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 708)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.705911761.1	x^8 - x^7 + x^6 - 4x^5 + 5x^4 - 8x^3 + 4x^2 - 8x + 16	\( 163^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.5887339441.1	x^8 - x^7 - 11x^6 + 13x^5 + 32x^4 - 41x^3 - 23x^2 + 32x - 1	\( 277^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.10093618089.1	x^8 + x^6 - 3x^5 - 3x^4 - 6x^3 + 4x^2 + 16	\( 3^{6}\cdot 61^{4} \)	$\SL(2,3)$ (as 8T12)	$[2]$
8.8.10093618089.1	x^8 - 4x^7 - 4x^6 + 23x^5 + 4x^4 - 38x^3 - x^2 + 16x + 4	\( 3^{6}\cdot 61^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.14835483601.1	x^8 - 4x^7 + 5x^6 + x^5 - 6x^4 + 7x^3 + 31x^2 + 34x + 12	\( 349^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.24840596881.1	x^8 - x^6 - 2x^5 - 5x^4 - 6x^3 - 9x^2 + 81	\( 397^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.57178852641.1	x^8 - 2x^7 - 13x^6 + 24x^5 + 48x^4 - 73x^3 - 38x^2 + 9x + 3	\( 3^{4}\cdot 163^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.89526025681.1	x^8 - 5x^6 - 3x^5 + 28x^4 - 12x^3 - 80x^2 + 256	\( 547^{4} \)	$\SL(2,3)$ (as 8T12)	$[3]$
8.8.135754665601.1	x^8 - 15x^6 + 47x^4 - 38x^2 + 9	\( 607^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.180713410816.1	x^8 - 9x^6 + 23x^4 - 14x^2 + 1	\( 2^{8}\cdot 163^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.212558803681.1	x^8 + 15x^6 + 60x^4 + 35x^2 + 1	\( 7^{4}\cdot 97^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.244242535681.1	x^8 - 2x^7 - 14x^6 + 17x^5 + 74x^4 - 26x^3 - 145x^2 - 43x + 29	\( 19^{4}\cdot 37^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.252688187761.1	x^8 + 19x^6 + 106x^4 + 215x^2 + 144	\( 709^{4} \)	$\SL(2,3)$ (as 8T12)	$[7]$
8.8.255551481441.1	x^8 - x^7 - 16x^6 + 7x^5 + 71x^4 - 31x^3 - 100x^2 + 61x + 1	\( 3^{8}\cdot 79^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.338920744561.1	x^8 - 19x^6 + 79x^4 - 98x^2 + 9	\( 7^{4}\cdot 109^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.441194850625.1	x^8 - 2x^7 + 15x^6 - 22x^5 + 68x^4 - 37x^3 + 188x^2 - 269x + 599	\( 5^{4}\cdot 163^{4} \)	$\SL(2,3)$ (as 8T12)	$[2]$
8.0.476874494721.1	x^8 - 3x^7 + 7x^6 - 5x^5 + 16x^4 - 31x^3 + 289x^2 - 180x + 69	\( 3^{4}\cdot 277^{4} \)	$\SL(2,3)$ (as 8T12)	$[4]$
8.0.529414856881.1	x^8 - x^7 - 10x^6 + 32x^5 + 43x^4 - 245x^3 + 393x^2 - 192x + 68	\( 853^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.770829564961.1	x^8 - 3x^7 + 6x^5 - 6x^4 + 8x^3 + 162x^2 + 284x + 173	\( 937^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.811082161201.1	x^8 + 19x^6 + 116x^4 + 255x^2 + 169	\( 13^{4}\cdot 73^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.1036488922561.1	x^8 - 3x^7 - 20x^6 + 49x^5 + 86x^4 - 188x^3 - 91x^2 + 190x - 53	\( 1009^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.1201674171681.1	x^8 - 4x^7 - 13x^6 + 36x^5 + 76x^4 - 34x^3 - 69x^2 + 10x + 16	\( 3^{4}\cdot 349^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.1507158896896.1	x^8 + 13x^6 + 52x^4 + 65x^2 + 9	\( 2^{8}\cdot 277^{4} \)	$\SL(2,3)$ (as 8T12)	$[2, 14]$
8.8.1616465588409.1	x^8 - 17x^6 - 15x^5 + 36x^4 + 15x^3 - 17x^2 + 1	\( 3^{6}\cdot 7^{4}\cdot 31^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.1616465588409.2	x^8 - 4x^7 + 17x^6 - 13x^5 + 73x^4 + 88x^3 + 248x^2 + 304x + 208	\( 3^{6}\cdot 7^{4}\cdot 31^{4} \)	$\SL(2,3)$ (as 8T12)	$[6]$
8.8.1694894138161.1	x^8 - x^7 - 26x^6 + 6x^5 + 101x^4 + 53x^3 - 33x^2 - 17x + 2	\( 7^{4}\cdot 163^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.1706808989601.1	x^8 - 17x^6 + 78x^4 - 53x^2 + 4	\( 3^{8}\cdot 127^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.1730827040881.1	x^8 + 17x^6 + 59x^4 + 46x^2 + 1	\( 31^{4}\cdot 37^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.2012088347361.1	x^8 - x^7 - 22x^6 + 16x^5 + 156x^4 - 61x^3 - 422x^2 + 30x + 319	\( 3^{4}\cdot 397^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.2052941630481.1	x^8 - 2x^7 - 6x^6 + 3x^5 + 9x^4 - 78x^3 + 704x^2 - 544x + 336	\( 3^{8}\cdot 7^{4}\cdot 19^{4} \)	$\SL(2,3)$ (as 8T12)	$[7]$
8.0.2299963332969.1	x^8 - x^7 + x^6 + 4x^5 - 19x^4 + 226x^3 + 310x^2 - 214x + 241	\( 3^{10}\cdot 79^{4} \)	$\SL(2,3)$ (as 8T12)	$[4]$
8.0.2576952773521.1	x^8 - x^7 - 8x^6 + 12x^5 - 4x^4 + 13x^3 + 642x^2 - 440x + 281	\( 7^{4}\cdot 181^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.2583966230784.1	x^8 + 15x^6 + 63x^4 + 54x^2 + 9	\( 2^{8}\cdot 3^{6}\cdot 61^{4} \)	$\SL(2,3)$ (as 8T12)	$[2, 4]$
8.8.2583966230784.1	x^8 - 18x^6 + 63x^4 - 45x^2 + 9	\( 2^{8}\cdot 3^{6}\cdot 61^{4} \)	$\SL(2,3)$ (as 8T12)	$[2]$
8.8.2713409501049.1	x^8 - 21x^6 + 108x^4 - 81x^2 + 9	\( 3^{6}\cdot 13^{4}\cdot 19^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.2713409501049.2	x^8 - x^7 - 4x^6 - 13x^5 + 7x^4 + 127x^3 + 182x^2 + 67x + 13	\( 3^{6}\cdot 13^{4}\cdot 19^{4} \)	$\SL(2,3)$ (as 8T12)	$[2]$
8.0.2891414573056.1	x^8 + 18x^6 + 92x^4 + 112x^2 + 16	\( 2^{12}\cdot 163^{4} \)	$\SL(2,3)$ (as 8T12)	$[2, 4]$
8.8.2891414573056.1	x^8 - 18x^6 + 92x^4 - 112x^2 + 16	\( 2^{12}\cdot 163^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.3157334518321.1	x^8 - 19x^6 + 113x^4 - 204x^2 + 16	\( 31^{4}\cdot 43^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.3320190535321.1	x^8 - x^7 - 21x^6 + 6x^5 + 109x^4 + 36x^3 - 85x^2 - 18x + 20	\( 11^{6}\cdot 37^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.3320190535321.2	x^8 - 2x^7 + 13x^6 + 18x^5 + 5x^4 + 126x^3 + 142x^2 - 70x + 47	\( 11^{6}\cdot 37^{4} \)	$\SL(2,3)$ (as 8T12)	$[14]$
8.0.3341024655409.1	x^8 - x^7 + 8x^6 + 8x^5 + 32x^4 + 66x^3 + 128x^2 + 204x + 179	\( 7^{6}\cdot 73^{4} \)	$\SL(2,3)$ (as 8T12)	$[2]$
8.8.3341024655409.1	x^8 - 2x^7 - 26x^6 + 25x^5 + 160x^4 + 60x^3 - 145x^2 - 107x - 13	\( 7^{6}\cdot 73^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.3679587150625.1	x^8 - 3x^7 - 23x^6 + 53x^5 + 132x^4 - 173x^3 + 29x^2 + 6x - 1	\( 5^{4}\cdot 277^{4} \)	$\SL(2,3)$ (as 8T12)	$[2]$
8.8.3797883801856.1	x^8 - 15x^6 + 74x^4 - 131x^2 + 64	\( 2^{8}\cdot 349^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.8.3830635754401.1	x^8 - 3x^7 - 19x^6 + 68x^5 + 61x^4 - 358x^3 + 126x^2 + 346x - 139	\( 1399^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.3873527824384.1	x^8 + 20x^6 + 42x^4 + 24x^2 + 4	\( 2^{22}\cdot 31^{4} \)	$\SL(2,3)$ (as 8T12)	$[6]$
8.8.3873527824384.1	x^8 - 12x^6 + 42x^4 - 40x^2 + 4	\( 2^{22}\cdot 31^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial
8.0.3873527824384.2	x^8 + 12x^6 + 42x^4 + 40x^2 + 4	\( 2^{22}\cdot 31^{4} \)	$\SL(2,3)$ (as 8T12)	$[26]$
8.8.3873527824384.2	x^8 - 20x^6 + 42x^4 - 24x^2 + 4	\( 2^{22}\cdot 31^{4} \)	$\SL(2,3)$ (as 8T12)	Trivial