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 20328)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.37822859361.1	x^8 - 4x^7 + 7x^6 - 7x^5 + 7x^4 - 7x^3 + 7x^2 + 5x + 1	\( 3^{8}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.40904253504.1	x^8 - x^7 + 7x^6 - x^5 + 33x^4 + x^3 + 61x^2 + 13x + 58	\( 2^{6}\cdot 3^{4}\cdot 53^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.46352367616.5	x^8 - 4x^7 + 14x^6 - 24x^5 + 29x^4 - 32x^3 + 18x^2 - 16x + 17	\( 2^{16}\cdot 29^{4} \)	$\PSL(2,7)$ (as 8T37)	Trivial
8.0.62816399424.1	x^8 - 3x^7 + 4x^6 + 2x^5 - 10x^4 + 16x^3 - 20x + 28	\( 2^{6}\cdot 3^{4}\cdot 59^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.64537845849.1	x^8 - 2x^7 + 10x^6 - 17x^5 + 28x^4 - 38x^3 + 34x^2 - 17x + 10	\( 3^{6}\cdot 97^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.82653950016.1	x^8 - 2x^7 + 2x^6 - 8x^5 + 16x^4 - 16x^3 + 14x^2 - 10x + 4	\( 2^{6}\cdot 3^{6}\cdot 11^{6} \)	$\PSL(2,7)$ (as 8T37)	$[6]$
8.0.89685275625.1	x^8 - 3x^7 + 9x^6 - 21x^5 + 44x^4 - 69x^3 + 84x^2 - 84x + 73	\( 3^{4}\cdot 5^{4}\cdot 11^{6} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.116101021696.1	x^8 - 4x^7 + 10x^6 - 12x^5 - 7x^4 + 44x^3 - 46x^2 - 4x + 95	\( 2^{16}\cdot 11^{6} \)	$\PSL(2,7)$ (as 8T37)	Trivial
8.0.118861526169.4	x^8 - 3x^7 + x^6 + 9x^5 - 3x^4 - 57x^3 + 133x^2 - 132x + 76	\( 3^{6}\cdot 113^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.119538913536.1	x^8 - 4x^7 + 14x^6 - 28x^5 + 49x^4 - 56x^3 + 56x^2 - 14x + 7	\( 2^{8}\cdot 3^{4}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.159507579456.5	x^8 - x^7 + 5x^6 - 19x^5 + 31x^4 - 47x^3 + 47x^2 - 17x + 4	\( 2^{6}\cdot 3^{6}\cdot 43^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.230592040000.1	x^8 - x^7 + 14x^4 - 28x^3 + 28x^2 - 14x + 14	\( 2^{6}\cdot 5^{4}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.264287499921.2	x^8 - 4x^7 + 11x^6 - 17x^5 + 37x^4 - 78x^3 + 132x^2 - 153x + 72	\( 3^{4}\cdot 239^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.268962555456.1	x^8 - x^7 - 7x^6 - 7x^5 + 7x^4 + 49x^3 + 77x^2 + 31x + 4	\( 2^{6}\cdot 3^{6}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.279841000000.2	x^8 - x^7 + x^6 - 11x^5 + 11x^4 + 35x^3 + 45x^2 + 35x + 10	\( 2^{6}\cdot 5^{6}\cdot 23^{4} \)	$\PSL(2,7)$ (as 8T37)	$[8]$
8.0.283449760000.1	x^8 - 2x^7 + 4x^6 + 2x^5 + 27x^4 - 46x^3 + 84x^2 - 10x + 59	\( 2^{8}\cdot 5^{4}\cdot 11^{6} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.296990121024.3	x^8 - 3x^7 + 6x^6 + 2x^5 + 6x^3 + 4x^2 + 6x + 6	\( 2^{6}\cdot 3^{8}\cdot 29^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.313044726016.12	x^8 - 2x^7 + 2x^6 - 14x^5 + 46x^4 - 86x^3 + 126x^2 - 118x + 49	\( 2^{8}\cdot 11^{4}\cdot 17^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.377801998336.1	x^8 - 4x^7 + 14x^6 - 28x^5 + 63x^4 - 84x^3 + 98x^2 - 52x + 19	\( 2^{16}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.377801998336.3	x^8 - 4x^7 + 14x^6 - 28x^5 + 49x^4 - 56x^3 + 56x^2 - 24x + 5	\( 2^{16}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.377801998336.4	x^8 + 28x^4 + 112x^2 - 32x + 84	\( 2^{16}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	Trivial
8.0.481481944321.1	x^8 - 4x^7 + 49x^4 - 42x^3 + 77x^2 - 31x + 19	\( 7^{8}\cdot 17^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.507422576896.1	x^8 - 4x^7 + 9x^6 - 12x^5 + 4x^4 - 4x^3 + 13x^2 + 4x + 1	\( 2^{8}\cdot 211^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.531901827856.1	x^8 + 10x^6 + 12x^4 - 28x^3 - 58x^2 + 28x + 51	\( 2^{4}\cdot 7^{4}\cdot 61^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.646274503744.1	x^8 - x^7 - 4x^6 - 12x^5 + 8x^4 + 64x^3 + 16x^2 - 32x + 24	\( 2^{6}\cdot 317^{4} \)	$\PSL(2,7)$ (as 8T37)	$[6]$
8.0.667841990656.8	x^8 - 2x^7 + 16x^6 - 34x^5 + 44x^4 - 22x^3 - 44x^2 + 26x + 23	\( 2^{12}\cdot 113^{4} \)	$\PSL(2,7)$ (as 8T37)	Trivial
8.0.731763906624.1	x^8 - 3x^7 + 19x^6 - 19x^5 + 41x^4 + 7x^3 + 9x^2 + 7x + 10	\( 2^{6}\cdot 3^{4}\cdot 109^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.743885550144.2	x^8 - x^7 - 16x^6 + 38x^5 + 34x^4 - 236x^3 + 380x^2 - 296x + 100	\( 2^{6}\cdot 3^{8}\cdot 11^{6} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.743885550144.3	x^8 - 2x^7 + 10x^6 - 16x^5 + 38x^4 - 34x^3 + 40x^2 - 50x + 148	\( 2^{6}\cdot 3^{8}\cdot 11^{6} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.767418048576.8	x^8 - 2x^7 - 2x^6 + 4x^5 + 12x^4 - 4x^3 - 20x^2 - 4x + 16	\( 2^{6}\cdot 3^{4}\cdot 23^{6} \)	$\PSL(2,7)$ (as 8T37)	$[12]$
8.0.922368160000.1	x^8 - 2x^7 + 14x^6 - 28x^5 + 147x^4 - 196x^3 + 518x^2 - 322x + 497	\( 2^{8}\cdot 5^{4}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.1151964303616.16	x^8 - 2x^7 + 8x^5 + 7x^4 - 68x^3 + 218x^2 - 336x + 239	\( 2^{8}\cdot 7^{4}\cdot 37^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.1156418486161.1	x^8 - 2x^7 - 11x^6 - 16x^5 + 49x^4 + 183x^3 + 303x^2 + 244x + 103	\( 17^{4}\cdot 61^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.1157018619904.4	x^8 - 28x^5 + 7x^4 + 196x^2 - 80x + 28	\( 2^{12}\cdot 7^{10} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.1157018619904.5	x^8 - 14x^5 + 49x^4 - 98x^3 + 126x^2 - 104x + 42	\( 2^{12}\cdot 7^{10} \)	$\PSL(2,7)$ (as 8T37)	Trivial
8.0.1292841769024.1	x^8 - x^7 + 4x^6 + 2x^5 - 6x^4 + 14x^3 - 2x^2 - 2x + 30	\( 2^{6}\cdot 13^{4}\cdot 29^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.1442919878656.7	x^8 - 6x^5 - 3x^4 + 10x^3 + 10x^2 - 8x + 2	\( 2^{12}\cdot 137^{4} \)	$\PSL(2,7)$ (as 8T37)	Trivial
8.0.1464351690816.2	x^8 - x^7 + 14x^5 - 28x^4 - 14x^3 + 70x^2 - 48x + 34	\( 2^{6}\cdot 3^{4}\cdot 7^{10} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.1636073786281.3	x^8 - 3x^7 - 2x^6 + 12x^5 - 36x^3 + 62x^2 - 51x + 18	\( 11^{6}\cdot 31^{4} \)	$\PSL(2,7)$ (as 8T37)	$[12]$
8.0.1636073786281.4	x^8 - x^7 - 3x^6 - 13x^5 + 78x^4 - 153x^3 + 222x^2 - 268x + 163	\( 11^{6}\cdot 31^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.1706808989601.1	x^8 - 3x^7 + 6x^6 - 6x^4 + 12x^2 + 9x + 9	\( 3^{8}\cdot 127^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.1853320108689.1	x^8 - 7x^5 + 21x^4 - 63x^3 + 112x^2 - 156x + 168	\( 3^{8}\cdot 7^{10} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.1912622616576.1	x^8 - 2x^7 + 14x^6 + 14x^4 + 168x^3 + 56x^2 - 176x + 184	\( 2^{12}\cdot 3^{4}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.1935192596544.2	x^8 - x^7 - 5x^6 - x^5 - 3x^4 + 13x^3 + 103x^2 + 181x + 106	\( 2^{6}\cdot 3^{4}\cdot 139^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2, 4]$
8.0.2046089933056.12	x^8 - 6x^6 - 2x^5 + 19x^4 + 6x^3 - 16x^2 + 16x + 25	\( 2^{8}\cdot 13^{4}\cdot 23^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.2048997570624.2	x^8 - 3x^7 - 3x^6 + 9x^5 + 21x^4 - 27x^3 - 15x^2 - 45x + 108	\( 2^{6}\cdot 3^{8}\cdot 47^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.2048997570624.3	x^8 - 3x^7 + 6x^5 + 18x^4 + 18x^3 + 36x^2 + 54x + 54	\( 2^{6}\cdot 3^{8}\cdot 47^{4} \)	$\PSL(2,7)$ (as 8T37)	$[4]$
8.0.2122409008801.1	x^8 - 4x^7 + 12x^6 + 12x^5 - 58x^4 + 80x^3 + 243x^2 + 88x + 13	\( 17^{4}\cdot 71^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.2214215424576.2	x^8 - 4x^7 + 20x^6 - 40x^5 + 88x^4 - 80x^3 + 68x^2 - 110x + 61	\( 2^{6}\cdot 3^{6}\cdot 83^{4} \)	$\PSL(2,7)$ (as 8T37)	$[2]$
8.0.2420662999104.1	x^8 - x^7 + 7x^6 + 21x^5 + 63x^4 + 105x^3 + 105x^2 + 51x + 12	\( 2^{6}\cdot 3^{8}\cdot 7^{8} \)	$\PSL(2,7)$ (as 8T37)	$[4]$