Number field search results

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions

Results (1-50 of 6157516 matches)

  There are too many results (6157516) to download.

Label	Polynomial	Discriminant	Galois group	Class group
6.0.9747.1	x^6 - x^5 + x^4 - 2x^3 + 4x^2 - 3x + 1	\( -\,3^{3}\cdot 19^{2} \)	$S_3\times C_3$ (as 6T5)	trivial
6.0.10051.1	x^6 - x^5 + 2x^4 - 2x^3 + 2x^2 - 2x + 1	\( -\,19\cdot 23^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.10571.1	x^6 - x^5 - x^4 + 2x^3 - x + 1	\( -\,11\cdot 31^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.10816.1	x^6 - x^4 - 2x^3 + 2x + 1	\( -\,2^{6}\cdot 13^{2} \)	$S_3\times C_3$ (as 6T5)	trivial
6.0.11691.1	x^6 - x^5 - x^2 + x + 1	\( -\,3^{3}\cdot 433 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.12167.1	x^6 - 3x^5 + 5x^4 - 5x^3 + 5x^2 - 3x + 1	\( -\,23^{3} \)	$S_3$ (as 6T2)	trivial
6.0.14283.1	x^6 - x^5 + x^4 - 2x^3 + x^2 + 1	\( -\,3^{3}\cdot 23^{2} \)	$D_{6}$ (as 6T3)	trivial
6.0.14731.1	x^6 - x^5 + x^3 - x^2 + 1	\( -\,14731 \)	$S_6$ (as 6T16)	trivial
6.0.16551.1	x^6 - x^5 - x^4 + 3x^3 - 2x + 1	\( -\,3^{3}\cdot 613 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.16807.1	x^6 - x^5 + x^4 - x^3 + x^2 - x + 1	\( -\,7^{5} \)	$C_6$ (as 6T1)	trivial
6.0.18515.1	x^6 + 2x^4 - x^3 + 2x^2 + 1	\( -\,5\cdot 7\cdot 23^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.19683.1	x^6 - x^3 + 1	\( -\,3^{9} \)	$C_6$ (as 6T1)	trivial
6.0.20627.1	x^6 - x^5 + x^4 - 2x^3 + 2x^2 - x + 1	\( -\,20627 \)	$S_6$ (as 6T16)	trivial
6.0.21168.1	x^6 - 3x^5 + 4x^4 - x^3 - 2x^2 + x + 1	\( -\,2^{4}\cdot 3^{3}\cdot 7^{2} \)	$S_3\times C_3$ (as 6T5)	trivial
6.0.21296.1	x^6 - x^5 + 2x^4 - 3x^3 + 2x^2 - x + 1	\( -\,2^{4}\cdot 11^{3} \)	$S_3$ (as 6T2)	trivial
6.0.22291.1	x^6 + x^4 - x^3 - x + 1	\( -\,22291 \)	$S_6$ (as 6T16)	trivial
6.0.22592.1	x^6 - 2x^5 + 2x^4 - x^2 + 1	\( -\,2^{6}\cdot 353 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.22707.1	x^6 - x^5 + 4x^4 - 4x^3 + 5x^2 - 3x + 1	\( -\,3^{3}\cdot 29^{2} \)	$D_{6}$ (as 6T3)	trivial
6.0.22747.1	x^6 - x^5 - 2x^3 + x^2 + x + 1	\( -\,23^{2}\cdot 43 \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.23031.1	x^6 + x^4 - x^3 + x^2 - 2x + 1	\( -\,3^{3}\cdot 853 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.24003.1	x^6 - x^5 + 3x^3 - x^2 - 2x + 1	\( -\,3^{3}\cdot 7\cdot 127 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.25747.1	x^6 - x^5 + 2x^4 - 2x^3 + 3x^2 - x + 1	\( -\,25747 \)	$S_6$ (as 6T16)	trivial
6.0.25947.1	x^6 - x^4 - 2x^3 + x^2 + x + 1	\( -\,3^{3}\cdot 31^{2} \)	$D_{6}$ (as 6T3)	trivial
6.0.27556.1	x^6 - x^5 + 2x^3 - x + 1	\( -\,2^{2}\cdot 83^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.27848.1	x^6 - x^5 + 2x^4 + 2x^2 - x + 1	\( -\,2^{3}\cdot 59^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.27971.1	x^6 - x^5 + x^4 - 2x^3 + 3x^2 - 2x + 1	\( -\,83\cdot 337 \)	$S_6$ (as 6T16)	trivial
6.2.28037.1	x^6 - 2x^5 + 3x^3 - 2x - 1	\( 23^{2}\cdot 53 \)	$S_4\times C_2$ (as 6T11)	trivial
6.2.29077.1	x^6 - x^5 + x^4 - x^2 + 2x - 1	\( 29077 \)	$S_6$ (as 6T16)	trivial
6.0.29095.1	x^6 - x^5 + 3x^4 - x^3 + 3x^2 - x + 1	\( -\,5\cdot 11\cdot 23^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.2.29189.1	x^6 - 2x^5 + x^4 + x^3 - 2x^2 + x + 1	\( 17^{2}\cdot 101 \)	$S_6$ (as 6T16)	trivial
6.0.29791.1	x^6 - 3x^5 + 7x^4 - 9x^3 + 7x^2 - 3x + 1	\( -\,31^{3} \)	$S_3$ (as 6T2)	trivial
6.2.30125.1	x^6 - x^5 + x^4 - 2x^2 + x - 1	\( 5^{3}\cdot 241 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.30808.1	x^6 - x^4 - x^3 + x^2 + x + 1	\( -\,2^{3}\cdot 3851 \)	$S_6$ (as 6T16)	trivial
6.0.30976.1	x^6 - 2x^5 + 2x^4 - 2x^3 + 4x^2 - 4x + 2	\( -\,2^{8}\cdot 11^{2} \)	$D_{6}$ (as 6T3)	trivial
6.2.31133.1	x^6 - 2x^4 - x^3 + 2x + 1	\( 163\cdot 191 \)	$S_6$ (as 6T16)	trivial
6.0.31211.1	x^6 - x^4 - x^3 + 2x^2 + 3x + 1	\( -\,23^{2}\cdot 59 \)	$S_4\times C_2$ (as 6T11)	trivial
6.2.31213.1	x^6 - 2x^5 + 2x^4 - 3x^3 + 2x^2 - 2x + 1	\( 7^{4}\cdot 13 \)	$A_4\times C_2$ (as 6T6)	trivial
6.0.31223.1	x^6 - x^5 + x^4 - x^3 + 2x^2 - x + 1	\( -\,31223 \)	$S_6$ (as 6T16)	trivial
6.0.31347.1	x^6 - 3x^4 - 2x^3 + 3x^2 + 3x + 1	\( -\,3^{6}\cdot 43 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.2.31709.1	x^6 - x^5 + 2x^3 - 2x^2 + 1	\( 37\cdot 857 \)	$S_6$ (as 6T16)	trivial
6.0.32171.1	x^6 - x^5 + 2x^4 - x^3 + x^2 + 1	\( -\,53\cdot 607 \)	$S_6$ (as 6T16)	trivial
6.2.32269.1	x^6 - 3x^5 + 4x^4 - 3x^3 + x^2 - 1	\( 23^{2}\cdot 61 \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.32911.1	x^6 - x^3 - x^2 + x + 1	\( -\,32911 \)	$S_6$ (as 6T16)	trivial
6.0.33791.1	x^6 - x^5 + x^4 + x^3 + x + 1	\( -\,33791 \)	$S_6$ (as 6T16)	trivial
6.0.33856.1	x^6 - x^4 + 1	\( -\,2^{6}\cdot 23^{2} \)	$S_4\times C_2$ (as 6T11)	trivial
6.0.33856.2	x^6 + x^4 + 2x^2 + 1	\( -\,2^{6}\cdot 23^{2} \)	$D_{6}$ (as 6T3)	trivial
6.2.33856.1	x^6 + x^4 - 1	\( 2^{6}\cdot 23^{2} \)	$S_4$ (as 6T7)	trivial
6.0.34371.1	x^6 - x^5 - 2x^3 + 2x + 1	\( -\,3^{3}\cdot 19\cdot 67 \)	$C_3^2:D_4$ (as 6T13)	trivial
6.0.34992.1	x^6 - 3x^5 + 5x^3 - 3x + 1	\( -\,2^{4}\cdot 3^{7} \)	$S_3$ (as 6T2)	trivial
6.0.35099.1	x^6 + x^4 + x^2 - x + 1	\( -\,35099 \)	$S_6$ (as 6T16)	trivial

  There are too many results (6157516) to download.