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 1839)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.2357947691.1	x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( -\,11^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.0.52089208083.1	x^10 - x^9 + 5x^8 - 2x^7 + 16x^6 - 7x^5 + 20x^4 + x^3 + 12x^2 - 3x + 1	\( -\,3^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.0.219503494144.1	x^10 + 9x^8 + 28x^6 + 35x^4 + 15x^2 + 1	\( -\,2^{10}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.10.572981288913.1	x^10 - x^9 - 10x^8 + 10x^7 + 34x^6 - 34x^5 - 43x^4 + 43x^3 + 12x^2 - 12x + 1	\( 3^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.10.669871503125.1	x^10 - x^9 - 13x^8 + 8x^7 + 46x^6 - 11x^5 - 52x^4 + 7x^3 + 18x^2 - 3x - 1	\( 5^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.10.762939453125.1	x^10 - 10x^8 + 35x^6 - x^5 - 50x^4 + 5x^3 + 25x^2 - 5x - 1	\( 5^{17} \)	$C_{10}$ (as 10T1)	Trivial
10.10.2414538435584.1	x^10 - 11x^8 + 44x^6 - 77x^4 + 55x^2 - 11	\( 2^{10}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.0.3602729712967.1	x^10 - x^9 + 14x^8 - 7x^7 + 85x^6 - 29x^5 + 218x^4 - 8x^3 + 216x^2 - 48x + 32	\( -\,7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[5]$
10.0.7024111812608.1	x^10 + 18x^8 + 112x^6 + 280x^4 + 240x^2 + 32	\( -\,2^{15}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[5]$
10.10.7024111812608.1	x^10 - 18x^8 + 112x^6 - 280x^4 + 240x^2 - 32	\( 2^{15}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.0.7368586534375.1	x^10 - x^9 + 12x^8 - 12x^7 + 56x^6 - 56x^5 + 133x^4 - 133x^3 + 188x^2 - 188x + 199	\( -\,5^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[4]$
10.0.26439622160671.1	x^10 - x^9 + 2x^8 + 16x^7 - 9x^6 + 11x^5 + 43x^4 - 6x^3 + 63x^2 - 20x + 25	\( -\,31^{9} \)	$C_{10}$ (as 10T1)	$[3]$
10.0.37078857421875.1	x^10 + 10x^8 - 10x^7 + 90x^6 - 49x^5 + 125x^4 + 70x^3 + 95x^2 + 10x + 1	\( -\,3^{5}\cdot 5^{16} \)	$C_{10}$ (as 10T1)	$[11]$
10.10.39630026842637.1	x^10 - x^9 - 21x^8 + 21x^7 + 155x^6 - 155x^5 - 461x^4 + 461x^3 + 419x^2 - 419x + 67	\( 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.10.53339349076992.1	x^10 - 2x^9 - 22x^8 + 38x^7 + 142x^6 - 194x^5 - 265x^4 + 236x^3 + 66x^2 - 24x + 1	\( 2^{10}\cdot 3^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.0.77265229938688.1	x^10 + 22x^8 + 176x^6 + 616x^4 + 880x^2 + 352	\( -\,2^{15}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[22]$
10.10.77265229938688.1	x^10 - 22x^8 + 176x^6 - 616x^4 + 880x^2 - 352	\( 2^{15}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.10.79589952003133.1	x^10 - 3x^9 - 21x^8 + 56x^7 + 130x^6 - 304x^5 - 204x^4 + 471x^3 - 61x^2 - 89x + 23	\( 11^{8}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	Trivial
10.0.156250000000000.1	x^10 + 20x^8 + 120x^6 + 225x^4 + 90x^2 + 1	\( -\,2^{10}\cdot 5^{16} \)	$C_{10}$ (as 10T1)	$[5]$
10.0.162778775259375.1	x^10 - 3x^9 + 14x^8 - 28x^7 + 130x^6 - 192x^5 + 706x^4 - 677x^3 + 2494x^2 - 1125x + 4531	\( -\,3^{5}\cdot 5^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[22]$
10.0.185394287109375.1	x^10 + 10x^8 - 5x^7 - 41x^5 - 25x^4 + 170x^3 + 65x^2 - 25x + 199	\( -\,3^{5}\cdot 5^{17} \)	$C_{10}$ (as 10T1)	$[2]$
10.0.207252522098163.1	x^10 - x^9 + 13x^8 - 30x^7 + 164x^6 - 255x^5 + 448x^4 - 99x^3 + 106x^2 - 5x + 25	\( -\,3^{5}\cdot 31^{8} \)	$C_{10}$ (as 10T1)	$[5]$
10.10.304358957700017.1	x^10 - 3x^9 - 26x^8 + 68x^7 + 210x^6 - 464x^5 - 526x^4 + 987x^3 + 166x^2 - 389x + 43	\( 11^{8}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	Trivial
10.10.327381934393961.1	x^10 - x^9 - 18x^8 + 13x^7 + 91x^6 - 47x^5 - 143x^4 + 7x^3 + 72x^2 + 23x + 1	\( 41^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.0.530773810885219.1	x^10 - 3x^9 + 19x^8 - 40x^7 + 210x^6 - 320x^5 + 1364x^4 - 1353x^3 + 5467x^2 - 2585x + 10879	\( -\,11^{8}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	$[55]$
10.0.586732839846912.1	x^10 + 33x^8 + 396x^6 + 2079x^4 + 4455x^2 + 2673	\( -\,2^{10}\cdot 3^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 22]$
10.0.685948419200000.1	x^10 - 2x^9 + 18x^8 - 26x^7 + 206x^6 - 242x^5 + 1447x^4 - 1204x^3 + 6258x^2 - 2936x + 13201	\( -\,2^{10}\cdot 5^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[62]$
10.0.781250000000000.1	x^10 + 20x^8 + 100x^6 + 125x^4 + 50x^2 + 5	\( -\,2^{10}\cdot 5^{17} \)	$C_{10}$ (as 10T1)	$[22]$
10.0.873360422339584.1	x^10 + 25x^8 + 188x^6 + 475x^4 + 211x^2 + 25	\( -\,2^{10}\cdot 31^{8} \)	$C_{10}$ (as 10T1)	$[41]$
10.10.875463320250981.1	x^10 - 3x^9 - 31x^8 + 80x^7 + 310x^6 - 660x^5 - 1076x^4 + 1807x^3 + 937x^2 - 1125x - 131	\( 3^{5}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.0.875489472034463.1	x^10 - x^9 + 34x^8 - 34x^7 + 430x^6 - 430x^5 + 2509x^4 - 2509x^3 + 6964x^2 - 6964x + 9637	\( -\,11^{9}\cdot 13^{5} \)	$C_{10}$ (as 10T1)	$[50]$
10.0.1379687283212183.1	x^10 - 3x^9 + 24x^8 - 52x^7 + 310x^6 - 484x^5 + 2334x^4 - 2373x^3 + 10496x^2 - 5129x + 22793	\( -\,11^{8}\cdot 23^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 6]$
10.0.1706859170463744.1	x^10 - 2x^9 + 23x^8 - 34x^7 + 304x^6 - 356x^5 + 2435x^4 - 2014x^3 + 11703x^2 - 5370x + 26839	\( -\,2^{15}\cdot 3^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[5, 10]$
10.10.1706859170463744.1	x^10 - 2x^9 - 37x^8 + 62x^7 + 448x^6 - 572x^5 - 2029x^4 + 1634x^3 + 2991x^2 - 978x - 989	\( 2^{15}\cdot 3^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.10.1790566527853125.1	x^10 - x^9 - 43x^8 + 43x^7 + 661x^6 - 661x^5 - 4267x^4 + 4267x^3 + 9813x^2 - 9813x - 1451	\( 3^{5}\cdot 5^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2]$
10.0.1940336830676403.1	x^10 - x^9 + 17x^8 + 26x^7 + 230x^6 + 131x^5 + 370x^4 + 183x^3 + 486x^2 + 189x + 81	\( -\,3^{5}\cdot 41^{8} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2]$
10.0.2564544677734375.1	x^10 - 5x^9 + 20x^7 + 50x^6 - 108x^5 + 240x^4 + 85x^3 + 660x^2 - 685x + 1849	\( -\,5^{16}\cdot 7^{5} \)	$C_{10}$ (as 10T1)	$[2, 2, 2, 2]$
10.10.2665284492003125.1	x^10 - 3x^9 - 27x^8 + 44x^7 + 228x^6 - 138x^5 - 634x^4 - 95x^3 + 435x^2 + 225x + 25	\( 5^{5}\cdot 31^{8} \)	$C_{10}$ (as 10T1)	Trivial
10.0.3347948534700187.1	x^10 - x^9 + 45x^8 - 45x^7 + 749x^6 - 749x^5 + 5677x^4 - 5677x^3 + 19757x^2 - 19757x + 31021	\( -\,11^{9}\cdot 17^{5} \)	$C_{10}$ (as 10T1)	$[82]$
10.10.3689195226078208.1	x^10 - 2x^9 - 42x^8 + 70x^7 + 590x^6 - 746x^5 - 3233x^4 + 2588x^3 + 6282x^2 - 2120x - 3191	\( 2^{10}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	Trivial (GRH)
10.10.4396746947664269.1	x^10 - 3x^9 - 41x^8 + 104x^7 + 570x^6 - 1160x^5 - 3100x^4 + 4647x^3 + 5959x^2 - 5129x - 3389	\( 11^{8}\cdot 29^{5} \)	$C_{10}$ (as 10T1)	Trivial (GRH)
10.0.5000000000000000.1	x^10 - 10x^8 - 10x^7 + 80x^6 + 118x^5 + 305x^4 + 560x^3 + 1410x^2 + 260x + 2393	\( -\,2^{15}\cdot 5^{16} \)	$C_{10}$ (as 10T1)	$[11]$
10.10.5000000000000000.1	x^10 - 30x^8 - 10x^7 + 240x^6 + 78x^5 - 655x^4 - 320x^3 + 570x^2 + 420x + 49	\( 2^{15}\cdot 5^{16} \)	$C_{10}$ (as 10T1)	Trivial
10.10.5838511919737409.1	x^10 - x^9 - 54x^8 + 54x^7 + 1046x^6 - 1046x^5 - 8579x^4 + 8579x^3 + 25796x^2 - 25796x - 8579	\( 11^{9}\cdot 19^{5} \)	$C_{10}$ (as 10T1)	Trivial
10.0.6136912772340031.1	x^10 - 3x^9 + 34x^8 - 76x^7 + 570x^6 - 920x^5 + 5450x^4 - 5733x^3 + 29914x^2 - 15269x + 76231	\( -\,11^{8}\cdot 31^{5} \)	$C_{10}$ (as 10T1)	$[93]$
10.10.6424828185043053.1	x^10 - x^9 - 29x^8 - 15x^7 + 239x^6 + 321x^5 - 515x^4 - 1029x^3 + 94x^2 + 910x + 397	\( 3^{5}\cdot 31^{9} \)	$C_{10}$ (as 10T1)	Trivial
10.10.7545432611200000.1	x^10 - 55x^8 + 1100x^6 - 9625x^4 + 34375x^2 - 34375	\( 2^{10}\cdot 5^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2]$
10.0.8176563434619904.1	x^10 + 33x^8 + 288x^6 + 679x^4 + 531x^2 + 81	\( -\,2^{10}\cdot 41^{8} \)	$C_{10}$ (as 10T1)	$[5]$
10.0.9630096522760791.1	x^10 - x^9 + 56x^8 - 56x^7 + 1156x^6 - 1156x^5 + 10781x^4 - 10781x^3 + 45156x^2 - 45156x + 79531	\( -\,3^{5}\cdot 7^{5}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[2, 66]$
10.0.11258530353021875.4	x^10 - 3x^9 + 39x^8 - 88x^7 + 730x^6 - 1192x^5 + 7716x^4 - 8217x^3 + 46199x^2 - 23945x + 126611	\( -\,5^{5}\cdot 7^{5}\cdot 11^{8} \)	$C_{10}$ (as 10T1)	$[110]$