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 988)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.224415603.1	x^10 + 2x^8 - 3x^7 + 3x^6 - 7x^5 + 8x^4 - 7x^3 + 7x^2 - 4x + 1	\( -\,3^{5}\cdot 31^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.246071287.1	x^10 - 3x^9 + 7x^8 - 12x^7 + 15x^6 - 15x^5 + 12x^4 - 7x^3 + 4x^2 - 2x + 1	\( -\,7^{5}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.400000000.1	x^10 - 4x^9 + 9x^8 - 14x^7 + 15x^6 - 10x^5 + 3x^4 + 2x^3 - 2x^2 + 1	\( -\,2^{10}\cdot 5^{8} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.479756288.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + 2x^4 + 2x^3 - x^2 - 2x + 1	\( -\,2^{15}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.2893579264.1	x^10 - 2x^9 + 4x^8 - 2x^7 + x^6 + 6x^5 - 2x^4 + 2x^3 + 4x^2 - 4x + 1	\( -\,2^{10}\cdot 41^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.3364539363.1	x^10 - 3x^9 + 4x^8 - 8x^7 + 10x^6 - 9x^5 + 16x^4 - 10x^3 + 11x^2 - 6x + 1	\( -\,3^{5}\cdot 61^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.14178141184.1	x^10 - 4x^9 + 12x^8 - 22x^7 + 36x^6 - 48x^5 + 57x^4 - 48x^3 + 28x^2 - 8x + 1	\( -\,2^{10}\cdot 61^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.36252565459.1	x^10 - 3x^9 + 4x^8 - 6x^7 + 5x^6 + 4x^5 - 7x^4 - 6x^3 + 8x^2 + 6x + 1	\( -\,11^{4}\cdot 19^{5} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.62910546875.1	x^10 - 4x^9 + 9x^8 - 9x^7 - 2x^6 + 12x^5 - 8x^4 - 12x^3 + 27x^2 - 14x + 5	\( -\,5^{8}\cdot 11^{5} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.92594536448.1	x^10 - 2x^9 + x^8 + 2x^7 + 8x^6 + 7x^4 + 10x^3 + 13x^2 + 2x + 1	\( -\,2^{15}\cdot 41^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.106557850624.1	x^10 - 2x^9 - 2x^8 + 8x^7 - 3x^6 - 8x^5 + 19x^4 - 2x^3 - 25x^2 + 10x + 17	\( -\,2^{10}\cdot 101^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.116580777984.1	x^10 - 4x^9 + 8x^8 - 10x^7 + 14x^6 - 26x^5 + 33x^4 - 20x^3 + 4x^2 + 1	\( -\,2^{15}\cdot 3^{5}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.126332201043.1	x^10 - 4x^9 - 2x^8 + 32x^7 - 48x^6 - 22x^5 + 143x^4 - 188x^3 + 140x^2 - 64x + 16	\( -\,3^{5}\cdot 151^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.148733980571.1	x^10 - x^9 + 2x^8 - 3x^7 + 6x^6 - 5x^5 + 11x^4 + 5x^3 + 13x^2 + 7x + 1	\( -\,11^{5}\cdot 31^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.260807798403.1	x^10 - x^9 + 11x^8 - 15x^7 + 44x^6 - 64x^5 + 79x^4 - 78x^3 + 54x^2 - 13x + 1	\( -\,3^{5}\cdot 181^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.427094122567.1	x^10 - x^9 + 4x^8 - x^7 + 9x^6 + 8x^5 + 9x^4 + 12x^3 + 9x^2 + 6x + 8	\( -\,7^{5}\cdot 71^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.481655024163.1	x^10 - 2x^9 + 14x^8 - 13x^7 + 55x^6 - 5x^5 + 71x^4 + 50x^3 + 30x^2 + 15x + 7	\( -\,3^{5}\cdot 211^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.701298759375.1	x^10 - 3x^9 + 8x^8 - 16x^7 + 28x^6 - 48x^5 + 76x^4 - 95x^3 + 100x^2 - 75x + 25	\( -\,3^{5}\cdot 5^{5}\cdot 31^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.768972771875.1	x^10 - 5x^9 + 16x^8 - 32x^7 + 51x^6 - 70x^5 + 92x^4 - 89x^3 + 65x^2 - 29x + 9	\( -\,5^{5}\cdot 7^{5}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.819736822323.1	x^10 - x^9 - 5x^8 + 8x^7 + 42x^6 + 26x^5 - 43x^4 - 29x^3 + 11x^2 + 2x + 4	\( -\,3^{5}\cdot 241^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.967226171875.1	x^10 - x^9 + 5x^8 - 11x^7 + 19x^6 - 36x^5 + 52x^4 - 60x^3 + 77x^2 - 68x + 23	\( -\,5^{8}\cdot 19^{5} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.1099041915904.2	x^10 - 4x^9 + 12x^7 + 24x^6 - 160x^5 + 349x^4 - 464x^3 + 366x^2 - 144x + 25	\( -\,2^{10}\cdot 181^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.1310640056883.1	x^10 - 3x^9 + 10x^8 + x^7 + 4x^6 + 39x^5 + 94x^4 + 68x^3 - 19x^2 - 27x + 13	\( -\,3^{5}\cdot 271^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.1320972497559.2	x^10 - 4x^9 + 9x^8 - 21x^7 + 46x^6 - 68x^5 + 70x^4 - 37x^3 + 24x^2 - 20x + 16	\( -\,3^{5}\cdot 11^{4}\cdot 13^{5} \)	$D_5\times C_5$ (as 10T6)	$[4]$
10.0.1499238400000.1	x^10 - 2x^9 - 9x^8 + 18x^7 + 33x^6 - 68x^5 - 2x^4 + 34x^3 + x^2 - 6x + 1	\( -\,2^{15}\cdot 5^{5}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.2152350613963.2	x^10 - 4x^9 + 16x^8 - 42x^7 + 80x^6 - 121x^5 + 123x^4 - 54x^3 - 11x^2 + 12x + 13	\( -\,11^{4}\cdot 43^{5} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.2916877891203.1	x^10 - 2x^9 - 11x^8 + 21x^7 + 41x^6 - 93x^5 + 76x^4 - 90x^3 + 61x^2 - 4x + 7	\( -\,3^{5}\cdot 331^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.3110400000000.1	x^10 - 4x^9 + 8x^8 - 8x^7 + 17x^6 - 22x^5 + 24x^4 + 2x^3 + 28x^2 + 8x + 1	\( -\,2^{15}\cdot 3^{5}\cdot 5^{8} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.3454364222464.1	x^10 - 2x^9 - 4x^8 - 8x^7 + 53x^6 - 14x^5 - 14x^4 - 224x^3 + 388x^2 - 280x + 136	\( -\,2^{10}\cdot 241^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial (GRH)
10.0.3602729712967.2	x^10 - 3x^8 + 19x^6 - 11x^5 - 40x^4 + 55x^3 + 23x^2 - 44x + 32	\( -\,7^{5}\cdot 11^{8} \)	$D_5\times C_5$ (as 10T6)	$[5]$
10.0.4092576636731.1	x^10 - 5x^9 + 13x^8 - 21x^7 + 33x^6 - 66x^5 + 116x^4 - 152x^3 + 169x^2 - 134x + 47	\( -\,11^{5}\cdot 71^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.5051514699891.1	x^10 - 3x^9 + 4x^8 + 2x^7 - 2x^6 - 12x^5 + 19x^4 + 22x^3 + 2x^2 - 15x + 25	\( -\,3^{5}\cdot 11^{4}\cdot 17^{5} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.5566567232512.2	x^10 + 7x^8 - 8x^7 + 17x^6 - 6x^5 + 18x^4 - 20x^3 + 45x^2 - 42x + 17	\( -\,2^{10}\cdot 11^{4}\cdot 13^{5} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.5944097923703.1	x^10 - x^9 + 8x^8 - 8x^7 - 9x^6 + 20x^5 + 3x^4 - 13x^3 + 25x^2 - 26x + 8	\( -\,23^{5}\cdot 31^{4} \)	$D_5\times C_5$ (as 10T6)	$[3]$
10.10.6194123253125.1	x^10 - 2x^9 - 12x^8 + 26x^7 + 25x^6 - 62x^5 - 4x^4 + 40x^3 - 11x^2 - 3x + 1	\( 5^{5}\cdot 211^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.10.6323239406592.1	x^10 - 2x^9 - 10x^8 + 22x^7 + 23x^6 - 60x^5 - 7x^4 + 40x^3 - x^2 - 6x + 1	\( 2^{10}\cdot 3^{5}\cdot 71^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.6384475669504.2	x^10 + 13x^8 - 18x^7 + 58x^6 - 90x^5 + 161x^4 - 170x^3 + 123x^2 - 54x + 13	\( -\,2^{10}\cdot 281^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.7024111812608.3	x^10 + 6x^8 + 21x^6 - 22x^5 + 12x^4 + 22x^3 - 28x^2 + 132x + 153	\( -\,2^{15}\cdot 11^{8} \)	$D_5\times C_5$ (as 10T6)	$[5]$
10.0.7353650479104.1	x^10 - 2x^9 + x^8 + 4x^7 + x^6 - 4x^5 - 3x^4 + 10x^3 + 18x^2 + 16x + 7	\( -\,2^{15}\cdot 3^{5}\cdot 31^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.8737717296007.1	x^10 - x^9 - 4x^8 - 4x^7 + 11x^6 + 17x^5 + 27x^4 - 68x^3 - 55x^2 + 32x + 67	\( -\,7^{5}\cdot 151^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.9042435200000.1	x^10 - 4x^9 + x^8 + 14x^7 - 5x^6 - 38x^5 + 28x^4 + 44x^3 - 39x^2 - 30x + 29	\( -\,2^{10}\cdot 5^{5}\cdot 41^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.9650173411328.1	x^10 + 4x^8 - 8x^7 - 5x^6 - 2x^5 + 40x^4 + 46x^3 + 46x^2 + 8x + 1	\( -\,2^{15}\cdot 131^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.10514185509375.1	x^10 - x^9 + 9x^7 - 5x^6 - 17x^5 + 43x^4 + 71x^3 + 54x^2 + 13x + 1	\( -\,3^{5}\cdot 5^{5}\cdot 61^{4} \)	$D_5\times C_5$ (as 10T6)	$[2]$
10.0.11183262109375.1	x^10 - 3x^9 + 6x^8 - 5x^7 - 24x^6 + 65x^5 + 27x^4 - 289x^3 + 430x^2 - 264x + 64	\( -\,5^{8}\cdot 31^{5} \)	$D_5\times C_5$ (as 10T6)	$[3]$
10.10.17872314453125.1	x^10 - 15x^8 - 10x^7 + 55x^6 + 53x^5 - 40x^4 - 50x^3 - 5x^2 + 5x + 1	\( 5^{13}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.18187567032023.1	x^10 - x^9 + 2x^8 + 7x^7 + 9x^6 + 44x^5 + 63x^4 + 70x^3 + 65x^2 + 80x + 124	\( -\,23^{5}\cdot 41^{4} \)	$D_5\times C_5$ (as 10T6)	$[3]$
10.0.21287041369088.1	x^10 - 4x^9 + 13x^8 - 32x^7 + 77x^6 - 94x^5 + 204x^4 - 116x^3 + 227x^2 - 60x + 81	\( -\,2^{10}\cdot 11^{4}\cdot 17^{5} \)	$D_5\times C_5$ (as 10T6)	$[4]$
10.0.22367820508327.1	x^10 - 5x^9 + 10x^8 + 5x^7 - 61x^6 + 95x^5 + 5x^4 - 175x^3 + 226x^2 - 115x + 25	\( -\,7^{5}\cdot 191^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.33313481444887.1	x^10 - 4x^9 + 12x^8 - 10x^7 + 12x^6 - 44x^5 + 33x^4 - 16x^3 + 56x^2 - 40x + 11	\( -\,7^{5}\cdot 211^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.34283673054259.1	x^10 - 4x^9 + 8x^8 - x^7 - 29x^6 + 31x^5 + 78x^4 - 213x^3 + 145x^2 + 1	\( -\,19^{5}\cdot 61^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial