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 199196)

Label	Polynomial	Discriminant	Galois group	Class group
10.10.443952558373.1	x^10 - 11x^8 - 3x^7 + 37x^6 + 14x^5 - 48x^4 - 22x^3 + 20x^2 + 12x + 1	\( 61^{2}\cdot 397^{2}\cdot 757 \)	$C_2 \wr S_5$ (as 10T39)	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
10.10.572981288913.1	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
10.10.617567936161.1	x^10 - x^9 - 12x^8 + 5x^7 + 39x^6 - 11x^5 - 47x^4 + 15x^3 + 18x^2 - 9x + 1	\( 11^{8}\cdot 43\cdot 67 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.10.645863308453.1	x^10 - 2x^9 - 9x^8 + 15x^7 + 29x^6 - 31x^5 - 43x^4 + 14x^3 + 23x^2 + 3x - 1	\( 11^{8}\cdot 23\cdot 131 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	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
10.10.669871503125.1	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
10.10.769611580061.1	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
10.10.782566688557.1	x^10 - 3x^9 - 6x^8 + 19x^7 + 15x^6 - 40x^5 - 20x^4 + 29x^3 + 11x^2 - 4x - 1	\( 17^{2}\cdot 157\cdot 4153^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.805213821197.1	x^10 - 2x^9 - 8x^8 + 13x^7 + 23x^6 - 28x^5 - 28x^4 + 22x^3 + 13x^2 - 4x - 1	\( 61^{2}\cdot 397^{2}\cdot 1373 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.820298081773.1	x^10 - 2x^9 - 8x^8 + 12x^7 + 22x^6 - 22x^5 - 24x^4 + 13x^3 + 10x^2 - 2x - 1	\( 1523\cdot 538606751 \)	$S_{10}$ (as 10T45)	Trivial
10.10.822624971833.1	x^10 - 10x^8 - 3x^7 + 29x^6 + 10x^5 - 32x^4 - 10x^3 + 12x^2 + 3x - 1	\( 7\cdot 79\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.823301450757.1	x^10 - 4x^9 - 3x^8 + 25x^7 - 8x^6 - 46x^5 + 27x^4 + 27x^3 - 18x^2 - x + 1	\( 3^{2}\cdot 19^{2}\cdot 37\cdot 2617^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.838055754181.1	x^10 - 2x^9 - 8x^8 + 17x^7 + 17x^6 - 43x^5 - 3x^4 + 31x^3 - 9x^2 - 3x + 1	\( 61^{2}\cdot 397^{2}\cdot 1429 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.901040998181.1	x^10 - 2x^9 - 8x^8 + 15x^7 + 22x^6 - 37x^5 - 24x^4 + 35x^3 + 7x^2 - 11x + 1	\( 31\cdot 1877\cdot 1933\cdot 8011 \)	$S_{10}$ (as 10T45)	Trivial
10.10.911025153125.1	x^10 - 4x^9 - 3x^8 + 22x^7 + 2x^6 - 41x^5 - 3x^4 + 27x^3 + 5x^2 - 4x - 1	\( 5^{5}\cdot 419\cdot 695771 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.913378895261.1	x^10 - 4x^9 - 3x^8 + 27x^7 - 15x^6 - 40x^5 + 30x^4 + 20x^3 - 13x^2 - 3x + 1	\( 7\cdot 31^{2}\cdot 135778043 \)	$S_{10}$ (as 10T45)	Trivial
10.10.925108450304.1	x^10 - 2x^9 - 8x^8 + 12x^7 + 24x^6 - 22x^5 - 29x^4 + 14x^3 + 12x^2 - 2x - 1	\( 2^{10}\cdot 9649\cdot 93629 \)	$S_{10}$ (as 10T45)	Trivial
10.10.928565973197.1	x^10 - 2x^9 - 8x^8 + 13x^7 + 24x^6 - 26x^5 - 32x^4 + 16x^3 + 16x^2 - 1	\( 2729\cdot 5659\cdot 60127 \)	$S_{10}$ (as 10T45)	Trivial
10.10.943765631693.1	x^10 - 2x^9 - 8x^8 + 12x^7 + 23x^6 - 20x^5 - 25x^4 + 10x^3 + 10x^2 - x - 1	\( 943765631693 \)	$S_{10}$ (as 10T45)	Trivial
10.10.944409985381.1	x^10 - x^9 - 11x^8 + 9x^7 + 38x^6 - 27x^5 - 51x^4 + 34x^3 + 22x^2 - 16x + 1	\( 709\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.950202516997.1	x^10 - 10x^8 - x^7 + 33x^6 + 3x^5 - 44x^4 - x^3 + 21x^2 - 2x - 1	\( 607\cdot 37649\cdot 41579 \)	$S_{10}$ (as 10T45)	Trivial
10.10.967077633761.1	x^10 - 5x^9 + 2x^8 + 22x^7 - 22x^6 - 32x^5 + 35x^4 + 19x^3 - 16x^2 - 4x + 1	\( 17\cdot 61^{2}\cdot 97\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.968074628125.1	x^10 - x^9 - 10x^8 + 8x^7 + 34x^6 - 23x^5 - 46x^4 + 28x^3 + 20x^2 - 13x + 1	\( 5^{5}\cdot 11\cdot 28162171 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.983282290021.1	x^10 - 4x^9 - 3x^8 + 23x^7 - 2x^6 - 42x^5 + 8x^4 + 28x^3 - 5x^2 - 6x + 1	\( 661\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.983479472873.1	x^10 - 2x^9 - 8x^8 + 15x^7 + 17x^6 - 28x^5 - 15x^4 + 17x^3 + 6x^2 - 3x - 1	\( 1567\cdot 627619319 \)	$S_{10}$ (as 10T45)	Trivial
10.10.993530403125.1	x^10 - x^9 - 10x^8 + 7x^7 + 34x^6 - 18x^5 - 46x^4 + 21x^3 + 20x^2 - 10x + 1	\( 5^{5}\cdot 13^{2}\cdot 1881241 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.995293579409.1	x^10 - 2x^9 - 8x^8 + 16x^7 + 17x^6 - 35x^5 - 11x^4 + 26x^3 - 6x + 1	\( 17783\cdot 55968823 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1056719528125.1	x^10 - x^9 - 11x^8 + 13x^7 + 35x^6 - 43x^5 - 36x^4 + 41x^3 + 10x^2 - 7x - 1	\( 5^{5}\cdot 89\cdot 1061\cdot 3581 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1071443843101.1	x^10 - 2x^9 - 8x^8 + 17x^7 + 17x^6 - 40x^5 - 12x^4 + 32x^3 + 3x^2 - 6x - 1	\( 41\cdot 283\cdot 92341967 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1086015136753.1	x^10 - 2x^9 - 8x^8 + 15x^7 + 19x^6 - 32x^5 - 18x^4 + 22x^3 + 8x^2 - 3x - 1	\( 43^{2}\cdot 4583\cdot 128159 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1102817328125.1	x^10 - 2x^9 - 10x^8 + 23x^7 + 15x^6 - 47x^5 - 5x^4 + 32x^3 - 2x^2 - 7x + 1	\( 5^{6}\cdot 1039\cdot 67931 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1125421834861.1	x^10 - 3x^9 - 6x^8 + 23x^7 + x^6 - 40x^5 + 11x^4 + 22x^3 - 8x^2 - 3x + 1	\( 1125421834861 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1129529628125.1	x^10 - x^9 - 10x^8 + 6x^7 + 36x^6 - 7x^5 - 53x^4 - 8x^3 + 25x^2 + 11x + 1	\( 5^{5}\cdot 41\cdot 521\cdot 16921 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1131659253125.1	x^10 - 4x^9 - 4x^8 + 28x^7 - 6x^6 - 48x^5 + 10x^4 + 31x^3 - 6x - 1	\( 5^{5}\cdot 5471\cdot 66191 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1136222450677.1	x^10 - 12x^8 - 6x^7 + 39x^6 + 26x^5 - 37x^4 - 22x^3 + 10x^2 + 3x - 1	\( 853\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.1140241465757.1	x^10 - 2x^9 - 8x^8 + 15x^7 + 22x^6 - 36x^5 - 25x^4 + 31x^3 + 10x^2 - 8x - 1	\( 29\cdot 4217\cdot 9323849 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1142405128125.1	x^10 - 3x^9 - 6x^8 + 23x^7 + 4x^6 - 49x^5 + 15x^4 + 27x^3 - 9x^2 - 3x + 1	\( 3^{2}\cdot 5^{5}\cdot 151\cdot 268999 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1148718338533.1	x^10 - x^9 - 11x^8 + 9x^7 + 35x^6 - 18x^5 - 44x^4 + 8x^3 + 19x^2 + 2x - 1	\( 1148718338533 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1172459165509.1	x^10 - 12x^8 - 6x^7 + 40x^6 + 29x^5 - 42x^4 - 38x^3 + 3x^2 + 7x + 1	\( 4723\cdot 7639\cdot 32497 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1175858493445.1	x^10 - 5x^9 + 28x^7 - 17x^6 - 55x^5 + 33x^4 + 43x^3 - 13x^2 - 9x - 1	\( 5\cdot 61^{2}\cdot 397^{2}\cdot 401 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.1185241902869.1	x^10 - 3x^9 - 8x^8 + 25x^7 + 20x^6 - 60x^5 - 30x^4 + 47x^3 + 26x^2 - 1	\( 43\cdot 47\cdot 61^{2}\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.10.1230634335821.1	x^10 - x^9 - 9x^8 + 7x^7 + 25x^6 - 13x^5 - 25x^4 + 7x^3 + 9x^2 - x - 1	\( 11^{8}\cdot 5741 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.10.1237140740093.1	x^10 - 2x^9 - 9x^8 + 17x^7 + 28x^6 - 50x^5 - 33x^4 + 59x^3 + 8x^2 - 23x + 5	\( 5659\cdot 218614727 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1253482128125.1	x^10 - x^9 - 10x^8 + 9x^7 + 31x^6 - 26x^5 - 31x^4 + 24x^3 + 8x^2 - 7x + 1	\( 5^{5}\cdot 181\cdot 2216101 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1261262503125.1	x^10 - 3x^9 - 7x^8 + 25x^7 + 10x^6 - 64x^5 + 9x^4 + 56x^3 - 18x^2 - 9x + 1	\( 3^{2}\cdot 5^{5}\cdot 109\cdot 411421 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1273821942101.1	x^10 - 2x^9 - 8x^8 + 14x^7 + 20x^6 - 31x^5 - 17x^4 + 24x^3 + 3x^2 - 6x + 1	\( 461\cdot 2763171241 \)	$S_{10}$ (as 10T45)	Trivial
10.10.1276520753125.1	x^10 - 4x^9 - 3x^8 + 24x^7 - 3x^6 - 45x^5 + 10x^4 + 28x^3 - 6x^2 - 4x + 1	\( 5^{5}\cdot 408486641 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.10.1311048326717.1	x^10 - x^9 - 10x^8 + 11x^7 + 31x^6 - 35x^5 - 33x^4 + 36x^3 + 7x^2 - 5x - 1	\( 31\cdot 127\cdot 333006941 \)	$S_{10}$ (as 10T45)	Trivial

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