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 )

Label	Polynomial	Discriminant	Galois group	Class group
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)	$[11]$
10.0.43913358828288.1	x^10 - 4x^9 + 5x^8 + 14x^7 - 52x^6 + 8x^5 + 337x^4 - 984x^3 + 1389x^2 - 1026x + 324	\( -\,2^{8}\cdot 3^{5}\cdot 163^{4} \)	$D_{10}$ (as 10T3)	$[11]$
10.0.47483866083328.2	x^10 - 4x^9 + 24x^7 - 29x^6 - 36x^5 + 78x^4 + 4x^3 - 22x^2 - 100x + 112	\( -\,2^{12}\cdot 103^{5} \)	$A_5\times C_2$ (as 10T11)	$[15]$
10.0.49294471550063.1	x^10 - 4x^9 + 16x^8 - 42x^7 + 99x^6 - 181x^5 + 297x^4 - 378x^3 + 432x^2 - 324x + 243	\( -\,23\cdot 1609\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.54025845694031.1	x^10 - 4x^9 + 16x^8 - 40x^7 + 93x^6 - 167x^5 + 279x^4 - 360x^3 + 432x^2 - 324x + 243	\( -\,36497^{2}\cdot 40559 \)	$C_2 \wr S_5$ (as 10T39)	$[14]$
10.0.54470105243231.1	x^10 - 2x^9 + 12x^8 - 18x^7 + 63x^6 - 73x^5 + 189x^4 - 162x^3 + 324x^2 - 162x + 243	\( -\,61^{2}\cdot 131\cdot 397^{2}\cdot 709 \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.55534384018432.1	x^10 + 22x^8 + 176x^6 + 605x^4 + 792x^2 + 253	\( -\,2^{10}\cdot 11^{9}\cdot 23 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 6]$
10.0.57910048116275.1	x^10 - x^9 + 9x^8 - 13x^7 + 39x^6 - 59x^5 + 117x^4 - 117x^3 + 243x^2 - 81x + 243	\( -\,5^{2}\cdot 37\cdot 47\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$
10.0.58551145104384.1	x^10 - 4x^9 + 17x^8 - 26x^7 + 25x^6 + 16x^5 + 19x^4 - 82x^3 + 282x^2 - 120x + 16	\( -\,2^{10}\cdot 3^{4}\cdot 163^{4} \)	$D_{10}$ (as 10T3)	$[11]$
10.0.64387371291203.1	x^10 - 3x^9 + 10x^8 - 15x^7 + 28x^6 - 32x^5 + 84x^4 - 135x^3 + 270x^2 - 243x + 243	\( -\,59\cdot 73^{2}\cdot 97\cdot 1453^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[14]$
10.0.65537725589747.1	x^10 - 4x^9 + 12x^8 - 23x^7 + 42x^6 - 65x^5 + 126x^4 - 207x^3 + 324x^2 - 324x + 243	\( -\,23\cdot 661\cdot 65657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.68196858635907.1	x^10 - 2x^9 + 8x^8 - 17x^7 + 28x^6 - 67x^5 + 84x^4 - 153x^3 + 216x^2 - 162x + 243	\( -\,3^{2}\cdot 37\cdot 43^{2}\cdot 71\cdot 1249^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.68279420878511.1	x^10 + 6x^8 - 6x^7 + 15x^6 - 37x^5 + 45x^4 - 54x^3 + 162x^2 + 243	\( -\,47\cdot 337\cdot 65657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.69831323872151.1	x^10 + 7x^8 - 9x^7 + 18x^6 - 53x^5 + 54x^4 - 81x^3 + 189x^2 + 243	\( -\,97\cdot 167\cdot 65657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[14]$
10.0.71786961877952.1	x^10 - x^9 + 5x^8 - 4x^7 + 14x^6 - 9x^5 + 28x^4 - 16x^3 + 40x^2 - 16x + 32	\( -\,2^{6}\cdot 47^{2}\cdot 71\cdot 73\cdot 313^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.72230580325103.1	x^10 + 3x^8 - 2x^7 + 7x^6 - 7x^5 + 14x^4 - 8x^3 + 24x^2 + 32	\( -\,2087\cdot 186037^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.77265229938688.1	x^10 + 22x^8 + 176x^6 + 616x^4 + 880x^2 + 352	\( -\,2^{15}\cdot 11^{9} \)	$C_{10}$ (as 10T1)	$[22]$
10.0.79184630786579.1	x^10 - 4x^9 + 14x^8 - 23x^7 + 46x^6 - 39x^5 + 77x^4 - 16x^3 + 97x^2 + 26x + 64	\( -\,157^{2}\cdot 937^{2}\cdot 3659 \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.79937203918592.2	x^10 + 20x^8 + 113x^6 + 248x^4 + 203x^2 + 47	\( -\,2^{8}\cdot 47\cdot 81509^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[14]$
10.0.92023536681203.1	x^10 - 4x^9 + 15x^8 - 27x^7 + 57x^6 - 56x^5 + 100x^4 - 38x^3 + 113x^2 + 7x + 75	\( -\,21347\cdot 65657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[15]$
10.0.92100620055287.1	x^10 + 9x^8 - x^7 + 40x^6 - 7x^5 + 120x^4 - 9x^3 + 243x^2 + 243	\( -\,36497^{2}\cdot 69143 \)	$C_2 \wr S_5$ (as 10T39)	$[16]$
10.0.92108708193359.1	x^10 + 8x^8 - 2x^7 + 39x^6 - 5x^5 + 117x^4 - 18x^3 + 216x^2 + 243	\( -\,11\cdot 13\cdot 433\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$
10.0.93289366800128.1	x^10 - x^9 + 4x^8 - 4x^7 + 12x^6 - 10x^5 + 24x^4 - 16x^3 + 32x^2 - 16x + 32	\( -\,2^{8}\cdot 863\cdot 20549^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[13]$
10.0.96032748066779.1	x^10 - 5x^9 + 15x^8 - 29x^7 + 54x^6 - 70x^5 + 108x^4 - 58x^3 + 145x^2 + x + 81	\( -\,12011\cdot 89417^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.99808561707863.1	x^10 - 3x^9 + 13x^8 - 28x^7 + 73x^6 - 118x^5 + 219x^4 - 252x^3 + 351x^2 - 243x + 243	\( -\,83\cdot 181\cdot 81509^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[18]$
10.0.100716196621499.1	x^10 - 3x^9 + 14x^8 - 30x^7 + 80x^6 - 127x^5 + 240x^4 - 270x^3 + 378x^2 - 243x + 243	\( -\,36497^{2}\cdot 75611 \)	$C_2 \wr S_5$ (as 10T39)	$[14]$
10.0.102394555692839.1	x^10 - x^9 + 10x^8 - 9x^7 + 47x^6 - 37x^5 + 141x^4 - 81x^3 + 270x^2 - 81x + 243	\( -\,36497^{2}\cdot 76871 \)	$C_2 \wr S_5$ (as 10T39)	$[3, 6]$
10.0.102602392460272.1	x^10 - 2x^9 + 3x^8 - 4x^7 + 4x^6 - 2x^5 + 8x^4 - 16x^3 + 24x^2 - 32x + 32	\( -\,2^{4}\cdot 103\cdot 249517^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[17]$
10.0.106079108279536.1	x^10 - 2x^9 + 5x^8 - 5x^7 + 8x^6 - 5x^5 + 16x^4 - 20x^3 + 40x^2 - 32x + 32	\( -\,2^{4}\cdot 7\cdot 313\cdot 55009^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.108266600324403.1	x^10 - x^9 + 7x^8 - 4x^7 + 38x^6 - 25x^5 + 42x^4 + 3x^3 + 14x^2 - 3x + 1	\( -\,3^{5}\cdot 19^{4}\cdot 43^{4} \)	$D_{10}$ (as 10T3)	$[11]$
10.0.109172417298176.1	x^10 - x^9 + 2x^8 - 6x^7 + 8x^6 - 10x^5 + 16x^4 - 24x^3 + 16x^2 - 16x + 32	\( -\,2^{8}\cdot 19^{2}\cdot 71\cdot 4079^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[13]$
10.0.111796920332863.1	x^10 + 3x^8 - 2x^7 + 3x^6 - 9x^5 + 6x^4 - 8x^3 + 24x^2 + 32	\( -\,1063\cdot 324301^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[11]$
10.0.112708546547687.1	x^10 - x^9 + 10x^8 - 11x^7 + 49x^6 - 47x^5 + 147x^4 - 99x^3 + 270x^2 - 81x + 243	\( -\,38569^{2}\cdot 75767 \)	$C_2 \wr S_5$ (as 10T39)	$[20]$
10.0.113647553656871.1	x^10 - x^9 + 10x^8 - 9x^7 + 51x^6 - 37x^5 + 153x^4 - 81x^3 + 270x^2 - 81x + 243	\( -\,13\cdot 6563\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[18]$
10.0.113700834897231.1	x^10 - x^9 + 10x^8 - 7x^7 + 49x^6 - 27x^5 + 147x^4 - 63x^3 + 270x^2 - 81x + 243	\( -\,3\cdot 37\cdot 769\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$
10.0.114339955792896.1	x^10 - 2x^9 + 3x^8 - 6x^7 + 10x^6 - 14x^5 + 20x^4 - 24x^3 + 24x^2 - 32x + 32	\( -\,2^{10}\cdot 3^{2}\cdot 71\cdot 13219^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[13]$
10.0.114768614675312.1	x^10 - 2x^9 + 4x^8 - 7x^7 + 11x^6 - 13x^5 + 22x^4 - 28x^3 + 32x^2 - 32x + 32	\( -\,2^{4}\cdot 13^{2}\cdot 983\cdot 6571^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[11]$
10.0.115457271885167.1	x^10 - 4x^9 + 13x^8 - 29x^7 + 68x^6 - 121x^5 + 204x^4 - 261x^3 + 351x^2 - 324x + 243	\( -\,26783\cdot 65657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[13]$
10.0.116117348402176.1	x^10 + 20x^8 + 149x^6 + 519x^4 + 851x^2 + 529	\( -\,2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 8]$
10.0.116117348402176.2	x^10 + 25x^8 + 206x^6 + 711x^4 + 1035x^2 + 529	\( -\,2^{10}\cdot 11^{8}\cdot 23^{2} \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[2, 8]$
10.0.117045666703175.1	x^10 - x^9 + 4x^8 - 3x^7 - 7x^6 - x^5 - 21x^4 - 27x^3 + 108x^2 - 81x + 243	\( -\,5^{2}\cdot 7^{2}\cdot 983\cdot 9859^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[11]$
10.0.117387761757872.1	x^10 - x^9 + 3x^8 + 3x^7 + 27x^6 + 35x^5 + 38x^4 + 35x^3 + 17x^2 - 4x + 24	\( -\,2^{4}\cdot 947\cdot 88019^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[13]$
10.0.120057286872179.1	x^10 - 2x^9 + 12x^8 - 19x^7 + 64x^6 - 79x^5 + 192x^4 - 171x^3 + 324x^2 - 162x + 243	\( -\,193\cdot 467\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 8]$
10.0.120285414532047.1	x^10 - 5x^9 + 18x^8 - 39x^7 + 80x^6 - 108x^5 + 168x^4 - 130x^3 + 198x^2 - 49x + 109	\( -\,3\cdot 71\cdot 131\cdot 65657^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[2, 6]$
10.0.120320641431296.1	x^10 - 2x^9 + 9x^8 - 16x^7 + 44x^6 - 64x^5 + 132x^4 - 144x^3 + 243x^2 - 162x + 243	\( -\,2^{8}\cdot 2399\cdot 13997^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[14]$
10.0.120560905159375.1	x^10 - 2x^9 + 7x^8 - 13x^7 - x^6 + 67x^5 + 54x^4 - 55x^3 - 340x^2 - 276x + 1424	\( -\,5^{5}\cdot 131^{5} \)	$D_{10}$ (as 10T3)	$[12]$
10.0.123121484415728.1	x^10 + 3x^8 - x^7 + 8x^6 - 3x^5 + 16x^4 - 4x^3 + 24x^2 + 32	\( -\,2^{4}\cdot 2543\cdot 55009^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[13]$
10.0.129517482801911.1	x^10 - 2x^9 + 7x^8 - 13x^7 + 32x^6 - 59x^5 + 96x^4 - 117x^3 + 189x^2 - 162x + 243	\( -\,97\cdot 167\cdot 89417^{2} \)	$C_2 \wr S_5$ (as 10T39)	$[12]$
10.0.130165572027392.1	x^10 + 21x^8 + 161x^6 + 575x^4 + 960x^2 + 593	\( -\,2^{10}\cdot 11^{8}\cdot 593 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	$[20]$
10.0.132489755594496.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 16x^6 - 22x^5 + 32x^4 - 40x^3 + 48x^2 - 48x + 32	\( -\,2^{8}\cdot 3^{2}\cdot 89^{2}\cdot 191^{2}\cdot 199 \)	$C_2 \wr S_5$ (as 10T39)	$[15]$

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