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 272805)

Label	Polynomial	Discriminant	Galois group	Class group
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
8.6.68856875.1	x^8 - 2x^7 - 2x^6 + x^5 + x^4 + 5x^3 - x^2 - 3x + 1	\( -\,5^{4}\cdot 29^{2}\cdot 131 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	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
8.6.73061875.1	x^8 - 4x^6 - 3x^4 - 5x^3 + 4x^2 + 5x + 1	\( -\,5^{4}\cdot 29^{2}\cdot 139 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.6.74671875.1	x^8 - 4x^7 + 5x^6 - x^5 - 6x^4 + 9x^3 - 4x + 1	\( -\,3^{4}\cdot 5^{6}\cdot 59 \)	$((C_8 : C_2):C_2):C_2$ (as 8T27)	Trivial
8.6.74906875.1	x^8 - 3x^6 - 3x^5 + 3x^4 + 7x^3 - 2x^2 - 3x + 1	\( -\,5^{4}\cdot 119851 \)	$S_4\wr C_2$ (as 8T47)	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
8.6.84356875.1	x^8 - 3x^6 - x^5 + 4x^3 + 3x^2 - 2x - 1	\( -\,5^{4}\cdot 71\cdot 1901 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.6.86606875.1	x^8 - x^7 - 3x^6 + 2x^5 - x^4 + 6x^3 + 3x^2 - 7x - 1	\( -\,5^{4}\cdot 138571 \)	$S_4\wr C_2$ (as 8T47)	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
8.6.94086875.1	x^8 - 2x^7 + x^6 + 4x^5 - 12x^4 + 3x^3 + 9x^2 - 6x + 1	\( -\,5^{4}\cdot 29^{2}\cdot 179 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	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
8.6.94856875.1	x^8 - x^7 - x^6 + 3x^5 - 5x^4 - 2x^3 + 6x^2 + x - 1	\( -\,5^{4}\cdot 151771 \)	$S_4\wr C_2$ (as 8T47)	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
8.6.96530491.1	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
8.6.103405923.1	x^8 - x^7 + x^5 - 8x^4 + x^3 + 8x^2 - 2x - 1	\( -\,3^{3}\cdot 19^{2}\cdot 103^{2} \)	$C_2 \wr S_4$ (as 8T44)	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
8.6.107781875.1	x^8 - 2x^7 - x^6 + 4x^5 - 5x^4 - 3x^3 + 5x^2 + x - 1	\( -\,5^{4}\cdot 331\cdot 521 \)	$S_4\wr C_2$ (as 8T47)	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
8.6.110906875.1	x^8 - 2x^7 - 4x^6 + 9x^5 - 9x^3 + 4x^2 + 3x - 1	\( -\,5^{4}\cdot 29^{2}\cdot 211 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	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
8.6.121587131.1	x^8 - 2x^7 - x^6 + 7x^5 - 7x^4 - 5x^3 + 8x^2 + x - 1	\( -\,23\cdot 271\cdot 19507 \)	$S_8$ (as 8T50)	Trivial
8.6.123531875.1	x^8 - 5x^6 - 3x^5 + 8x^4 + 10x^3 - 4x^2 - 7x + 1	\( -\,5^{4}\cdot 197651 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.6.128782547.1	x^8 - 2x^7 + 5x^5 - 8x^4 - 3x^3 + 8x^2 - x - 1	\( -\,157\cdot 820271 \)	$S_8$ (as 8T50)	Trivial
8.6.129062827.1	x^8 - 2x^7 - 4x^6 + 5x^5 + 8x^4 - 3x^3 - 6x^2 + x + 1	\( -\,17\cdot 31\cdot 244901 \)	$S_8$ (as 8T50)	Trivial
8.6.131931875.1	x^8 - x^7 - 5x^6 + 5x^5 + 3x^4 - 3x + 1	\( -\,5^{4}\cdot 29^{2}\cdot 251 \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.6.132655867.1	x^8 - 2x^6 - 2x^5 - 3x^4 + 3x^3 + 4x^2 - x - 1	\( -\,137\cdot 968291 \)	$S_8$ (as 8T50)	Trivial
8.6.132761875.1	x^8 - x^7 - 5x^6 + 2x^5 + 11x^4 - x^3 - 9x^2 + 1	\( -\,5^{4}\cdot 212419 \)	$S_4\wr C_2$ (as 8T47)	Trivial
8.6.134560000.1	x^8 - 3x^6 + 4x^2 - 1	\( -\,2^{8}\cdot 5^{4}\cdot 29^{2} \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.6.134560000.2	x^8 - 6x^4 + 5x^2 - 1	\( -\,2^{8}\cdot 5^{4}\cdot 29^{2} \)	$C_2 \wr C_2\wr C_2$ (as 8T35)	Trivial
8.6.135123147.1	x^8 - 4x^6 - 4x^5 + 9x^4 + 5x^3 - 6x^2 - x + 1	\( -\,3^{4}\cdot 257\cdot 6491 \)	$S_8$ (as 8T50)	Trivial
8.6.136128151.1	x^8 - 2x^7 + x^6 + 2x^5 - 7x^4 + 2x^3 + 6x^2 - x - 1	\( -\,97\cdot 1403383 \)	$S_8$ (as 8T50)	Trivial

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