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 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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