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
7.1.10083695.1	x^7 - 2x^6 + 2x^5 - 3x^4 + 5x^3 - 7x^2 + 4x - 1	\( -\,5\cdot 2016739 \)	$S_7$ (as 7T7)	$[2]$
7.1.10336279.1	x^7 - 3x^6 + 4x^5 - 5x^4 + 4x^3 + x^2 - 2x - 1	\( -\,149\cdot 69371 \)	$S_7$ (as 7T7)	$[2]$
7.1.11976527.1	x^7 - 3x^6 + 7x^5 - 13x^4 + 15x^3 - 11x^2 + 4x - 1	\( -\,1193\cdot 10039 \)	$S_7$ (as 7T7)	$[2]$
7.1.12959975.1	x^7 - 3x^6 + 4x^5 - 4x^4 + 4x^2 - 1	\( -\,5^{2}\cdot 7\cdot 103\cdot 719 \)	$S_7$ (as 7T7)	$[2]$
7.1.13750883.1	x^7 - x^6 + 3x^4 - 5x^3 + 2x^2 + 1	\( -\,1217\cdot 11299 \)	$S_7$ (as 7T7)	$[2]$
7.1.13841499.1	x^7 + 5x^5 - 2x^4 + 7x^3 - 3x^2 + 2x - 1	\( -\,3\cdot 7\cdot 797\cdot 827 \)	$S_7$ (as 7T7)	$[2]$
7.1.14060315.1	x^7 - x^6 + 2x^5 + 2x^4 - 4x^3 + 5x^2 - 2x + 1	\( -\,5\cdot 2812063 \)	$S_7$ (as 7T7)	$[2]$
7.1.14201651.1	x^7 - 2x^6 + x^5 - x^4 + 4x^3 - 5x^2 + 4x - 1	\( -\,14201651 \)	$S_7$ (as 7T7)	$[2]$
7.1.14352952.1	x^7 - 2x^5 - 2x^4 + x^3 + 5x^2 - 4	\( -\,2^{3}\cdot 41\cdot 43759 \)	$S_7$ (as 7T7)	$[2]$
7.1.14621967.1	x^7 - x^6 - 2x^5 + 3x^4 + 2x^2 - 3x + 1	\( -\,3^{2}\cdot 1624663 \)	$S_7$ (as 7T7)	$[2]$
7.1.15293507.1	x^7 - x^6 - x^5 - 2x^4 + 6x^2 + 5x + 1	\( -\,15293507 \)	$S_7$ (as 7T7)	$[2]$
7.1.15395703.1	x^7 + 2x^5 - 2x^4 - 3x^3 - 6x^2 - 1	\( -\,3\cdot 743\cdot 6907 \)	$S_7$ (as 7T7)	$[2]$
7.1.15793499.1	x^7 - 2x^6 + x^5 - x^4 + 2x^3 + 2x^2 - 3x + 1	\( -\,15793499 \)	$S_7$ (as 7T7)	$[2]$
7.1.15972400.1	x^7 - 2x^6 + 3x^5 - 3x^4 + 3x^3 - 3x^2 - 2x - 1	\( -\,2^{4}\cdot 5^{2}\cdot 73\cdot 547 \)	$S_7$ (as 7T7)	$[2]$
7.1.15992471.1	x^7 - 3x^6 + 7x^5 - 11x^4 + 10x^3 - 4x^2 + 1	\( -\,11\cdot 19\cdot 76519 \)	$S_7$ (as 7T7)	$[2]$
7.1.16126423.1	x^7 - 2x^5 + 4x^3 - 4x^2 + x - 1	\( -\,3041\cdot 5303 \)	$S_7$ (as 7T7)	$[2]$
7.1.16142827.1	x^7 - 2x^6 - x^4 + 5x^3 - 2x^2 - x + 1	\( -\,16142827 \)	$S_7$ (as 7T7)	$[2]$
7.1.16368832.1	x^7 - 2x^6 + 3x^5 - x^4 - x^3 - 3x^2 - 1	\( -\,2^{6}\cdot 255763 \)	$S_7$ (as 7T7)	$[2]$
7.1.16528892.1	x^7 - 2x^6 + 2x^5 - 2x^4 - 2x^3 + 3x^2 + 3x + 1	\( -\,2^{2}\cdot 523\cdot 7901 \)	$S_7$ (as 7T7)	$[2]$
7.1.16645243.1	x^7 - 2x^6 + x^5 - 3x^4 + 6x^3 - 4x^2 + 3x - 1	\( -\,347\cdot 47969 \)	$S_7$ (as 7T7)	$[2]$
7.1.16804051.1	x^7 - 2x^6 + 3x^5 - 6x^4 + 9x^3 - 9x^2 + 4x - 1	\( -\,11\cdot 47\cdot 32503 \)	$S_7$ (as 7T7)	$[2]$
7.1.16868779.1	x^7 - 2x^6 + 3x^5 + x^4 - 6x^3 + 5x^2 - 2x + 1	\( -\,193\cdot 87403 \)	$S_7$ (as 7T7)	$[2]$
7.1.17030407.1	x^7 - x^6 + 2x^5 + x^4 - 3x^2 + 2x - 1	\( -\,61\cdot 279187 \)	$S_7$ (as 7T7)	$[2]$
7.1.17179595.1	x^7 - 2x^6 + 5x^4 - 9x^3 + 8x^2 - 3x + 1	\( -\,5\cdot 101\cdot 34019 \)	$S_7$ (as 7T7)	$[2]$
7.1.17186635.1	x^7 - x^6 + 4x^5 - 6x^4 + 9x^3 - 11x^2 + 6x - 1	\( -\,5\cdot 23\cdot 199\cdot 751 \)	$S_7$ (as 7T7)	$[2]$
7.1.17241884.1	x^7 + 2x^5 - 4x^4 - 2x^3 - 5x^2 - x - 1	\( -\,2^{2}\cdot 11\cdot 391861 \)	$S_7$ (as 7T7)	$[2]$
7.1.17258864.1	x^7 - 2x^5 - x^4 + 3x^3 + 2x + 1	\( -\,2^{4}\cdot 7\cdot 154097 \)	$S_7$ (as 7T7)	$[2]$
7.1.17721559.1	x^7 - x^6 + x^4 + 2x^3 - 5x^2 + 2x + 1	\( -\,3323\cdot 5333 \)	$S_7$ (as 7T7)	$[2]$
7.1.17854963.1	x^7 - 3x^6 + 3x^5 - x^4 + 8x^3 - 4x^2 - x + 1	\( -\,7^{2}\cdot 109\cdot 3343 \)	$S_7$ (as 7T7)	$[2]$
7.1.18179396.1	x^7 - 4x^5 + 7x^3 - 3x^2 - 4x + 4	\( -\,2^{2}\cdot 4544849 \)	$S_7$ (as 7T7)	$[2]$
7.1.18233127.1	x^7 - 2x^6 + 3x^4 - 4x^3 + 6x^2 - 4x + 1	\( -\,3^{3}\cdot 11^{2}\cdot 5581 \)	$S_7$ (as 7T7)	$[2]$
7.1.18257047.1	x^7 - 2x^6 + x^5 - 4x^4 + 7x^3 - 2x^2 - x + 1	\( -\,31\cdot 588937 \)	$S_7$ (as 7T7)	$[2]$
7.1.18290639.1	x^7 - x^4 + 4x^3 - 2x^2 - 1	\( -\,18290639 \)	$S_7$ (as 7T7)	$[2]$
7.1.18538123.1	x^7 - 3x^6 + 4x^5 - 3x^4 + 3x^3 - x^2 - x - 1	\( -\,18538123 \)	$S_7$ (as 7T7)	$[2]$
7.1.18884027.2	x^7 - x^5 - 2x^4 + 2x^3 + 2x^2 - 2x + 1	\( -\,229\cdot 82463 \)	$S_7$ (as 7T7)	$[2]$
7.1.19083235.1	x^7 - 3x^6 + 2x^5 + 3x^4 - 3x^3 - 4x^2 + 4x - 1	\( -\,5\cdot 3816647 \)	$S_7$ (as 7T7)	$[2]$
7.1.19202359.1	x^7 - x^6 - 3x^5 + x^4 + 8x^3 + 5x^2 - x - 1	\( -\,11\cdot 1745669 \)	$S_7$ (as 7T7)	$[2]$
7.1.19252547.1	x^7 - x^4 + 2x^3 + x^2 + 2x - 1	\( -\,2129\cdot 9043 \)	$S_7$ (as 7T7)	$[2]$
7.1.19275243.1	x^7 - 3x^6 + 4x^5 - 5x^4 + 5x^3 - 2x + 1	\( -\,3\cdot 13\cdot 494237 \)	$S_7$ (as 7T7)	$[2]$
7.1.19543760.1	x^7 - 2x^6 + x^5 - 3x^4 + 3x^3 - x^2 - 2x - 1	\( -\,2^{4}\cdot 5\cdot 244297 \)	$S_7$ (as 7T7)	$[2]$
7.1.19810672.1	x^7 + 2x^5 - x^4 - 3x^3 - 2x^2 - 1	\( -\,2^{4}\cdot 7\cdot 79\cdot 2239 \)	$S_7$ (as 7T7)	$[2]$
7.1.19844884.1	x^7 - x^6 + 2x^4 + 4x^2 + 9x + 1	\( -\,2^{2}\cdot 101\cdot 49121 \)	$S_7$ (as 7T7)	$[2]$
7.1.19922352.1	x^7 - x^6 - 4x^5 + 3x^4 + 4x^3 - x^2 + 3x + 4	\( -\,2^{4}\cdot 3\cdot 113\cdot 3673 \)	$S_7$ (as 7T7)	$[2]$
7.1.20021539.1	x^7 - x^6 + 2x^3 - 5x^2 + 3x - 1	\( -\,20021539 \)	$S_7$ (as 7T7)	$[2]$
7.1.20057031.1	x^7 - 3x^6 + 4x^5 - 2x^4 - x^3 - 2x^2 + 3x - 1	\( -\,3^{3}\cdot 31^{2}\cdot 773 \)	$S_7$ (as 7T7)	$[2]$
7.1.20260912.1	x^7 - 2x^6 + 3x^5 - 5x^4 + 5x^3 + x^2 + 2x - 1	\( -\,2^{4}\cdot 7^{2}\cdot 43\cdot 601 \)	$S_7$ (as 7T7)	$[2]$
7.1.20408504.1	x^7 - 2x^6 + 7x^5 - 9x^4 + 10x^3 - 6x^2 + 4x - 1	\( -\,2^{3}\cdot 2551063 \)	$S_7$ (as 7T7)	$[2]$
7.1.20417491.1	x^7 - 2x^6 + x^5 - x^4 + 4x^3 - 4x^2 + x - 1	\( -\,23\cdot 887717 \)	$S_7$ (as 7T7)	$[2]$
7.1.20550475.1	x^7 - 3x^6 + 6x^5 - 7x^4 + 7x^3 - x^2 - x - 1	\( -\,5^{2}\cdot 11\cdot 74729 \)	$S_7$ (as 7T7)	$[2]$
7.1.20590192.1	x^7 + 4x^5 - x^4 + 3x^3 - 2x^2 + 1	\( -\,2^{4}\cdot 7^{2}\cdot 26263 \)	$S_7$ (as 7T7)	$[2]$

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