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 5148)

Label	Polynomial	Discriminant	Galois group	Class group
10.0.236438047.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + x^5 + x^4 - x + 1	\( -\,236438047 \)	$S_{10}$ (as 10T45)	Trivial
10.0.240232739.1	x^10 - 2x^9 + 2x^8 - 2x^6 + 4x^5 - 4x^4 + x^3 + 3x^2 - 3x + 1	\( -\,467\cdot 514417 \)	$S_{10}$ (as 10T45)	Trivial
10.0.243415027.1	x^10 - x^7 + x^6 + 2x^5 - x^3 - 2x^2 + 1	\( -\,17\cdot 14318531 \)	$S_{10}$ (as 10T45)	Trivial
10.0.278005859.1	x^10 - x^9 - x^8 + 4x^7 - 2x^6 - 3x^5 + 4x^4 - 2x^2 + 1	\( -\,278005859 \)	$S_{10}$ (as 10T45)	Trivial
10.2.801214577.1	x^10 - 3x^9 + 3x^8 - x^7 + x^5 - 3x^4 + 4x^3 - x^2 - x + 1	\( 801214577 \)	$S_{10}$ (as 10T45)	Trivial
10.2.802448461.1	x^10 - 2x^7 - x^6 + 2x^5 + x^4 - 2x^2 - x + 1	\( 53\cdot 71\cdot 213247 \)	$S_{10}$ (as 10T45)	Trivial
10.2.803282693.1	x^10 - 3x^9 + 7x^8 - 11x^7 + 12x^6 - 8x^5 + 2x^4 + 4x^3 - 6x^2 + 4x - 1	\( 803282693 \)	$S_{10}$ (as 10T45)	Trivial
10.2.809040437.1	x^10 - 2x^9 + 4x^7 - 4x^6 + 3x^4 - x^3 - x^2 + 1	\( 809040437 \)	$S_{10}$ (as 10T45)	Trivial
10.2.814270253.1	x^10 - x^9 - 2x^8 + 4x^7 - x^6 - 5x^5 + 5x^4 + x^3 - 3x^2 + x + 1	\( 47\cdot 1753\cdot 9883 \)	$S_{10}$ (as 10T45)	Trivial
10.2.817298432.1	x^10 + x^8 - 2x^7 + x^4 + 2x^3 - x^2 - 1	\( 2^{10}\cdot 798143 \)	$S_{10}$ (as 10T45)	Trivial
10.2.827119069.1	x^10 - x^9 + 4x^8 - 4x^7 + 7x^6 - 8x^5 + 7x^4 - 7x^3 + 4x^2 - 3x + 1	\( 7^{2}\cdot 61\cdot 276721 \)	$S_{10}$ (as 10T45)	Trivial
10.2.838803593.1	x^10 - x^9 - 2x^8 + 3x^7 + x^6 - x^5 - x^4 - x^3 + 2x^2 + x - 1	\( 79\cdot 10617767 \)	$S_{10}$ (as 10T45)	Trivial
10.2.856749056.1	x^10 - x^8 - 2x^7 + x^6 + 2x^5 - x^4 - 2x^3 + 2x + 1	\( 2^{10}\cdot 103\cdot 8123 \)	$S_{10}$ (as 10T45)	Trivial
10.2.860443648.1	x^10 + x^8 - 2x^7 - x^6 - 2x^5 + 2x^3 + x^2 + 2x - 1	\( 2^{10}\cdot 840277 \)	$S_{10}$ (as 10T45)	Trivial
10.2.875753293.1	x^10 - 2x^9 + 4x^8 - 4x^7 + 3x^6 - 3x^4 + 4x^3 - 4x^2 + 3x - 1	\( 875753293 \)	$S_{10}$ (as 10T45)	Trivial
10.2.880280981.1	x^10 - x^9 + x^7 - x^5 + 2x^4 - x^3 - x^2 + 2x - 1	\( 880280981 \)	$S_{10}$ (as 10T45)	Trivial
10.2.917035997.1	x^10 - 2x^7 + x^5 + 2x^4 + 3x^3 - 3x^2 - 2x + 1	\( 59\cdot 61\cdot 254803 \)	$S_{10}$ (as 10T45)	Trivial
10.2.1336784689.1	x^10 - x^8 - 2x^6 - 2x^5 + 4x^4 + 2x^3 - 3x^2 - x + 1	\( 113\cdot 199\cdot 59447 \)	$S_{10}$ (as 10T45)	Trivial
10.4.3316535227.1	x^10 - x^7 + x^6 + 3x^5 - 2x^3 - 3x^2 + x + 1	\( -\,1483\cdot 2236369 \)	$S_{10}$ (as 10T45)	Trivial
10.4.3393524187.1	x^10 - 4x^9 + 7x^8 - 4x^7 - 6x^6 + 13x^5 - 9x^4 - x^3 + 5x^2 - 4x + 1	\( -\,3^{3}\cdot 1367\cdot 91943 \)	$S_{10}$ (as 10T45)	Trivial
10.4.3409004107.1	x^10 - x^8 - x^7 - x^6 - 3x^5 + 3x^4 + x^3 + 3x - 1	\( -\,3409004107 \)	$S_{10}$ (as 10T45)	Trivial
10.4.3607983971.1	x^10 - x^9 + 2x^8 - x^7 + x^5 - 3x^4 + x^3 - x^2 - x + 1	\( -\,3607983971 \)	$S_{10}$ (as 10T45)	Trivial
10.4.3851489219.1	x^10 - x^9 + x^7 + x^6 - 3x^4 + 4x^3 - 3x + 1	\( -\,23\cdot 167456053 \)	$S_{10}$ (as 10T45)	Trivial
10.4.3911509571.1	x^10 - x^9 + x^8 - 3x^7 - x^6 - x^5 + 3x^3 + x - 1	\( -\,167\cdot 1609\cdot 14557 \)	$S_{10}$ (as 10T45)	Trivial
10.0.9612579511.1	x^10 - x + 1	\( -\,29\cdot 4127\cdot 80317 \)	$S_{10}$ (as 10T45)	Trivial
10.2.10387420489.1	x^10 - x - 1	\( 173\cdot 60042893 \)	$S_{10}$ (as 10T45)	Trivial
10.6.19388527573.1	x^10 - 3x^8 - x^7 + 2x^6 + x^5 + 3x^3 - 3x + 1	\( 16493\cdot 1175561 \)	$S_{10}$ (as 10T45)	Trivial
10.6.22442338621.1	x^10 - x^9 - 2x^8 - x^6 + 2x^5 + 2x^4 + 2x^3 - 3x + 1	\( 277\cdot 81019273 \)	$S_{10}$ (as 10T45)	Trivial
10.6.33051297589.1	x^10 - 2x^9 - x^6 + 5x^5 - 2x^2 - 3x + 1	\( 47903\cdot 689963 \)	$S_{10}$ (as 10T45)	Trivial
10.6.39910805693.1	x^10 - x^9 - 3x^8 + 2x^7 + x^6 + 2x^4 + x^2 - x - 1	\( 11\cdot 3628255063 \)	$S_{10}$ (as 10T45)	Trivial
10.6.40659383389.1	x^10 - x^8 - x^7 - 3x^6 + x^5 + 3x^2 - 1	\( 10753\cdot 3781213 \)	$S_{10}$ (as 10T45)	Trivial
10.6.70042903433.1	x^10 - 2x^9 + x^5 - x^4 + 3x^3 + 2x^2 - 2x - 1	\( 43\cdot 751\cdot 967\cdot 2243 \)	$S_{10}$ (as 10T45)	Trivial
10.6.70926158429.1	x^10 - 2x^8 - 2x^6 - x^5 + x^3 + 3x^2 - 1	\( 7^{3}\cdot 29\cdot 7130407 \)	$S_{10}$ (as 10T45)	Trivial
10.6.90403855741.1	x^10 - x^9 - 2x^8 + 4x^5 + x^4 - x^2 - 2x + 1	\( 31\cdot 2916253411 \)	$S_{10}$ (as 10T45)	Trivial
10.8.94822656283.1	x^10 - x^9 - 4x^8 + 3x^7 + 6x^5 + 4x^4 - 11x^3 + 4x - 1	\( -\,111847\cdot 847789 \)	$S_{10}$ (as 10T45)	Trivial
10.8.192422158163.1	x^10 - 4x^9 + x^8 + 15x^7 - 19x^6 - 9x^5 + 25x^4 - 2x^3 - 9x^2 + x + 1	\( -\,1483\cdot 129751961 \)	$S_{10}$ (as 10T45)	Trivial
10.2.231378450041.1	x^10 - 3x - 2	\( 43\cdot 5380894187 \)	$S_{10}$ (as 10T45)	Trivial
10.8.255275929283.1	x^10 - 4x^9 + 12x^7 - 3x^6 - 7x^5 - 4x^4 - 4x^3 + 6x^2 + 3x - 1	\( -\,79\cdot 3231340877 \)	$S_{10}$ (as 10T45)	Trivial
10.8.304597739107.1	x^10 - 3x^9 + x^8 + 10x^7 - 15x^6 - 12x^5 + 21x^4 + 4x^3 - 9x^2 + 1	\( -\,19\cdot 863\cdot 18576431 \)	$S_{10}$ (as 10T45)	Trivial
10.8.369566563328.1	x^10 - 4x^9 - x^8 + 18x^7 - 11x^6 - 20x^5 + 18x^4 + 6x^3 - 9x^2 + 1	\( -\,2^{10}\cdot 360904847 \)	$S_{10}$ (as 10T45)	Trivial
10.8.386784463643.1	x^10 - 2x^9 - 6x^8 + 9x^7 + 15x^6 - 11x^5 - 18x^4 + 2x^3 + 9x^2 + x - 1	\( -\,386784463643 \)	$S_{10}$ (as 10T45)	Trivial
10.2.396728346361.1	x^10 - 4x - 1	\( 1637\cdot 242350853 \)	$S_{10}$ (as 10T45)	Trivial
10.2.399218580736.1	x^10 - 8x - 4	\( 2^{8}\cdot 317\cdot 4919393 \)	$S_{10}$ (as 10T45)	Trivial
10.2.406718580736.1	x^10 - 2x - 1	\( 2^{11}\cdot 13\cdot 15276389 \)	$S_{10}$ (as 10T45)	Trivial
10.8.418370073091.1	x^10 - 3x^9 + 3x^7 + 2x^6 + 7x^5 - 13x^4 - 8x^3 + 11x^2 - 1	\( -\,418370073091 \)	$S_{10}$ (as 10T45)	Trivial
10.8.488269224944.1	x^10 - 2x^9 - 4x^8 + 7x^7 + x^6 + 3x^5 + 3x^4 - 11x^3 + 4x - 1	\( -\,2^{4}\cdot 30516826559 \)	$S_{10}$ (as 10T45)	Trivial
10.10.513087549389.1	x^10 - 4x^9 - 2x^8 + 23x^7 - 11x^6 - 40x^5 + 30x^4 + 21x^3 - 18x^2 + 1	\( 460181\cdot 1114969 \)	$S_{10}$ (as 10T45)	Trivial
10.8.523513623879.1	x^10 - 3x^9 - 4x^8 + 18x^7 - 34x^5 + 11x^4 + 23x^3 - 8x^2 - 4x + 1	\( -\,3^{5}\cdot 2154377053 \)	$S_{10}$ (as 10T45)	Trivial
10.10.653113904957.1	x^10 - x^9 - 9x^8 + 9x^7 + 25x^6 - 23x^5 - 24x^4 + 17x^3 + 8x^2 - 3x - 1	\( 37\cdot 47\cdot 239\cdot 1571417 \)	$S_{10}$ (as 10T45)	Trivial
10.10.769611580061.1	x^10 - 4x^9 - 3x^8 + 22x^7 + 3x^6 - 41x^5 - 8x^4 + 25x^3 + 8x^2 - 3x - 1	\( 769611580061 \)	$S_{10}$ (as 10T45)	Trivial