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 523)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.9300278979.1	x^10 - 4x^9 + 7x^8 - 11x^7 + 18x^6 - 19x^5 + 16x^4 - 17x^3 + 10x^2 - 3x + 3	\( -\,3^{5}\cdot 337^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.19911454263.1	x^10 - 2x^9 + 6x^8 - 10x^7 + 16x^6 - 17x^5 + 19x^4 - 12x^3 + 6x^2 - x + 1	\( -\,3^{5}\cdot 19^{2}\cdot 61^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.21141825471.1	x^10 - 2x^9 + 6x^8 - 12x^7 + 21x^6 - 29x^5 + 32x^4 - 29x^3 + 22x^2 - 12x + 3	\( -\,3^{5}\cdot 13^{3}\cdot 199^{2} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.2.47280848896.1	x^10 - 4x^9 + 6x^8 - 17x^6 + 34x^5 - 36x^4 + 22x^3 - 6x^2 + 1	\( 2^{15}\cdot 113^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.50316807879.1	x^10 - x^9 + 5x^8 - x^7 + 9x^6 + 3x^5 + 12x^4 + 2x^3 + 16x^2 - 3x + 9	\( -\,3^{5}\cdot 13^{3}\cdot 307^{2} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.52750877643.1	x^10 - x^9 - x^8 + 3x^7 - x^6 - 9x^5 + 5x^4 + 32x^3 + 34x^2 + 15x + 3	\( -\,3^{5}\cdot 601^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.60897409375.1	x^10 - 3x^9 + x^8 + 5x^7 - 6x^6 - x^5 + 11x^4 - 17x^3 + 15x^2 - 8x + 3	\( -\,5^{5}\cdot 11^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.80561164032.1	x^10 - 2x^9 - 5x^8 + 10x^7 + 5x^6 - 22x^5 + 29x^4 - 12x^3 + 7x^2 + 1	\( -\,2^{8}\cdot 3^{5}\cdot 109^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.90731184128.1	x^10 - 4x^9 + 9x^8 - 8x^7 - 2x^6 + 16x^5 - 14x^4 + 10x^2 - 8x + 2	\( -\,2^{29}\cdot 13^{2} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.101928170799.1	x^10 - x^9 + 7x^8 - 3x^7 + 17x^6 + 3x^5 + 22x^4 + 6x^3 + 10x^2 + x + 1	\( -\,3^{5}\cdot 7^{2}\cdot 13^{2}\cdot 37^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.102294880256.1	x^10 - 2x^9 + 8x^8 - 8x^7 + 20x^6 - 8x^5 + 24x^4 + 18x^2 + 4x + 4	\( -\,2^{22}\cdot 29^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.103010321491.1	x^10 - x^9 + 4x^7 + 6x^6 - 7x^5 - 3x^4 + 2x^2 + 5x + 2	\( -\,7^{5}\cdot 11^{2}\cdot 37^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.103737344000.1	x^10 - 4x^9 + 4x^8 + 2x^6 - 6x^5 + 8x^4 - 4x^3 - 6x^2 - 4x + 10	\( -\,2^{14}\cdot 5^{3}\cdot 37^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.107150045184.1	x^10 - 2x^9 + 2x^8 + 2x^7 - 4x^5 + 6x^4 + 2x^3 - 2x^2 - 2x + 1	\( -\,2^{12}\cdot 3^{5}\cdot 7^{2}\cdot 13^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.114445392399.1	x^10 - x^9 + 8x^8 - 5x^7 + 24x^6 - 11x^5 + 42x^4 - 17x^3 + 40x^2 - 10x + 13	\( -\,3^{5}\cdot 13^{3}\cdot 463^{2} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.209715200000.1	x^10 - 4x^9 + 5x^8 + 4x^6 - 8x^5 - 4x^4 + 5x^2 + 4x + 1	\( -\,2^{26}\cdot 5^{5} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.2.265306590625.1	x^10 - 2x^9 - 2x^8 + 5x^7 + 5x^6 - 8x^5 - 4x^4 + 7x^3 + 5x^2 - 2x - 1	\( 5^{5}\cdot 29^{3}\cdot 59^{2} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.265420800000.1	x^10 - 4x^9 + 7x^8 - 12x^7 + 14x^6 - 4x^5 - 4x^4 + 12x^3 - 2x^2 - 16x + 10	\( -\,2^{20}\cdot 3^{4}\cdot 5^{5} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.327680000000.1	x^10 - 2x^9 + 11x^8 - 12x^7 + 34x^6 - 12x^5 + 28x^4 + 16x^3 - 2x^2 + 4x + 2	\( -\,2^{22}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.327680000000.2	x^10 - 4x^9 + 7x^8 - 8x^7 + 18x^6 - 52x^5 + 100x^4 - 120x^3 + 90x^2 - 40x + 10	\( -\,2^{22}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.512000000000.1	x^10 - 4x^9 - x^8 + 16x^7 + 2x^6 - 20x^5 - 2x^4 + 12x^3 + 3x^2 - 4x + 1	\( -\,2^{18}\cdot 5^{9} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.560163396123.1	x^10 - 4x^9 + 6x^8 - 3x^7 - x^6 + 21x^4 - 16x^3 + 10x^2 - 3x + 1	\( -\,3^{5}\cdot 1321^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.597196800000.1	x^10 - 2x^8 - 4x^7 + 16x^6 + 44x^5 + 70x^4 + 56x^3 + 37x^2 + 12x + 4	\( -\,2^{18}\cdot 3^{6}\cdot 5^{5} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.679477248000.1	x^10 - 2x^9 + 5x^8 + 4x^6 - 24x^5 + 4x^4 + 20x^2 - 8x + 4	\( -\,2^{26}\cdot 3^{4}\cdot 5^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.1677721600000.1	x^10 - 4x^9 + 5x^8 + 2x^6 - 8x^5 - 6x^4 + 10x^2 + 8x + 2	\( -\,2^{29}\cdot 5^{5} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.1677721600000.2	x^10 - 4x^9 + 5x^8 - 6x^6 + 8x^5 + 2x^4 + 10x^2 + 8x + 2	\( -\,2^{29}\cdot 5^{5} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.2.1852746653125.1	x^10 + x^8 - 6x^7 - 10x^5 + 7x^4 - 4x^3 - 6x + 1	\( 5^{5}\cdot 29^{2}\cdot 89^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.2048000000000.1	x^10 - 4x^9 + 13x^8 - 16x^7 + 12x^6 + 16x^5 - 12x^4 - 16x^3 + 12x^2 + 16x + 4	\( -\,2^{20}\cdot 5^{9} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.2830974609375.1	x^10 - 3x^9 + 11x^8 - 22x^7 + 44x^6 - 61x^5 + 80x^4 - 75x^3 + 65x^2 - 35x + 15	\( -\,3^{2}\cdot 5^{9}\cdot 11^{5} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.3110400000000.2	x^10 - 3x^9 + 4x^8 - 10x^7 + 31x^6 - 45x^5 + 22x^4 + 4x^3 - 10x^2 + 6x + 4	\( -\,2^{15}\cdot 3^{5}\cdot 5^{8} \)	$F_5 \wr C_2$ (as 10T33)	$[2]$
10.0.5435817984000.1	x^10 - 2x^9 - 6x^8 + 8x^7 + 38x^6 - 60x^5 + 36x^4 - 24x^3 + 21x^2 - 10x + 2	\( -\,2^{29}\cdot 3^{4}\cdot 5^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.6115295232000.2	x^10 - 4x^9 + 8x^8 - 16x^7 + 18x^6 - 16x^5 + 36x^4 + 8x^3 + 34x^2 + 8x + 8	\( -\,2^{26}\cdot 3^{6}\cdot 5^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.8388608000000.2	x^10 - 2x^9 + x^8 - 16x^7 + 64x^6 - 104x^5 + 84x^4 - 32x^3 + 12x^2 - 8x + 4	\( -\,2^{29}\cdot 5^{6} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.8388608000000.3	x^10 - 2x^9 + 9x^8 - 8x^7 + 36x^6 - 24x^5 + 88x^4 - 16x^3 + 117x^2 - 34x + 65	\( -\,2^{29}\cdot 5^{6} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.9784472371200.4	x^10 - 4x^9 + 12x^8 - 32x^7 + 60x^6 - 72x^5 + 96x^4 - 184x^3 + 249x^2 - 164x + 40	\( -\,2^{29}\cdot 3^{6}\cdot 5^{2} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.6.9932496465625.1	x^10 - 4x^9 + x^8 + 16x^7 - 31x^6 + 22x^5 + 32x^4 - 87x^3 + 36x^2 + 22x + 1	\( 5^{5}\cdot 19^{4}\cdot 29^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.12800000000000.4	x^10 - 4x^9 + 5x^8 - 10x^6 - 10x^4 + 125x^2 + 100x + 25	\( -\,2^{18}\cdot 5^{11} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.12800000000000.5	x^10 - 20x^7 + 10x^6 + 16x^5 + 100x^4 - 100x^3 - 135x^2 + 80x + 68	\( -\,2^{18}\cdot 5^{11} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.41472000000000.1	x^10 - 4x^9 + 3x^8 - 8x^7 + 38x^6 - 52x^5 + 90x^4 - 100x^3 + 175x^2 - 100x + 25	\( -\,2^{18}\cdot 3^{4}\cdot 5^{9} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.41472000000000.2	x^10 - 2x^9 + 3x^8 + 8x^7 - 22x^6 + 40x^5 + 54x^4 - 116x^3 + 19x^2 + 154x + 61	\( -\,2^{18}\cdot 3^{4}\cdot 5^{9} \)	$F_5 \wr C_2$ (as 10T33)	Trivial (GRH)
10.0.41943040000000.1	x^10 - 4x^9 + 5x^8 + 6x^6 - 8x^5 - 2x^4 + 10x^2 + 8x + 2	\( -\,2^{29}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.41943040000000.2	x^10 - 4x^9 + 5x^8 - 2x^6 + 8x^5 + 6x^4 + 10x^2 + 8x + 2	\( -\,2^{29}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.41943040000000.3	x^10 - 4x^9 + 5x^8 + 4x^6 - 16x^5 - 12x^4 + 40x^2 + 32x + 8	\( -\,2^{29}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.41943040000000.4	x^10 - 4x^9 + 5x^8 - 12x^6 + 16x^5 + 4x^4 + 40x^2 + 32x + 8	\( -\,2^{29}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.41943040000000.5	x^10 - 2x^9 - 3x^8 + 16x^7 - 4x^6 - 16x^5 + 8x^4 - 8x^3 + 141x^2 + 86x + 13	\( -\,2^{29}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial (GRH)
10.0.41943040000000.9	x^10 - 4x^9 + 13x^8 - 32x^7 + 80x^6 - 152x^5 + 260x^4 - 320x^3 + 385x^2 - 300x + 185	\( -\,2^{29}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.48922361856000.2	x^10 - 4x^9 + 32x^7 - 52x^6 - 24x^5 + 184x^4 - 280x^3 + 225x^2 - 100x + 20	\( -\,2^{29}\cdot 3^{6}\cdot 5^{3} \)	$F_5 \wr C_2$ (as 10T33)	Trivial (GRH)
10.0.51200000000000.5	x^10 - 10x^8 + 60x^6 - 100x^5 + 50x^4 + 60x^3 - 95x^2 + 36	\( -\,2^{20}\cdot 5^{11} \)	$F_5 \wr C_2$ (as 10T33)	Trivial
10.0.51200000000000.8	x^10 - 4x^9 + x^8 + 16x^7 - 4x^6 - 56x^5 + 24x^4 + 144x^3 - 96x^2 - 176x + 200	\( -\,2^{20}\cdot 5^{11} \)	$F_5 \wr C_2$ (as 10T33)	Trivial (GRH)
10.0.59719680000000.1	x^10 - 2x^9 - 9x^8 + 8x^7 + 30x^6 + 24x^5 - 48x^4 - 116x^3 + 282x^2 - 100x + 10	\( -\,2^{20}\cdot 3^{6}\cdot 5^{7} \)	$F_5 \wr C_2$ (as 10T33)	Trivial