Global number field search results

Further refine search

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 4255)

Label	Polynomial	Discriminant	Galois group	Class group
8.0.1282789.1	x^8 - x^7 + 2x^6 - 3x^5 + 3x^4 - 3x^3 + 3x^2 - 2x + 1	\( 1103\cdot 1163 \)	$S_8$ (as 8T50)	Trivial
8.0.1385533.1	x^8 - 2x^7 + 3x^6 - 3x^5 + x^4 + 1	\( 29\cdot 47777 \)	$S_8$ (as 8T50)	Trivial
8.0.1474013.1	x^8 - x^7 + x^6 - x^4 + x^3 - x^2 + 1	\( 617\cdot 2389 \)	$S_8$ (as 8T50)	Trivial
8.0.1590773.1	x^8 - x^7 + 2x^5 - 2x^4 + x^3 + x^2 - 2x + 1	\( 179\cdot 8887 \)	$S_8$ (as 8T50)	Trivial
8.0.1740113.1	x^8 - 2x^7 + 3x^6 - 4x^5 + 4x^4 - 4x^3 + 3x^2 - x + 1	\( 1740113 \)	$S_8$ (as 8T50)	Trivial
8.0.1867553.1	x^8 - x^7 + x^5 - 2x^4 + x^3 + x^2 - x + 1	\( 1867553 \)	$S_8$ (as 8T50)	Trivial
8.0.2105893.1	x^8 - x^7 + 2x^6 - x^5 + x^4 - x^3 + x^2 - 2x + 1	\( 29\cdot 72617 \)	$S_8$ (as 8T50)	Trivial
8.2.4296211.1	x^8 - x^7 + 3x^5 - 4x^4 + 2x^3 + 2x^2 - 3x + 1	\( -\,199\cdot 21589 \)	$S_8$ (as 8T50)	Trivial
8.2.4297507.1	x^8 - x^7 - 2x^6 + x^5 + x^3 + 2x^2 - 1	\( -\,2011\cdot 2137 \)	$S_8$ (as 8T50)	Trivial
8.2.4364587.1	x^8 - x^7 + 2x^6 - 3x^5 + 3x^4 - 4x^3 + 2x^2 - 2x + 1	\( -\,29\cdot 150503 \)	$S_8$ (as 8T50)	Trivial
8.2.4386467.1	x^8 - x^7 - x^6 + 3x^5 - x^4 - 2x^3 + 2x^2 + x - 1	\( -\,41\cdot 83\cdot 1289 \)	$S_8$ (as 8T50)	Trivial
8.2.4421387.1	x^8 - 2x^7 + 2x^6 + x^5 - 2x^4 + x^3 + x^2 - 1	\( -\,1321\cdot 3347 \)	$S_8$ (as 8T50)	Trivial
8.2.4570723.1	x^8 - 2x^7 + 3x^6 - 3x^5 + 2x^3 - 4x^2 + 3x - 1	\( -\,4570723 \)	$S_8$ (as 8T50)	Trivial
8.2.4584491.1	x^8 - x^7 + 2x^6 - 2x^5 + 4x^4 - 5x^3 + 4x^2 - 3x + 1	\( -\,19\cdot 101\cdot 2389 \)	$S_8$ (as 8T50)	Trivial
8.4.15908237.1	x^8 - x^6 - x^5 - 3x^4 + 4x^2 - 1	\( 43\cdot 369959 \)	$S_8$ (as 8T50)	Trivial
8.4.16374773.1	x^8 - x^7 - x^6 - 2x^4 + 2x^3 + 4x^2 - x - 1	\( 1753\cdot 9341 \)	$S_8$ (as 8T50)	Trivial
8.4.16526789.1	x^8 - 3x^6 - x^3 + 3x^2 - 1	\( 19\cdot 607\cdot 1433 \)	$S_8$ (as 8T50)	Trivial
8.4.17025973.1	x^8 - 3x^7 + 2x^6 + 4x^5 - 8x^4 + 3x^3 + 3x^2 - 4x + 1	\( 67\cdot 254119 \)	$S_8$ (as 8T50)	Trivial
8.4.17383253.1	x^8 - x^6 - x^5 - 2x^4 + x^2 + 2x + 1	\( 17383253 \)	$S_8$ (as 8T50)	Trivial
8.2.17600759.1	x^8 - x - 1	\( -\,11\cdot 1600069 \)	$S_8$ (as 8T50)	Trivial
8.2.30703951.1	x^8 - 2x^7 - 2x^6 + 4x^5 + 2x^4 - x^3 - 2x^2 - 2x + 1	\( -\,421\cdot 72931 \)	$S_8$ (as 8T50)	Trivial
8.6.65106259.1	x^8 - 5x^6 - x^5 + 7x^4 + 4x^3 - 4x^2 - 2x + 1	\( -\,89\cdot 731531 \)	$S_8$ (as 8T50)	Trivial
8.6.68494627.1	x^8 - 2x^7 - 3x^6 + 10x^5 - 2x^4 - 11x^3 + 5x^2 + 2x - 1	\( -\,811\cdot 84457 \)	$S_8$ (as 8T50)	Trivial
8.6.69367411.1	x^8 - x^6 - 3x^5 - 3x^4 + 6x^3 + 4x^2 - 2x - 1	\( -\,69367411 \)	$S_8$ (as 8T50)	Trivial
8.6.75272867.1	x^8 - 2x^7 - 3x^6 + 9x^5 - x^4 - 10x^3 + 3x^2 + 3x - 1	\( -\,31\cdot 2428157 \)	$S_8$ (as 8T50)	Trivial
8.6.83260171.1	x^8 - 2x^7 - 3x^6 + 4x^5 + 3x^4 + x^3 - x^2 - 3x - 1	\( -\,47\cdot 1771493 \)	$S_8$ (as 8T50)	Trivial
8.6.93594547.1	x^8 - x^7 - 6x^6 + 4x^5 + 11x^4 - 3x^3 - 7x^2 + x + 1	\( -\,1117\cdot 83791 \)	$S_8$ (as 8T50)	Trivial
8.6.94156147.1	x^8 - 5x^6 - x^5 + 7x^4 + 4x^3 - 3x^2 - 3x + 1	\( -\,94156147 \)	$S_8$ (as 8T50)	Trivial
8.6.95029219.1	x^8 - x^7 - 3x^6 + 3x^5 - x^4 - 2x^3 + 4x^2 + x - 1	\( -\,1291\cdot 73609 \)	$S_8$ (as 8T50)	Trivial
8.0.95879424.1	x^8 + 4x^6 + 6x^4 + 4x^2 - 2x + 1	\( 2^{8}\cdot 3\cdot 131\cdot 953 \)	$S_8$ (as 8T50)	Trivial
8.6.96530491.1	x^8 - 2x^7 - 3x^6 + 7x^5 - 6x^3 + 4x^2 + x - 1	\( -\,96530491 \)	$S_8$ (as 8T50)	Trivial
8.6.96598171.1	x^8 - 3x^7 + x^6 + 4x^5 - 7x^4 + 5x^3 + 5x^2 - 6x + 1	\( -\,53\cdot 1229\cdot 1483 \)	$S_8$ (as 8T50)	Trivial
8.6.97161811.1	x^8 - 5x^6 - x^5 + 6x^4 + 3x^3 - 2x - 1	\( -\,43\cdot 521\cdot 4337 \)	$S_8$ (as 8T50)	Trivial
8.6.98070859.1	x^8 - 2x^7 - x^6 + 3x^5 - 5x^4 + 10x^3 - 4x^2 - 2x + 1	\( -\,61\cdot 263\cdot 6113 \)	$S_8$ (as 8T50)	Trivial
8.6.98151947.1	x^8 - 4x^6 - x^5 + 3x^4 + 3x^3 + 2x^2 - 2x - 1	\( -\,7297\cdot 13451 \)	$S_8$ (as 8T50)	Trivial
8.6.98915419.1	x^8 - 4x^6 - x^5 + 2x^4 + x^3 + 3x^2 - 1	\( -\,151\cdot 655069 \)	$S_8$ (as 8T50)	Trivial
8.6.104081867.1	x^8 - 3x^7 - x^6 + 10x^5 - 5x^4 - 10x^3 + 7x^2 + 3x - 1	\( -\,19\cdot 73\cdot 75041 \)	$S_8$ (as 8T50)	Trivial
8.6.104429827.1	x^8 - x^7 - 2x^6 + x^5 - 2x^4 + 5x^3 + 2x^2 - 4x + 1	\( -\,17\cdot 199\cdot 30869 \)	$S_8$ (as 8T50)	Trivial
8.6.106143931.1	x^8 - 4x^7 + 3x^6 + 5x^5 - 8x^4 + 2x^3 + 5x^2 - 2x - 1	\( -\,3659\cdot 29009 \)	$S_8$ (as 8T50)	Trivial
8.6.106899371.1	x^8 - 3x^7 + 3x^5 + 3x^4 - 6x^2 + 1	\( -\,67\cdot 1595513 \)	$S_8$ (as 8T50)	Trivial
8.6.107555299.1	x^8 - 3x^7 - x^6 + 9x^5 - 5x^4 - 5x^3 + 6x^2 - 1	\( -\,1153\cdot 93283 \)	$S_8$ (as 8T50)	Trivial
8.6.108493747.1	x^8 - x^7 - 5x^6 + 5x^5 + 7x^4 - 8x^3 - 3x^2 + 4x + 1	\( -\,108493747 \)	$S_8$ (as 8T50)	Trivial
8.6.108714131.1	x^8 - x^7 - 4x^6 + 5x^5 + 3x^4 - 9x^3 + x^2 + 4x - 1	\( -\,103\cdot 971\cdot 1087 \)	$S_8$ (as 8T50)	Trivial
8.6.109020787.1	x^8 - 5x^6 - 3x^5 + 8x^4 + 9x^3 - 4x^2 - 6x - 1	\( -\,109020787 \)	$S_8$ (as 8T50)	Trivial
8.6.109380619.1	x^8 - 2x^7 - 2x^6 + 2x^5 + x^4 + 5x^3 + x^2 - 4x - 1	\( -\,109380619 \)	$S_8$ (as 8T50)	Trivial
8.6.111219379.1	x^8 - 2x^7 - 2x^6 + 7x^5 - 3x^4 - 7x^3 + 4x^2 + 2x - 1	\( -\,29\cdot 389\cdot 9859 \)	$S_8$ (as 8T50)	Trivial
8.6.112129379.1	x^8 - x^7 - 4x^6 + 2x^5 + 4x^4 + 3x^3 - x^2 - 4x - 1	\( -\,1427\cdot 78577 \)	$S_8$ (as 8T50)	Trivial
8.6.114655339.1	x^8 - 4x^7 + 3x^6 + 4x^5 - 5x^4 + 3x^3 - x^2 - 3x + 1	\( -\,233\cdot 492083 \)	$S_8$ (as 8T50)	Trivial
8.6.118871243.1	x^8 - 2x^6 - 2x^5 - 3x^4 + 5x^3 + 5x^2 - 2x - 1	\( -\,101\cdot 1176943 \)	$S_8$ (as 8T50)	Trivial
8.6.119649419.1	x^8 - x^7 - 4x^6 + 6x^5 + 6x^4 - 9x^3 - 4x^2 + 3x + 1	\( -\,119649419 \)	$S_8$ (as 8T50)	Trivial