x^7 + 39x^6 + 28x^5 - 42x^4 + 10x^3 + 9x^2 - 6x + 1	\( -\,2^{24}\cdot 3^{2}\cdot 5^{8}\cdot 41^{2}\cdot 431 \)	16T1769	Trivial
16.4.49981004185600000000.3	x^16 - 6x^15 + 11x^14 + 2x^13 - 28x^12 + 30x^11 - 9x^10 - 10x^9 + 25x^8 - 72x^7 + 34x^6 + 12x^5 - 50x^4 + 32x^3 - 4x^2 - 8x + 4	\( 2^{32}\cdot 5^{8}\cdot 31^{3} \)	16T1769	Trivial
16.6.53644879462400000000.1	x^16 - 4x^15 + 2x^14 + 18x^13 - 48x^12 + 42x^11 + 35x^10 - 146x^9 + 199x^8 - 146x^7 + 35x^6 + 42x^5 - 48x^4 + 18x^3 + 2x^2 - 4x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 151^{2}\cdot 359 \)	16T1769	Trivial
16.2.97443748249600000000.1	x^16 + 4x^14 + 19x^8 - 28x^6 - 22x^4 - 4x^2 - 1	\( -\,2^{32}\cdot 5^{8}\cdot 241^{2} \)	16T1769	Trivial
16.4.103508711833600000000.2	x^16 + 2x^14 - 8x^13 - 5x^12 - 12x^11 + 22x^10 + 20x^9 + x^8 - 36x^7 - 28x^6 + 40x^5 + 24x^4 - 8x^3 - 16x^2 + 4	\( 2^{40}\cdot 5^{8}\cdot 241 \)	16T1769	Trivial
16.4.113715190169600000000.1	x^16 - 4x^15 + 16x^14 - 42x^13 + 100x^12 - 194x^11 + 335x^10 - 514x^9 + 665x^8 - 810x^7 + 787x^6 - 722x^5 + 506x^4 - 290x^3 + 114x^2 - 20x + 1	\( 2^{24}\cdot 5^{8}\cdot 151^{2}\cdot 761 \)	16T1769	Trivial
16.8.113715190169600000000.1	x^16 - 6x^14 - 10x^13 + 18x^12 + 26x^11 - 5x^10 - 72x^9 + 31x^8 + 84x^7 - 121x^6 + 98x^5 - 65x^4 + 20x^3 + 7x^2 - 6x + 1	\( 2^{24}\cdot 5^{8}\cdot 151^{2}\cdot 761 \)	16T1769	Trivial (GRH)
16.4.113715190169600000000.2	x^16 - 4x^15 + 8x^14 - 14x^13 + 24x^12 - 38x^11 + 51x^10 - 62x^9 + 77x^8 - 54x^7 - 19x^6 + 50x^5 - 8x^4 - 18x^3 + 4x + 1	\( 2^{24}\cdot 5^{8}\cdot 151^{2}\cdot 761 \)	16T1769	Trivial
16.6.117655148953600000000.1	x^16 - 6x^15 + 11x^14 - 2x^13 - 22x^12 + 36x^11 - 17x^10 - 20x^9 + 39x^8 - 20x^7 - 17x^6 + 36x^5 - 22x^4 - 2x^3 + 11x^2 - 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 31\cdot 761^{2} \)	16T1769	Trivial
16.6.127539812761600000000.1	x^16 - 2x^15 - 5x^14 + 6x^13 + 19x^12 + 6x^11 - 76x^10 - 24x^9 + 149x^8 + 20x^7 - 140x^6 - 50x^5 + 37x^4 + 54x^3 + 29x^2 + 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 151\cdot 359^{2} \)	16T1769	Trivial
16.8.181941311897600000000.1	x^16 - 6x^14 - 6x^13 + 19x^12 + 38x^11 - 29x^10 - 108x^9 - 17x^8 + 178x^7 + 92x^6 - 152x^5 - 74x^4 + 52x^3 + 15x^2 - 6x - 1	\( 2^{24}\cdot 5^{8}\cdot 191^{2}\cdot 761 \)	16T1769	Trivial (GRH)
16.10.269468244377600000000.1	x^16 - 4x^14 - 8x^13 - 4x^12 + 40x^11 + 22x^10 - 24x^9 - 64x^8 + 124x^6 - 52x^5 - 75x^4 + 32x^3 + 16x^2 - 4x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 71\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.6.299830863462400000000.1	x^16 - 2x^15 - 3x^14 - 2x^13 + 4x^12 + 12x^11 + 13x^10 + 12x^9 + 9x^8 + 12x^7 + 13x^6 + 12x^5 + 4x^4 - 2x^3 - 3x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 79\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.4.337784137318400000000.1	x^16 - 6x^15 + 17x^14 - 20x^13 - 11x^12 + 66x^11 - 85x^10 + 20x^9 + 69x^8 - 168x^7 + 237x^6 - 102x^5 - 16x^4 - 6x^3 + 18x^2 - 4x - 1	\( 2^{24}\cdot 5^{8}\cdot 89\cdot 761^{2} \)	16T1769	Trivial
16.4.337784137318400000000.2	x^16 - 8x^15 + 42x^14 - 154x^13 + 437x^12 - 984x^11 + 1793x^10 - 2662x^9 + 3211x^8 - 3120x^7 + 2387x^6 - 1384x^5 + 562x^4 - 130x^3 + 3x^2 + 6x - 1	\( 2^{24}\cdot 5^{8}\cdot 89\cdot 761^{2} \)	16T1769	Trivial
16.6.537420808551376355328.1	x^16 - 4x^10 - 5x^8 + 10x^4 + 4x^2 - 2	\( -\,2^{41}\cdot 3^{8}\cdot 193^{2} \)	16T1769	Trivial
16.10.573094435225600000000.1	x^16 - 2x^15 - 11x^14 + 16x^13 + 57x^12 - 54x^11 - 147x^10 + 96x^9 + 142x^8 - 58x^7 - 46x^6 + 102x^5 - 61x^4 - 70x^3 + 17x^2 + 10x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 151\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.6.573094435225600000000.1	x^16 - 6x^15 + 11x^14 - 2x^13 - 17x^12 + 26x^11 - 22x^10 + 20x^9 - 21x^8 + 20x^7 - 22x^6 + 26x^5 - 17x^4 - 2x^3 + 11x^2 - 6x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 151\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.6.573094435225600000000.2	x^16 - 4x^15 + 4x^14 + 10x^13 - 40x^12 + 58x^11 - 9x^10 - 154x^9 + 303x^8 - 106x^7 - 359x^6 + 438x^5 - 34x^4 - 178x^3 + 98x^2 - 20x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 151\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.10.724907530649600000000.1	x^16 - 4x^15 - 4x^14 + 36x^13 - 32x^12 - 24x^11 - 12x^10 + 26x^9 + 87x^8 - 24x^7 - 48x^6 - 42x^5 + 15x^4 + 34x^3 - x^2 - 6x - 1	\( -\,2^{24}\cdot 5^{8}\cdot 191\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.10.755270149734400000000.1	x^16 - 6x^15 + 9x^14 + 6x^13 - 27x^12 + 44x^11 - 36x^10 - 118x^9 + 202x^8 + 140x^7 - 280x^6 - 84x^5 + 150x^4 + 24x^3 - 25x^2 - 2x + 1	\( -\,2^{24}\cdot 5^{8}\cdot 199\cdot 761^{2} \)	16T1769	Trivial (GRH)
16.8.1425696652737330020352.1	x^16 - 8x^14 - 8x^13 + 28x^12 + 32x^11 - 12x^10 - 80x^9 - 37x^8 + 24x^7 + 208x^6 - 88x^5 - 206x^4 + 136x^3 + 20x^2 - 16x - 2	\( 2^{50}\cdot 3^{8}\cdot 193 \)	16T1769	Trivial (GRH)
16.8.1656139389337600000000.1	x^16 - 16x^14 - 8x^13 + 74x^12 + 112x^11 - 136x^10 - 408x^9 + 75x^8 + 480x^7 + 264x^6 - 232x^5 - 350x^4 - 32x^3 + 88x^2 + 48x + 9	\( 2^{44}\cdot 5^{8}\cdot 241 \)	16T1769	Trivial (GRH)
16.4.1865870796390400000000.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 207x^12 - 332x^11 + 407x^10 - 374x^9 + 246x^8 - 104x^7 + 21x^6 - 2x^5 - 2x^4 + 10x^3 - 14x^2 + 8x + 1	\( 2^{24}\cdot 5^{8}\cdot 41^{2}\cdot 169369 \)	16T1769	Trivial
16.10.9792954931609600000000.1	x^16 - 6x^14 + 15x^12 - 52x^10 + 105x^8 - 84x^6 + 21x^4 + 2x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 151^{2} \)	16T1769	Trivial (GRH)
16.2.9792954931609600000000.1	x^16 - 12x^12 - 10x^10 + 20x^8 - 49x^4 - 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 151^{2} \)	16T1769	Trivial
16.10.9792954931609600000000.2	x^16 - 12x^12 + 10x^10 + 20x^8 - 49x^4 + 30x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 151^{2} \)	16T1769	Trivial (GRH)
16.2.9792954931609600000000.2	x^16 + 6x^14 + 15x^12 + 52x^10 + 105x^8 + 84x^6 + 21x^4 - 2x^2 - 1	\( -\,2^{40}\cdot 5^{8}\cdot 151^{2} \)	16T1769	Trivial
16.8.11841095080345600000000.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 101x^12 + 60x^11 + 191x^10 - 218x^9 - 146x^8 + 264x^7 + 13x^6 - 118x^5 + 30x^4 - 14x^3 - 10x^2 + 24x + 9	\( 2^{24}\cdot 5^{8}\cdot 41^{2}\cdot 569\cdot 1889 \)	16T1769	Trivial (GRH)
16.4.11845886286233600000000.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 164x^12 - 256x^11 + 334x^10 - 372x^9 + 352x^8 - 276x^7 + 172x^6 - 80x^5 + 17x^4 + 12x^3 - 16x^2 + 8x - 1	\( 2^{24}\cdot 5^{8}\cdot 241^{2}\cdot 31121 \)	16T1769	Trivial (GRH)
16.12.49987720634880296484864.1	x^16 - 8x^15 + 20x^14 - 70x^12 + 56x^11 + 104x^10 - 80x^9 - 164x^8 + 36x^7 + 246x^6 + 4x^5 - 197x^4 - 24x^3 + 60x^2 + 16x + 1	\( 2^{32}\cdot 3^{8}\cdot 47^{2}\cdot 803041 \)	16T1769	Trivial (GRH)
16.12.62125713974886400000000.1	x^16 - 8x^15 + 16x^14 + 28x^13 - 130x^12 + 52x^11 + 290x^10 - 306x^9 - 215x^8 + 408x^7 - 18x^6 - 210x^5 + 81x^4 + 34x^3 - 25x^2 + 2x + 1	\( 2^{24}\cdot 5^{8}\cdot 761^{2}\cdot 16369 \)	16T1769	Trivial (GRH)
16.12.83530755611033600000000.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 101x^12 + 60x^11 + 179x^10 - 158x^9 - 204x^8 + 136x^7 + 221x^6 - 42x^5 - 168x^4 - 14x^3 + 54x^2 + 12x - 1	\( 2^{24}\cdot 5^{8}\cdot 151^{2}\cdot 559001 \)	16T1769	Trivial (GRH)
16.0.83672834873753600000000.1	x^16 + 12x^14 - 8x^13 + 44x^12 + 16x^11 + 100x^10 + 64x^9 + 168x^8 + 224x^7 + 132x^6 + 232x^5 + 496x^4 - 80x^3 + 572x^2 - 128x + 431	\( 2^{48}\cdot 5^{8}\cdot 761 \)	16T1769	Trivial (GRH)
16.0.83672834873753600000000.2	x^16 - 16x^13 - 2x^12 + 16x^11 + 96x^10 + 16x^9 - 203x^8 - 272x^7 + 432x^6 + 664x^5 - 238x^4 - 888x^3 - 296x^2 + 400x + 569	\( 2^{48}\cdot 5^{8}\cdot 761 \)	16T1769	Trivial (GRH)
16.8.169717007705702400000000.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 18x^12 + 108x^11 - 152x^10 + 56x^9 + 118x^8 - 192x^7 + 106x^6 + 20x^5 - 59x^4 + 28x^3 - 4x + 1	\( 2^{24}\cdot 3^{4}\cdot 5^{8}\cdot 281^{2}\cdot 4049 \)	16T1769	Trivial (GRH)
16.8.173998144592281600000000.1	x^16 - 18x^14 + 137x^12 - 572x^10 + 1423x^8 - 2152x^6 + 1947x^4 - 998x^2 + 241	\( 2^{40}\cdot 5^{8}\cdot 41^{2}\cdot 241 \)	16T1769	Trivial (GRH)