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
16.2.194097037021484375.1	x^16 - 3x^15 + 3x^14 - 6x^12 + 10x^11 - 2x^10 - 6x^9 + 7x^8 + 9x^7 - 4x^6 - 12x^5 + 7x^4 + 7x^3 - 4x^2 - 3x + 1	\( -\,5^{10}\cdot 101^{4}\cdot 191 \)	16T1776	Trivial
16.0.3277882760000000000.1	x^16 - x^15 + 3x^14 + x^13 + 7x^12 - 4x^11 + 8x^10 + 9x^9 + 18x^8 + 8x^7 + 32x^6 + 23x^5 + 27x^4 + 7x^3 + 7x^2 + 2x + 1	\( 2^{12}\cdot 5^{10}\cdot 29\cdot 41^{4} \)	16T1776	Trivial
16.0.3277882760000000000.2	x^16 - 5x^15 + 10x^14 - 11x^13 + 9x^12 + x^11 - 26x^10 + 23x^9 + 28x^8 - 23x^7 - 26x^6 - x^5 + 9x^4 + 11x^3 + 10x^2 + 5x + 1	\( 2^{12}\cdot 5^{10}\cdot 29\cdot 41^{4} \)	16T1776	Trivial
16.6.4852425925537109375.1	x^16 - 5x^15 + 7x^14 - 3x^13 + 7x^12 - 2x^11 - 31x^10 + 46x^9 - 40x^8 + 34x^7 - 13x^6 + x^5 + 12x^4 - 32x^3 + 27x^2 - 9x + 1	\( -\,5^{12}\cdot 101^{4}\cdot 191 \)	16T1776	Trivial
16.4.12793128790908203125.1	x^16 - 8x^15 + 33x^14 - 91x^13 + 183x^12 - 279x^11 + 324x^10 - 278x^9 + 155x^8 - 19x^7 - 64x^6 + 76x^5 - 43x^4 + 9x^3 + 5x^2 - 4x + 1	\( 5^{10}\cdot 101^{4}\cdot 12589 \)	16T1776	Trivial
16.8.38260057887119140625.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 100x^12 + 54x^11 + 197x^10 - 193x^9 - 193x^8 + 236x^7 + 106x^6 - 128x^5 - 40x^4 + 27x^3 + 11x^2 - 2x - 1	\( 5^{10}\cdot 7^{4}\cdot 19^{5}\cdot 659 \)	16T1776	Trivial (GRH)
16.0.38311352526520188928.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 29x^12 + 8x^11 - 29x^10 + 24x^9 - 10x^8 - 16x^7 + 33x^6 - 12x^5 - 11x^4 + 8x^3 + x^2 - 2x + 1	\( 2^{34}\cdot 47^{4}\cdot 457 \)	16T1776	Trivial
16.4.49211583122119140625.1	x^16 - 8x^15 + 34x^14 - 98x^13 + 208x^12 - 338x^11 + 425x^10 - 409x^9 + 289x^8 - 132x^7 + 18x^6 + 24x^5 - 24x^4 + 15x^3 - 11x^2 + 6x - 1	\( 5^{11}\cdot 7^{4}\cdot 19^{4}\cdot 3221 \)	16T1776	Trivial
16.2.66598656640000000000.1	x^16 + 4x^14 + 2x^12 - 11x^10 - 24x^8 - 25x^6 - 13x^4 - 4x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 101^{4} \)	16T1776	Trivial
16.6.66598656640000000000.1	x^16 - 4x^14 + 2x^12 + 11x^10 - 24x^8 + 25x^6 - 13x^4 + 4x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.4.90475365703994140625.1	x^16 - 2x^15 + 9x^13 - 16x^12 + 6x^11 + 24x^10 - 40x^9 + 8x^8 + 49x^7 - 67x^6 + 26x^5 + 26x^4 - 42x^3 + 26x^2 - 8x + 1	\( 5^{10}\cdot 7^{4}\cdot 19^{4}\cdot 29\cdot 1021 \)	16T1776	Trivial (GRH)
16.2.99674642579677734375.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 157x^12 - 214x^11 + 208x^10 - 127x^9 + 18x^8 + 52x^7 - 57x^6 + 26x^5 - 5x^4 + 3x^3 - 6x^2 + 4x - 1	\( -\,3^{4}\cdot 5^{10}\cdot 59^{4}\cdot 10399 \)	16T1776	Trivial
16.4.105569354742431640625.1	x^16 - 2x^15 - 6x^14 + 3x^13 + 13x^12 - 2x^11 - 19x^10 - 6x^9 + 53x^8 + 33x^7 - 41x^6 + 24x^5 + 38x^4 - 9x^3 + x^2 - x + 1	\( 5^{14}\cdot 41^{4}\cdot 6121 \)	16T1776	Trivial
16.8.118268100867001953125.1	x^16 - 8x^15 + 25x^14 - 35x^13 + 8x^12 + 43x^11 - 60x^10 + 25x^9 + 14x^8 - 19x^7 + 7x^6 - 4x^5 + 6x^4 - 4x^3 - 2x^2 + 3x + 1	\( 5^{10}\cdot 101^{4}\cdot 116381 \)	16T1776	Trivial (GRH)
16.2.200256461440000000000.1	x^16 - 2x^14 + 3x^12 + 19x^10 - 4x^8 - 30x^6 - 20x^4 - 7x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{4} \)	16T1776	Trivial
16.6.200256461440000000000.1	x^16 - 9x^14 + 32x^12 - 54x^10 + 46x^8 - 25x^6 + 12x^4 - x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{4} \)	16T1776	Trivial (GRH)
16.6.200256461440000000000.2	x^16 - 2x^14 + 2x^12 - 5x^10 + 14x^8 - 33x^6 + 32x^4 - 7x^2 - 1	\( -\,2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{4} \)	16T1776	Trivial (GRH)
16.0.342379331200000000000.1	x^16 - 8x^15 + 20x^14 - 67x^12 + 38x^11 + 139x^10 - 90x^9 - 209x^8 + 78x^7 + 247x^6 + 10x^5 - 180x^4 - 98x^3 + 49x^2 + 70x + 25	\( 2^{16}\cdot 5^{11}\cdot 19^{4}\cdot 821 \)	16T1776	Trivial
16.4.732065035021923828125.1	x^16 - 8x^15 + 27x^14 - 49x^13 + 46x^12 - 3x^11 - 52x^10 + 73x^9 - 50x^8 + 15x^7 + 3x^6 - 4x^5 - 2x^4 + 6x^3 - 4x^2 + x + 1	\( 5^{11}\cdot 61\cdot 181^{4}\cdot 229 \)	16T1776	Trivial (GRH)
16.8.1194886765275595703125.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 111x^12 + 29x^11 + 270x^10 - 162x^9 - 377x^8 + 225x^7 + 354x^6 - 128x^5 - 211x^4 + 5x^3 + 55x^2 + 20x + 5	\( 5^{10}\cdot 101^{4}\cdot 1175821 \)	16T1776	Trivial (GRH)
16.0.2956702521675048828125.1	x^16 - 6x^15 + 31x^14 - 99x^13 + 279x^12 - 578x^11 + 1082x^10 - 1542x^9 + 2099x^8 - 2241x^7 + 2596x^6 - 2287x^5 + 2053x^4 - 1068x^3 + 526x^2 - 36x + 1	\( 5^{12}\cdot 101^{4}\cdot 116381 \)	16T1776	$[4]$
16.10.3662926115200000000000.1	x^16 - 4x^15 + x^14 - 2x^13 + 36x^12 - 28x^11 - 26x^10 - 30x^9 + 52x^8 + 82x^7 - 125x^6 + 22x^5 + 59x^4 - 46x^3 + 6x^2 + 4x - 1	\( -\,2^{16}\cdot 5^{11}\cdot 11\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.6.3662926115200000000000.1	x^16 - 4x^15 - x^14 + 18x^13 - 32x^12 + 20x^11 + 15x^10 - 48x^9 + 61x^8 - 48x^7 + 15x^6 + 20x^5 - 32x^4 + 18x^3 - x^2 - 4x + 1	\( -\,2^{16}\cdot 5^{11}\cdot 11\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.0.3804872767360000000000.1	x^16 + 4x^14 - 7x^12 - 10x^10 + 69x^8 + 61x^6 + 23x^4 + 171x^2 + 19	\( 2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{5} \)	16T1776	Trivial
16.4.3804872767360000000000.1	x^16 - 6x^14 + 7x^12 + 4x^10 - 29x^8 + 35x^6 - 13x^4 - 19x^2 + 19	\( 2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{5} \)	16T1776	Trivial (GRH)
16.8.3804872767360000000000.1	x^16 - 10x^14 + 30x^12 - 93x^10 + 206x^8 - 285x^6 + 251x^4 - 114x^2 + 19	\( 2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{5} \)	16T1776	Trivial (GRH)
16.0.3804872767360000000000.2	x^16 + 5x^14 + 5x^12 - 13x^10 - 29x^8 + 10x^6 + 81x^4 + 76x^2 + 19	\( 2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{5} \)	16T1776	Trivial
16.4.3804872767360000000000.2	x^16 - 8x^14 + 18x^12 + 33x^10 - 229x^8 + 415x^6 - 307x^4 + 57x^2 + 19	\( 2^{16}\cdot 5^{10}\cdot 7^{4}\cdot 19^{5} \)	16T1776	Trivial (GRH)
16.10.4728504621440000000000.1	x^16 - 16x^14 - 10x^13 + 55x^12 + 44x^11 - 67x^10 - 112x^9 - 59x^8 + 62x^7 + 82x^6 + 12x^5 + 9x^4 - 10x^3 - 25x^2 + 5	\( -\,2^{16}\cdot 5^{10}\cdot 71\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.6.4728504621440000000000.1	x^16 - 4x^15 + 10x^14 - 30x^13 + 35x^12 - 32x^11 - 46x^10 + 150x^9 - 334x^8 + 398x^7 - 204x^6 - 124x^5 + 429x^4 - 538x^3 + 640x^2 - 444x + 109	\( -\,2^{16}\cdot 5^{10}\cdot 71\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.12.5927280440960000000000.1	x^16 - 8x^15 + 24x^14 - 28x^13 - 21x^12 + 126x^11 - 177x^10 + 16x^9 + 252x^8 - 290x^7 + 31x^6 + 222x^5 - 156x^4 - 50x^3 + 52x^2 + 6x - 1	\( 2^{16}\cdot 5^{10}\cdot 89\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.8.5927280440960000000000.1	x^16 - 8x^15 + 25x^14 - 18x^13 - 125x^12 + 470x^11 - 787x^10 + 676x^9 - 112x^8 - 386x^7 + 439x^6 - 308x^5 + 235x^4 - 122x^3 + 16x^2 + 6x - 1	\( 2^{16}\cdot 5^{10}\cdot 89\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.4.9656805212800000000000.1	x^16 - 4x^15 - 6x^14 + 28x^13 - 27x^12 + 10x^10 + 12x^9 - 29x^8 + 12x^7 + 10x^6 - 27x^4 + 28x^3 - 6x^2 - 4x + 1	\( 2^{16}\cdot 5^{11}\cdot 29\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.8.9656805212800000000000.1	x^16 - 4x^15 + x^14 + 18x^13 - 49x^12 + 12x^11 + 214x^10 - 200x^9 - 458x^8 + 342x^7 + 475x^6 - 138x^5 - 121x^4 + 24x^3 + x^2 + 4x - 1	\( 2^{16}\cdot 5^{11}\cdot 29\cdot 101^{4} \)	16T1776	Trivial (GRH)
16.2.11473438035052230344704.1	x^16 + 8x^14 + 30x^12 + 68x^10 + 87x^8 + 44x^6 - 28x^4 - 48x^2 - 16	\( -\,2^{46}\cdot 113^{4} \)	16T1776	Trivial
16.6.11473438035052230344704.1	x^16 + 2x^14 - 15x^12 + 14x^10 - 18x^8 + 54x^6 - 45x^4 + 10x^2 - 1	\( -\,2^{46}\cdot 113^{4} \)	16T1776	Trivial (GRH)
16.2.11473438035052230344704.2	x^16 - 2x^14 - 15x^12 - 14x^10 - 18x^8 - 54x^6 - 45x^4 - 10x^2 - 1	\( -\,2^{46}\cdot 113^{4} \)	16T1776	Trivial (GRH)
16.6.11473438035052230344704.2	x^16 - 8x^14 + 30x^12 - 68x^10 + 87x^8 - 44x^6 - 28x^4 + 48x^2 - 16	\( -\,2^{46}\cdot 113^{4} \)	16T1776	Trivial (GRH)
16.6.12720343418240000000000.1	x^16 - 4x^15 - x^14 + 14x^13 + 26x^12 - 118x^11 + 2x^10 + 440x^9 - 530x^8 - 208x^7 + 777x^6 - 220x^5 - 460x^4 + 292x^3 + 39x^2 - 62x + 11	\( -\,2^{16}\cdot 5^{10}\cdot 101^{4}\cdot 191 \)	16T1776	Trivial (GRH)
16.6.12720343418240000000000.2	x^16 - 4x^15 - 2x^14 + 20x^13 - x^12 - 12x^11 - 148x^10 + 384x^9 - 585x^8 + 1116x^7 - 2510x^6 + 5104x^5 - 7428x^4 + 6552x^3 - 3048x^2 + 544x + 16	\( -\,2^{16}\cdot 5^{10}\cdot 101^{4}\cdot 191 \)	16T1776	Trivial (GRH)
16.4.18301625875548095703125.1	x^16 - 2x^15 + 2x^14 - 11x^13 - 8x^12 + 24x^11 - 22x^10 + 187x^9 - 125x^8 + 86x^7 - 211x^6 + 44x^5 + 668x^4 + 384x^3 + 315x^2 - 162x + 81	\( 5^{13}\cdot 61\cdot 181^{4}\cdot 229 \)	16T1776	Trivial (GRH)
16.0.29872169131889892578125.1	x^16 - 4x^15 + 14x^14 - 29x^13 + 76x^12 - 167x^11 + 336x^10 - 437x^9 + 762x^8 - 883x^7 + 2551x^6 - 3253x^5 + 3996x^4 - 2056x^3 - 996x^2 + 329x + 331	\( 5^{12}\cdot 101^{4}\cdot 1175821 \)	16T1776	$[2]$
16.10.907610275348357845090304.1	x^16 - 10x^14 + 29x^12 + 6x^10 - 138x^8 + 106x^6 + 167x^4 - 126x^2 - 81	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.14.907610275348357845090304.1	x^16 - 18x^14 + 115x^12 - 342x^10 + 505x^8 - 352x^6 + 88x^4 + 8x^2 - 4	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.2.907610275348357845090304.1	x^16 + 18x^14 + 115x^12 + 342x^10 + 505x^8 + 352x^6 + 88x^4 - 8x^2 - 4	\( -\,2^{46}\cdot 337^{4} \)	16T1776	$[2]$ (GRH)
16.6.907610275348357845090304.1	x^16 + 4x^14 - 36x^12 - 108x^10 + 228x^8 + 252x^6 - 32x^4 - 20x^2 - 1	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.10.907610275348357845090304.2	x^16 - 6x^14 - 7x^12 + 74x^10 - 54x^8 - 154x^6 + 211x^4 - 66x^2 - 1	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.6.907610275348357845090304.2	x^16 + 6x^14 - 7x^12 - 74x^10 - 54x^8 + 154x^6 + 211x^4 + 66x^2 - 1	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.10.907610275348357845090304.3	x^16 - 4x^14 - 36x^12 + 108x^10 + 228x^8 - 252x^6 - 32x^4 + 20x^2 - 1	\( -\,2^{46}\cdot 337^{4} \)	16T1776	Trivial (GRH)
16.10.3630441101393431380361216.1	x^16 - 10x^14 + 17x^12 + 70x^10 - 150x^8 - 106x^6 + 229x^4 - 42x^2 - 1	\( -\,2^{48}\cdot 337^{4} \)	16T1776	Trivial (GRH)