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 1196864 matches)

  There are too many results (1196864) to download.

Label	Polynomial	Discriminant	Galois group	Class group
10.0.209352647.1	x^10 - 3x^9 + 7x^8 - 11x^7 + 13x^6 - 12x^5 + 9x^4 - 5x^3 + 3x^2 - 2x + 1	\( -\,7^{2}\cdot 23\cdot 431^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.212309359.1	x^10 - 3x^9 + 5x^8 - 7x^7 + 9x^6 - 10x^5 + 9x^4 - 7x^3 + 5x^2 - 2x + 1	\( -\,31\cdot 2617^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.214816879.1	x^10 - 2x^9 + 4x^8 - 7x^7 + 9x^6 - 10x^5 + 10x^4 - 8x^3 + 6x^2 - 3x + 1	\( -\,17^{2}\cdot 79\cdot 97^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.220168975.1	x^10 - x^9 - x^8 + 2x^7 - x^6 - x^5 + 4x^4 - x^3 - 3x^2 + x + 1	\( -\,5^{2}\cdot 13^{2}\cdot 31\cdot 41^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.224198759.1	x^10 - x^9 - 2x^8 + 4x^7 - 4x^5 + 3x^4 + x^3 - 2x^2 + 1	\( -\,71\cdot 1777^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.226876987.1	x^10 - 2x^9 + 3x^8 - 3x^7 + 2x^6 + x^5 - x^4 - 3x^3 + 6x^2 - 4x + 1	\( -\,43\cdot 2297^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.262091507.1	x^10 - x^9 - 2x^6 + 3x^5 + 3x^4 - 4x^3 - 2x^2 + 2x + 1	\( -\,83\cdot 1777^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.263786699.1	x^10 - 2x^9 + 2x^8 - 2x^7 + 4x^6 - 5x^5 + 4x^4 - 2x^3 + 3x^2 - 3x + 1	\( -\,11\cdot 59^{2}\cdot 83^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.277010267.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + 3x^5 - 2x^4 + 3x^2 - 3x + 1	\( -\,107\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.290954507.1	x^10 - x^9 + 2x^8 + 2x^7 - x^6 + 4x^5 + 4x^4 + 2x^2 + 3x + 1	\( -\,17^{2}\cdot 97^{2}\cdot 107 \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.325246087.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 13x^6 - 13x^5 + 11x^4 - 8x^3 + 5x^2 - 2x + 1	\( -\,103\cdot 1777^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.328787887.1	x^10 - 2x^9 + 3x^8 - 3x^7 + 5x^6 - 6x^5 + 3x^4 - 3x^3 + 3x^2 - x + 1	\( -\,127\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.328787887.2	x^10 - 2x^9 + 3x^6 - x^5 - x^4 - 2x^3 + 2x^2 + 1	\( -\,127\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.330230659.1	x^10 - x^9 + x^8 + 2x^7 - 3x^6 + 2x^5 - 2x^3 + x^2 - x + 1	\( -\,11^{2}\cdot 19\cdot 379^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.339143411.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 6x^6 - 4x^5 + x^4 + 2x^3 - 2x^2 + 1	\( -\,131\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.359854459.1	x^10 - 3x^9 + 6x^8 - 9x^7 + 11x^6 - 10x^5 + 8x^4 - 5x^3 + 3x^2 - 2x + 1	\( -\,139\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.364067099.1	x^10 - x^9 - 2x^6 + x^5 + 2x^4 - 2x^3 + 3x^2 - 2x + 1	\( -\,11^{3}\cdot 523^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.370209983.1	x^10 + 2x^8 + 3x^6 - x^5 + 3x^4 + 2x^2 + 1	\( -\,11\cdot 13\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.377968939.1	x^10 - 2x^9 + 4x^8 - 5x^7 + 5x^6 - 6x^5 + 7x^4 - 4x^3 + 3x^2 - 3x + 1	\( -\,17^{2}\cdot 97^{2}\cdot 139 \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.379908823.1	x^10 + x^8 - x^7 - x^5 - x^3 + x^2 + 1	\( -\,7\cdot 53^{2}\cdot 139^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.386633299.1	x^10 - x^9 + 2x^8 - 2x^7 + 2x^6 - 3x^5 + 2x^4 - 2x^3 + 2x^2 - x + 1	\( -\,13^{2}\cdot 19\cdot 347^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.386864567.1	x^10 - x^9 + 3x^8 - x^7 + 4x^6 + 5x^4 + x^3 + 3x^2 + x + 1	\( -\,19^{2}\cdot 47\cdot 151^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.432343127.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 5x^6 - 6x^5 + 7x^4 - 5x^3 + 3x^2 - 2x + 1	\( -\,167\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.437865967.1	x^10 - x^9 - x^8 + 2x^7 + 2x^6 - 5x^5 + 2x^4 + 2x^3 - x^2 - x + 1	\( -\,7\cdot 11^{2}\cdot 719^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.437925347.1	x^10 - 3x^9 + 6x^8 - 10x^7 + 14x^6 - 15x^5 + 14x^4 - 10x^3 + 6x^2 - 3x + 1	\( -\,83\cdot 2297^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.440866291.1	x^10 - x^9 + x^8 - 3x^7 + 3x^6 - x^5 + 3x^4 - 3x^3 + x^2 - x + 1	\( -\,19\cdot 4817^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.443229763.1	x^10 - 3x^9 + 4x^8 - 4x^7 + 4x^6 - 5x^4 + 4x^3 - x + 1	\( -\,17^{2}\cdot 97^{2}\cdot 163 \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.449448427.1	x^10 - 2x^9 + 2x^8 - 3x^7 + 8x^6 - 11x^5 + 8x^4 - 3x^3 + 2x^2 - 2x + 1	\( -\,43\cdot 53^{2}\cdot 61^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.454106567.1	x^10 - 2x^9 + 2x^8 - x^7 + 2x^6 - 3x^5 + x^4 + 2x^3 - x^2 - x + 1	\( -\,17^{2}\cdot 97^{2}\cdot 167 \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.476322007.1	x^10 - x^9 - 2x^8 + 4x^7 + x^6 - 5x^5 + x^4 + 4x^3 - x^2 - 2x + 1	\( -\,7\cdot 73^{2}\cdot 113^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.484120747.1	x^10 - x^9 + x^8 - x^7 + x^6 - 4x^5 + 3x^4 - x^3 + x + 1	\( -\,11\cdot 17\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.484176016.1	x^10 - x^8 + x^6 + 2x^2 + 1	\( -\,2^{4}\cdot 5501^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.485605687.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 7x^6 - 7x^5 + 6x^4 - 5x^3 + 4x^2 - 2x + 1	\( -\,7\cdot 8329^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.486045407.1	x^10 - x^9 + 2x^8 - 4x^7 + 5x^6 - 6x^5 + 7x^4 - 6x^3 + 5x^2 - 3x + 1	\( -\,23\cdot 4597^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.486736979.1	x^10 - 2x^9 + 3x^8 - 4x^7 + 7x^6 - 10x^5 + 9x^4 - 4x^3 + x^2 - x + 1	\( -\,17^{2}\cdot 97^{2}\cdot 179 \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.486736979.2	x^10 - 2x^9 - 2x^8 + 4x^7 + 4x^6 - 4x^5 - 4x^4 + x^3 + x^2 + x + 1	\( -\,17^{2}\cdot 97^{2}\cdot 179 \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.501239855.1	x^10 - x^9 - x^8 + x^7 + x^5 + x^4 - 2x^3 - x^2 + x + 1	\( -\,5\cdot 19\cdot 2297^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.508490587.1	x^10 + 2x^8 - x^7 + 4x^6 - x^5 + 4x^4 - x^3 + 2x^2 + 1	\( -\,11\cdot 17^{3}\cdot 97^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.514709827.1	x^10 - 4x^9 + 9x^8 - 14x^7 + 16x^6 - 13x^5 + 8x^4 - 4x^3 + 2x^2 - x + 1	\( -\,163\cdot 1777^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.526794304.1	x^10 - 4x^9 + 8x^8 - 9x^7 + 8x^6 - 8x^5 + 8x^4 - 4x^3 + x^2 - x + 1	\( -\,2^{6}\cdot 19^{2}\cdot 151^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.526794304.2	x^10 + 3x^6 - x^4 + 4x^2 + 1	\( -\,2^{6}\cdot 19^{2}\cdot 151^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.530439175.1	x^10 - x^9 + x^7 + x^6 - 3x^5 + x^4 + x^3 - x + 1	\( -\,5^{2}\cdot 7\cdot 1741^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.546253891.1	x^10 - 2x^9 + 2x^8 - x^7 - 2x^6 + 2x^5 - 2x^3 + 4x^2 - 2x + 1	\( -\,211\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.552906407.1	x^10 - x^9 + 2x^8 - 3x^7 + 3x^6 - 3x^5 + 3x^4 - 3x^3 + 2x^2 - x + 1	\( -\,23\cdot 4903^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.562874607.1	x^10 - 4x^9 + 8x^8 - 11x^7 + 14x^6 - 15x^5 + 11x^4 - 4x^3 + x^2 - x + 1	\( -\,3^{2}\cdot 17^{2}\cdot 23\cdot 97^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.562973339.1	x^10 - x^9 + 3x^8 - 2x^7 + 6x^6 - 3x^5 + 6x^4 - 2x^3 + 4x^2 + 1	\( -\,59\cdot 3089^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.587675987.1	x^10 - 2x^8 + 2x^6 - x^5 - 2x^4 - x^3 + x^2 + 2x + 1	\( -\,227\cdot 1609^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.590495323.1	x^10 - x^9 + 2x^8 - 2x^7 + 2x^6 - 3x^5 + 3x^4 - 4x^3 + 4x^2 - 2x + 1	\( -\,11\cdot 17\cdot 1777^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.592440064.1	x^10 - x^9 + 3x^8 - 4x^7 + 5x^6 - 7x^5 + 7x^4 - 6x^3 + 5x^2 - 3x + 1	\( -\,2^{8}\cdot 19\cdot 349^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial
10.0.621349399.1	x^10 - x^9 - x^8 + 3x^6 - 2x^5 - 3x^4 + 4x^3 - x + 1	\( -\,11^{4}\cdot 31\cdot 37^{2} \)	$C_2 \wr S_5$ (as 10T39)	trivial

  There are too many results (1196864) to download.