Global number field search results

Degree	Signature	Galois group	Class number	Class group structure
Regulator	Number of ramified primes	Ram. primes	Unramified primes	CM field
Discriminant	Root discriminant	Intermediate field

Results (displaying matches 1-50 of 2809588)

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
10.0.215067767.1	x^10 - x^9 - x^8 + 2x^7 + x^6 - 3x^5 + 3x^3 - x^2 - x + 1	\( -\,215067767 \)	$S_{10}$ (as 10T45)	Trivial
10.0.216670707.1	x^10 - 3x^9 + 5x^8 - 6x^7 + 6x^6 - 4x^5 + 2x^4 - x^3 + x^2 - x + 1	\( -\,3^{5}\cdot 11^{2}\cdot 7369 \)	$S_5^2 \wr C_2$ (as 10T43)	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
10.0.220506347.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 3x^6 - x^4 + x^3 - x + 1	\( -\,37\cdot 677\cdot 8803 \)	$S_{10}$ (as 10T45)	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
10.0.224415603.1	x^10 + 2x^8 - 3x^7 + 3x^6 - 7x^5 + 8x^4 - 7x^3 + 7x^2 - 4x + 1	\( -\,3^{5}\cdot 31^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.226173952.1	x^10 - x^8 - 2x^7 - x^6 + 2x^5 + 2x^4 - x^2 + 1	\( -\,2^{10}\cdot 220873 \)	$S_5^2 \wr C_2$ (as 10T43)	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
10.0.227991979.1	x^10 - x^9 - x^8 + 3x^7 - x^6 - 3x^5 + 3x^4 + x^3 - 2x^2 + 1	\( -\,599\cdot 380621 \)	$S_{10}$ (as 10T45)	Trivial
10.0.229203619.1	x^10 - x^9 + 2x^8 - 3x^7 + 4x^6 - 4x^5 + 4x^4 - 4x^3 + 3x^2 - 2x + 1	\( -\,229203619 \)	$S_{10}$ (as 10T45)	Trivial
10.0.229345007.1	x^10 - x^9 + 6x^8 - 3x^7 + 11x^6 - 3x^5 + 11x^4 - 3x^3 + 6x^2 - x + 1	\( -\,47^{5} \)	$D_5$ (as 10T2)	Trivial
10.0.233043179.1	x^10 - x^9 + 2x^8 - 4x^7 + 4x^6 - 5x^5 + 5x^4 - 4x^3 + 3x^2 - x + 1	\( -\,97\cdot 463\cdot 5189 \)	$S_{10}$ (as 10T45)	Trivial
10.0.236184579.1	x^10 - 3x^9 + 5x^8 - 7x^7 + 7x^6 - 6x^5 + 4x^4 - 2x^3 + x^2 + 1	\( -\,3^{5}\cdot 37\cdot 109\cdot 241 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.0.236438047.1	x^10 - 2x^9 + x^8 + 2x^7 - 3x^6 + x^5 + x^4 - x + 1	\( -\,236438047 \)	$S_{10}$ (as 10T45)	Trivial
10.0.240232739.1	x^10 - 2x^9 + 2x^8 - 2x^6 + 4x^5 - 4x^4 + x^3 + 3x^2 - 3x + 1	\( -\,467\cdot 514417 \)	$S_{10}$ (as 10T45)	Trivial
10.0.243226747.1	x^10 - 3x^9 + 4x^8 - 3x^7 + 2x^6 - x^5 + x^4 - 2x^3 + 3x^2 - 2x + 1	\( -\,243226747 \)	$S_{10}$ (as 10T45)	Trivial
10.0.243415027.1	x^10 - x^7 + x^6 + 2x^5 - x^3 - 2x^2 + 1	\( -\,17\cdot 14318531 \)	$S_{10}$ (as 10T45)	Trivial
10.0.244175707.1	x^10 - x^9 + x^7 - x^6 - x^4 + x^3 + x^2 - x + 1	\( -\,19^{2}\cdot 676387 \)	$S_{10}$ (as 10T45)	Trivial
10.0.246071287.1	x^10 - 3x^9 + 7x^8 - 12x^7 + 15x^6 - 15x^5 + 12x^4 - 7x^3 + 4x^2 - 2x + 1	\( -\,7^{5}\cdot 11^{4} \)	$D_5\times C_5$ (as 10T6)	Trivial
10.0.246944619.1	x^10 - x^9 + x^6 - x^5 - x^4 + 3x^3 - x^2 - x + 1	\( -\,3^{5}\cdot 73\cdot 13921 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.0.250679267.1	x^10 - x^9 - 2x^8 + x^7 + 3x^6 - 2x^4 - 2x^3 + 2x + 1	\( -\,250679267 \)	$S_{10}$ (as 10T45)	Trivial
10.0.252486127.1	x^10 - x^9 + 2x^8 - 4x^7 + 4x^6 - 4x^5 + 5x^4 - 3x^3 + 2x^2 - 2x + 1	\( -\,787\cdot 320821 \)	$S_{10}$ (as 10T45)	Trivial
10.0.254121139.1	x^10 - 2x^8 - x^7 + 2x^6 + 3x^5 - 3x^3 - x^2 + x + 1	\( -\,149\cdot 991\cdot 1721 \)	$S_{10}$ (as 10T45)	Trivial
10.0.260270739.1	x^10 - x^8 - 2x^7 + x^6 + 3x^5 - 2x^4 - 4x^3 + x^2 + 3x + 1	\( -\,3^{5}\cdot 163\cdot 6571 \)	$S_5^2 \wr C_2$ (as 10T43)	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
10.0.262477979.1	x^10 - x^9 + x^8 - 2x^6 + x^5 - x^4 + x^2 + 1	\( -\,251\cdot 1045729 \)	$S_{10}$ (as 10T45)	Trivial
10.0.262864627.1	x^10 - 2x^8 - x^7 + x^6 + 2x^5 - x^4 - 2x^3 + x^2 + x + 1	\( -\,353\cdot 744659 \)	$S_{10}$ (as 10T45)	Trivial
10.0.262909719.1	x^10 - x^8 - x^7 - 2x^6 + 4x^4 + x^3 - 2x^2 + 1	\( -\,3^{5}\cdot 73\cdot 14821 \)	$S_5^2 \wr C_2$ (as 10T43)	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
10.0.268043264.1	x^10 - 2x^9 + 3x^8 - 6x^7 + 6x^6 - 6x^5 + 7x^4 - 4x^3 + 3x^2 - 2x + 1	\( -\,2^{10}\cdot 261761 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.0.274127275.1	x^10 - x^9 + x^8 - 3x^7 + 3x^6 - x^5 + 3x^4 - 3x^3 + 1	\( -\,5^{2}\cdot 59\cdot 185849 \)	$S_{10}$ (as 10T45)	Trivial
10.0.274550779.1	x^10 - x^9 + 2x^8 - 2x^7 + 3x^6 - 3x^5 + 3x^4 - 3x^3 + 2x^2 - 2x + 1	\( -\,19\cdot 14450041 \)	$S_{10}$ (as 10T45)	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
10.0.278005859.1	x^10 - x^9 - x^8 + 4x^7 - 2x^6 - 3x^5 + 4x^4 - 2x^2 + 1	\( -\,278005859 \)	$S_{10}$ (as 10T45)	Trivial
10.0.278645219.1	x^10 + 3x^8 - x^7 + 4x^6 - x^5 + 4x^4 + 2x^2 + 1	\( -\,317\cdot 879007 \)	$S_{10}$ (as 10T45)	Trivial
10.0.281268947.1	x^10 + 3x^8 - x^7 + 4x^6 - x^5 + 4x^4 - x^3 + 2x^2 - x + 1	\( -\,281268947 \)	$S_{10}$ (as 10T45)	Trivial
10.0.282748447.1	x^10 - x^9 - 2x^8 + 3x^7 + 2x^6 - 5x^5 + x^4 + 4x^3 - 2x^2 - x + 1	\( -\,282748447 \)	$S_{10}$ (as 10T45)	Trivial
10.0.283885691.1	x^10 - x^9 + 2x^8 - 4x^7 + 3x^6 - 4x^5 + 3x^4 - 2x^3 + 2x^2 + 1	\( -\,8941\cdot 31751 \)	$S_{10}$ (as 10T45)	Trivial
10.0.284152779.1	x^10 - x^9 - 2x^8 + 3x^7 + 2x^6 - 3x^5 - 2x^4 + 3x^3 + x^2 - 2x + 1	\( -\,3^{5}\cdot 1169353 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.0.285267739.1	x^10 - x^9 + x^8 - x^7 - x^5 + 3x^4 - 4x^3 + 4x^2 - 2x + 1	\( -\,285267739 \)	$S_{10}$ (as 10T45)	Trivial
10.0.288806267.1	x^10 - x^9 - x^8 + 2x^7 - x^5 + x^3 - x + 1	\( -\,1321\cdot 218627 \)	$S_{10}$ (as 10T45)	Trivial
10.0.290432899.1	x^10 - 3x^8 - x^7 + 4x^6 + 3x^5 - 2x^4 - 4x^3 + 2x + 1	\( -\,89\cdot 3263291 \)	$S_{10}$ (as 10T45)	Trivial
10.0.290491759.1	x^10 - 3x^9 + 5x^8 - 5x^7 + 5x^6 - 6x^5 + 6x^4 - 3x^3 + x^2 - x + 1	\( -\,290491759 \)	$S_{10}$ (as 10T45)	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
10.0.291458939.1	x^10 - x^9 + 2x^8 - 2x^6 + 3x^5 - 3x^4 + 2x^2 - 2x + 1	\( -\,197\cdot 1479487 \)	$S_{10}$ (as 10T45)	Trivial
10.0.292693979.1	x^10 - 3x^9 + 4x^8 - 3x^7 + 3x^6 - 4x^5 + 3x^4 - x + 1	\( -\,127\cdot 239\cdot 9643 \)	$S_{10}$ (as 10T45)	Trivial
10.0.293025059.1	x^10 - 2x^9 + 3x^8 - 4x^7 + 5x^6 - 6x^5 + 8x^4 - 8x^3 + 6x^2 - 3x + 1	\( -\,293025059 \)	$S_{10}$ (as 10T45)	Trivial

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