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 51)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.5190614520439741.1	x^16 - 3x^15 + 7x^14 - 12x^13 + 15x^12 - 15x^11 + 12x^10 - 5x^9 - 2x^8 + 4x^7 - 5x^6 + 6x^5 + 3x^4 - 5x^3 - x^2 + 1	\( 617^{2}\cdot 2389^{3} \)	16T1948	Trivial
16.0.5821863490955437.1	x^16 - 4x^15 + 10x^14 - 17x^13 + 23x^12 - 27x^11 + 30x^10 - 30x^9 + 25x^8 - 14x^7 + 6x^6 - 7x^5 + 15x^4 - 20x^3 + 15x^2 - 6x + 1	\( 19^{2}\cdot 101^{2}\cdot 277\cdot 2389^{2} \)	16T1948	Trivial
16.0.12297659713016077.1	x^16 - 3x^15 + 4x^14 - 3x^13 + 2x^12 - 4x^11 + 15x^10 - 33x^9 + 51x^8 - 59x^7 + 54x^6 - 40x^5 + 25x^4 - 14x^3 + 7x^2 - 3x + 1	\( 29^{2}\cdot 47\cdot 59\cdot 72617^{2} \)	16T1948	Trivial
16.2.17968112315819999.1	x^16 - x^15 - 4x^14 + 5x^13 + 7x^12 - 9x^11 - 10x^10 + 11x^9 + 14x^8 - 14x^7 - 13x^6 + 17x^5 + 4x^4 - 11x^3 + 2x^2 + 3x - 1	\( -\,43^{2}\cdot 71\cdot 369959^{2} \)	16T1948	Trivial
16.2.21004976369198027.1	x^16 - 4x^15 + 6x^14 - x^13 - 6x^12 + 2x^11 + 10x^10 - 18x^9 + 19x^8 - 18x^7 + 10x^6 + 2x^5 - 6x^4 - x^3 + 6x^2 - 4x + 1	\( -\,43^{2}\cdot 83\cdot 369959^{2} \)	16T1948	Trivial
16.0.37707728662777181.1	x^16 - x^15 + 3x^14 - 6x^13 + 8x^12 - 12x^11 + 16x^10 - 18x^9 + 19x^8 - 18x^7 + 16x^6 - 12x^5 + 8x^4 - 6x^3 + 3x^2 - x + 1	\( 43^{2}\cdot 149\cdot 369959^{2} \)	16T1948	Trivial
16.0.65210096503388693.1	x^16 - 2x^15 + 3x^13 - 5x^12 - 2x^11 + 10x^10 + 4x^9 - 2x^8 - 17x^7 + x^6 + 5x^5 + 10x^4 - 3x^3 - x^2 - 2x + 1	\( 199^{2}\cdot 3533\cdot 21589^{2} \)	16T1948	Trivial
16.4.83903202023925689.1	x^16 - x^15 + 5x^14 + 2x^13 + 4x^12 + 17x^11 + 7x^10 + 13x^9 + 24x^8 + 11x^7 + 9x^6 + 14x^5 + 2x^4 + 2x^2 - 2x - 1	\( 89\cdot 421^{2}\cdot 72931^{2} \)	16T1948	Trivial
16.4.124470628948573741.1	x^16 - x^15 - 2x^14 - 4x^13 + 6x^12 + 9x^11 - 4x^10 - 24x^9 - 19x^8 + 23x^7 + 37x^6 + 10x^5 - 24x^4 - 19x^3 + 6x^2 + 5x - 1	\( 41^{2}\cdot 83^{2}\cdot 1289^{2}\cdot 6469 \)	16T1948	Trivial
16.4.156836523556077997.1	x^16 - 5x^15 + 11x^14 - 17x^13 + 19x^12 - 11x^11 - 6x^10 + 24x^9 - 31x^8 + 24x^7 - 6x^6 - 11x^5 + 19x^4 - 17x^3 + 11x^2 - 5x + 1	\( 37\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.2.199224773165828807.1	x^16 - 3x^15 + 6x^14 - 8x^13 + 7x^12 - 4x^11 + 3x^9 - 5x^8 + 3x^7 - 4x^5 + 7x^4 - 8x^3 + 6x^2 - 3x + 1	\( -\,47\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.4.258568322619479941.1	x^16 - 6x^15 + 13x^14 - 7x^13 - 20x^12 + 42x^11 - 31x^10 + 4x^9 + 8x^8 - 7x^7 + 5x^6 - 3x^5 + 2x^4 - x^3 - 2x^2 + 2x + 1	\( 61\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.4.265744202146140061.1	x^16 - 2x^15 + 3x^14 - 5x^13 - x^12 + 19x^11 - 33x^10 + 35x^9 - 38x^8 + 3x^7 + 75x^6 - 99x^5 + 38x^4 + 12x^3 - 10x^2 + 1	\( 2011^{2}\cdot 2137^{2}\cdot 14389 \)	16T1948	Trivial
16.2.284452595367842719.1	x^16 - x^15 - 2x^14 - 4x^13 + 9x^12 + 4x^11 + 2x^10 - 11x^9 - 5x^8 - 5x^7 + 12x^6 + 2x^5 + 4x^4 - 6x^3 - x^2 - x + 1	\( -\,1321^{2}\cdot 3347^{2}\cdot 14551 \)	16T1948	Trivial
16.2.300956572229230751.1	x^16 - 3x^15 + 3x^14 - x^13 - x^12 + 6x^11 - 12x^10 + 16x^9 - 17x^8 + 16x^7 - 12x^6 + 6x^5 - x^4 - x^3 + 3x^2 - 3x + 1	\( -\,71\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.4.391402103414196593.1	x^16 - 5x^15 + 12x^14 - 19x^13 + 19x^12 - 6x^11 - 19x^10 + 42x^9 - 46x^8 + 22x^7 + 4x^6 - x^5 - 10x^4 - x^3 + 3x^2 + 4x + 1	\( 19^{2}\cdot 607^{2}\cdot 1433^{3} \)	16T1948	Trivial
16.6.453554270824333667.1	x^16 - 2x^14 - 3x^13 - 2x^12 + 13x^11 + 9x^10 - x^9 - 14x^8 - 40x^7 - 13x^6 + 3x^5 + 2x^4 + 5x^3 - 5x^2 - x + 1	\( -\,89^{2}\cdot 107\cdot 731531^{2} \)	16T1948	Trivial
16.6.555286069887735611.1	x^16 - 3x^14 - 4x^13 + 8x^12 + 6x^11 - 9x^10 - 5x^9 + 12x^8 - 13x^7 - 6x^6 + 30x^5 - 10x^4 - 15x^3 + 9x^2 + x - 1	\( -\,89^{2}\cdot 131\cdot 731531^{2} \)	16T1948	Trivial
16.2.686056255602477631.1	x^16 - 3x^15 + 2x^14 + 2x^12 + x^11 - 12x^10 + 8x^9 + 9x^8 - 5x^7 - 2x^6 - 7x^5 + 5x^4 + 12x^3 - 3x^2 - 6x - 1	\( -\,32839\cdot 4570723^{2} \)	16T1948	Trivial
16.6.1873431282147923539.1	x^16 - 7x^15 + 18x^14 - 12x^13 - 39x^12 + 98x^11 - 63x^10 - 73x^9 + 143x^8 - 54x^7 - 36x^6 + 30x^5 - 13x^4 + 8x^3 + 7x^2 - 8x + 1	\( -\,19^{5}\cdot 607^{2}\cdot 1433^{2} \)	16T1948	Trivial
16.4.2504632135277082389.1	x^16 - 3x^15 + 2x^14 + 4x^13 - 11x^12 + 6x^11 + 39x^10 - 125x^9 + 162x^8 - 49x^7 - 175x^6 + 344x^5 - 341x^4 + 207x^3 - 76x^2 + 15x - 1	\( 1753^{2}\cdot 9341^{3} \)	16T1948	Trivial
16.8.6775050767527611461.1	x^16 - x^15 - 8x^14 + 3x^13 + 12x^12 - 8x^11 + 6x^10 + 13x^9 - 7x^8 + 13x^7 + 6x^6 - 8x^5 + 12x^4 + 3x^3 - 8x^2 - x + 1	\( 29\cdot 483345053^{2} \)	16T1948	Trivial
16.8.6775050767527611461.2	x^16 - x^15 - 8x^14 + 11x^13 + 12x^12 - 19x^11 - 5x^10 + 2x^9 + 15x^8 + 2x^7 - 5x^6 - 19x^5 + 12x^4 + 11x^3 - 8x^2 - x + 1	\( 29\cdot 483345053^{2} \)	16T1948	Trivial
16.6.7436639964869735267.1	x^16 + 5x^14 - 8x^13 + 7x^12 - 29x^11 + 24x^10 - 27x^9 + 54x^8 - 33x^7 + 34x^6 - 35x^5 + 17x^4 + 2x^3 - 21x^2 + 9x - 1	\( -\,19^{3}\cdot 607^{2}\cdot 1433^{3} \)	16T1948	Trivial
16.8.7470129603273724489.1	x^16 - 8x^15 + 20x^14 - 71x^12 + 62x^11 + 102x^10 - 125x^9 - 102x^8 + 124x^7 + 82x^6 - 67x^5 - 44x^4 + 14x^3 + 13x^2 - x - 1	\( 59\cdot 419\cdot 17383253^{2} \)	16T1948	Trivial
16.4.9578520050642485169.1	x^16 - x^15 - 4x^14 + 15x^13 - 24x^12 + 18x^11 + 9x^10 - 42x^9 + 57x^8 - 42x^7 + 9x^6 + 18x^5 - 24x^4 + 15x^3 - 4x^2 - x + 1	\( 41\cdot 483345053^{2} \)	16T1948	Trivial
16.8.18709387534509486389.1	x^16 - 5x^15 + 12x^14 - 19x^13 + 13x^12 + 14x^11 - 42x^10 + 40x^9 - 19x^8 + 32x^7 - 20x^6 - 19x^5 - 12x^4 + 23x^3 + 7x^2 - 6x - 1	\( 67^{2}\cdot 233\cdot 277\cdot 254119^{2} \)	16T1948	Trivial
16.6.24997601107774290563.1	x^16 - 3x^15 - x^14 + 9x^13 - 13x^12 + 15x^11 - 12x^10 + 6x^9 - 3x^8 + 6x^7 - 12x^6 + 15x^5 - 13x^4 + 9x^3 - x^2 - 3x + 1	\( -\,107\cdot 483345053^{2} \)	16T1948	Trivial
16.6.24997601107774290563.2	x^16 - 2x^15 - x^14 - 3x^12 + 13x^11 - 12x^10 + 16x^9 - 23x^8 + 16x^7 - 12x^6 + 13x^5 - 3x^4 - x^2 - 2x + 1	\( -\,107\cdot 483345053^{2} \)	16T1948	Trivial
16.10.29670049912965746743.1	x^16 - 5x^15 + 4x^14 + 9x^13 - 3x^12 - 11x^11 - 29x^10 + 40x^9 + 50x^8 - 86x^7 - 23x^6 + 87x^5 + 2x^4 - 41x^3 - 2x^2 + 7x + 1	\( -\,127\cdot 483345053^{2} \)	16T1948	Trivial
16.2.29670049912965746743.1	x^16 - x^15 + 2x^13 - 6x^12 + 11x^11 - 16x^10 + 20x^9 - 21x^8 + 20x^7 - 16x^6 + 11x^5 - 6x^4 + 2x^3 - x + 1	\( -\,127\cdot 483345053^{2} \)	16T1948	Trivial
16.10.32473519196080620451.1	x^16 - 2x^15 - 9x^14 + 21x^13 + 27x^12 - 69x^11 - 54x^10 + 71x^9 + 53x^8 - 10x^7 + 25x^6 + 33x^5 - 31x^4 - 47x^3 - 12x^2 + 3x + 1	\( -\,139\cdot 483345053^{2} \)	16T1948	Trivial
16.2.32473519196080620451.1	x^16 - x^15 + 3x^13 - 7x^12 + 12x^11 - 17x^10 + 21x^9 - 23x^8 + 21x^7 - 17x^6 + 12x^5 - 7x^4 + 3x^3 - x + 1	\( -\,139\cdot 483345053^{2} \)	16T1948	Trivial
16.10.39165688288992519439.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 102x^12 + 66x^11 + 180x^10 - 218x^9 - 124x^8 + 242x^7 + 19x^6 - 125x^5 + 16x^4 + 33x^3 - 9x^2 - 3x + 1	\( -\,17\cdot 263\cdot 1117^{2}\cdot 83791^{2} \)	16T1948	Trivial
16.4.45089130970097552137.1	x^16 - 2x^15 - 4x^14 + 5x^13 + 16x^12 - 2x^11 - 38x^10 - 9x^9 + 40x^8 + 34x^7 - 41x^6 - 29x^5 + 19x^4 + 2x^3 + x^2 - 5x + 1	\( 193\cdot 483345053^{2} \)	16T1948	Trivial
16.10.277795632642462908416.1	x^16 - 3x^14 + x^12 - 3x^10 + 19x^8 - 18x^6 - 2x^4 + 5x^2 - 1	\( -\,2^{16}\cdot 89^{2}\cdot 731531^{2} \)	16T1948	Trivial
16.12.284052722662986805169.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 98x^12 + 42x^11 + 213x^10 - 163x^9 - 270x^8 + 232x^7 + 208x^6 - 162x^5 - 88x^4 + 49x^3 + 16x^2 - 4x - 1	\( 43^{2}\cdot 521^{2}\cdot 4337^{2}\cdot 30089 \)	16T1948	Trivial (GRH)
16.0.340103026334754340864.1	x^16 + 9x^14 + 32x^12 + 57x^10 + 56x^8 + 46x^6 + 60x^4 + 57x^2 + 19	\( 2^{16}\cdot 19^{3}\cdot 607^{2}\cdot 1433^{2} \)	16T1948	Trivial
16.8.396231191806043027953.1	x^16 - x^15 - 9x^14 + 15x^13 + 17x^12 - 28x^11 + 53x^10 - 129x^9 - 154x^8 + 345x^7 + 151x^6 - 346x^5 - 31x^4 + 166x^3 - 51x^2 - x + 1	\( 811^{2}\cdot 84457^{3} \)	16T1948	Trivial
16.8.675185733520236244081.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 27x^12 + 20x^11 - 54x^10 + 39x^9 - 3x^8 - 2x^7 - 6x^6 - 13x^5 + 21x^4 - 2x^3 - 6x^2 + 2x + 1	\( 61^{2}\cdot 263^{2}\cdot 6113^{2}\cdot 70201 \)	16T1948	Trivial
16.12.813503926129374655621.1	x^16 - 8x^15 + 17x^14 + 21x^13 - 111x^12 + 29x^11 + 272x^10 - 172x^9 - 373x^8 + 269x^7 + 315x^6 - 207x^5 - 147x^4 + 80x^3 + 26x^2 - 12x + 1	\( 53^{2}\cdot 1229^{2}\cdot 1483^{2}\cdot 87181 \)	16T1948	Trivial
16.12.4989156858715408722397.1	x^16 - 6x^15 + 5x^14 + 17x^13 - 7x^12 - 9x^11 - 59x^10 + 17x^9 + 75x^8 - 35x^7 + 13x^6 + 34x^5 - 38x^4 - 24x^3 + 9x^2 + 7x + 1	\( 9973^{3}\cdot 70921^{2} \)	16T1948	Trivial
16.12.4989156858715408722397.2	x^16 - x^15 - 8x^14 + 16x^13 + 4x^12 - 78x^11 + 128x^10 + 94x^9 - 406x^8 + 261x^7 + 266x^6 - 688x^5 + 464x^4 + 266x^3 - 509x^2 + 214x - 23	\( 9973^{3}\cdot 70921^{2} \)	16T1948	Trivial
16.14.15310680244851363610624.1	x^16 - 10x^14 + 28x^12 - x^10 - 96x^8 + 133x^6 - 67x^4 + 14x^2 - 1	\( -\,2^{16}\cdot 483345053^{2} \)	16T1948	Trivial (GRH)
16.14.15310680244851363610624.2	x^16 - 11x^14 + 40x^12 - 42x^10 - 56x^8 + 153x^6 - 105x^4 + 20x^2 - 1	\( -\,2^{16}\cdot 483345053^{2} \)	16T1948	Trivial (GRH)
16.0.21829877031155017908224.1	x^16 + 6x^14 - x^12 - 39x^10 + 63x^8 + 434x^6 + 622x^4 + 354x^2 + 71	\( 2^{16}\cdot 71\cdot 811^{2}\cdot 84457^{2} \)	16T1948	Trivial
16.0.24723811305179198849024.1	x^16 + 19x^14 + 144x^12 + 568x^10 + 1278x^8 + 1691x^6 + 1299x^4 + 534x^2 + 89	\( 2^{16}\cdot 89^{3}\cdot 731531^{2} \)	16T1948	Trivial
16.0.521554443205992264826880.1	x^16 + 17x^14 + 110x^12 + 345x^10 + 561x^8 + 489x^6 + 229x^4 + 54x^2 + 5	\( 2^{16}\cdot 5\cdot 397^{2}\cdot 3177857^{2} \)	16T1948	$[18]$
16.16.521554443205992264826880.1	x^16 - 17x^14 + 110x^12 - 345x^10 + 561x^8 - 489x^6 + 229x^4 - 54x^2 + 5	\( 2^{16}\cdot 5\cdot 397^{2}\cdot 3177857^{2} \)	16T1948	Trivial (GRH)
16.0.566495169059500453593088.1	x^16 + 17x^14 + 119x^12 + 444x^10 + 955x^8 + 1195x^6 + 833x^4 + 288x^2 + 37	\( 2^{16}\cdot 37\cdot 483345053^{2} \)	16T1948	$[24]$