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 5262)

Label	Polynomial	Discriminant	Galois group	Class group
10.8.70952789611.1	x^10 - x^9 - 6x^8 + 9x^7 + 5x^6 - 18x^5 + 9x^4 + 12x^3 - 10x^2 - 3x + 1	\( -\,11^{8}\cdot 331 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.85992371875.1	x^10 - 2x^9 - x^8 - x^6 + 12x^5 - x^4 - 12x^3 + 3x^2 + 3x - 1	\( -\,5^{5}\cdot 27517559 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.88642871875.1	x^10 - x^9 - 2x^8 - 3x^7 - x^6 + 20x^5 + 4x^4 - 25x^3 - 3x^2 + 8x + 1	\( -\,5^{5}\cdot 3169\cdot 8951 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.90213934375.1	x^10 - 3x^9 - 2x^8 + 12x^7 - 9x^6 - 9x^5 + 26x^4 - 9x^3 - 15x^2 + 10x - 1	\( -\,5^{5}\cdot 28868459 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.90614121875.1	x^10 - x^9 - 7x^8 + 9x^7 + 9x^6 - 15x^5 + 4x^4 + 3x^3 - 8x^2 + 3x + 1	\( -\,5^{5}\cdot 28996519 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.91588346875.1	x^10 - x^9 - 7x^8 + 5x^7 + 14x^6 - x^5 - 11x^4 - 8x^3 + 2x^2 + 4x + 1	\( -\,5^{5}\cdot 29308271 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.94136471875.1	x^10 - 5x^8 - 2x^7 + 8x^5 + 11x^4 - 5x^3 - 8x^2 + 1	\( -\,5^{5}\cdot 30123671 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.94459871875.1	x^10 - 3x^9 + 5x^7 - 5x^6 + 9x^5 + x^4 - 16x^3 + x^2 + 5x + 1	\( -\,5^{5}\cdot 89\cdot 339631 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.94822656283.1	x^10 - x^9 - 4x^8 + 3x^7 + 6x^5 + 4x^4 - 11x^3 + 4x - 1	\( -\,111847\cdot 847789 \)	$S_{10}$ (as 10T45)	Trivial
10.8.97939335863.1	x^10 - 3x^9 - x^8 + 5x^7 + 7x^5 - 3x^4 - 16x^3 + x^2 + 7x + 1	\( -\,61^{2}\cdot 167\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.99136309375.1	x^10 - 3x^9 - 4x^8 + 17x^7 + 3x^6 - 32x^5 + 3x^4 + 21x^3 - 4x^2 - 4x + 1	\( -\,5^{5}\cdot 31723619 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.99667039987.1	x^10 - x^9 - 7x^8 + 7x^7 + 15x^6 - 17x^5 - 11x^4 + 15x^3 + 4x^2 - 4x - 1	\( -\,67\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.103196621875.1	x^10 - 4x^9 + 2x^8 + 7x^7 - 9x^6 + 6x^5 + 3x^4 - 12x^3 + 3x^2 + 3x - 1	\( -\,5^{5}\cdot 2129\cdot 15511 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.103545471875.1	x^10 - 2x^9 - x^8 + 3x^7 - 6x^6 + 8x^5 + 12x^4 - 16x^3 - 7x^2 + 6x + 1	\( -\,5^{5}\cdot 1009\cdot 32839 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.114458329088.1	x^10 - 2x^9 - 5x^8 + 12x^7 + x^6 - 20x^5 + 13x^4 + 10x^3 - 10x^2 + 1	\( -\,2^{15}\cdot 3492991 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.117161033728.1	x^10 - 6x^8 - 2x^7 + 10x^6 + 10x^5 - 5x^4 - 12x^3 + 2x^2 + 4x - 1	\( -\,2^{15}\cdot 3575471 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial
10.8.146407115723.1	x^10 - 2x^9 - 4x^8 + 7x^7 - 3x^6 - 11x^5 + 17x^4 + 6x^3 - 12x^2 + x + 1	\( -\,11^{8}\cdot 683 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.155838906487.1	x^10 - 2x^9 - 3x^8 + 12x^7 - 7x^6 - 20x^5 + 17x^4 + 16x^3 - 6x^2 - 6x - 1	\( -\,11^{8}\cdot 727 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.182390020679.1	x^10 - 3x^8 - 2x^7 - 5x^6 + 10x^5 + 16x^4 - 8x^3 - 11x^2 + 1	\( -\,61^{2}\cdot 311\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.184134278779.1	x^10 - 4x^9 - x^8 + 19x^7 - 13x^6 - 13x^5 - x^4 + 13x^3 + 4x^2 - 3x - 1	\( -\,11^{8}\cdot 859 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.192422158163.1	x^10 - 4x^9 + x^8 + 15x^7 - 19x^6 - 9x^5 + 25x^4 - 2x^3 - 9x^2 + x + 1	\( -\,1483\cdot 129751961 \)	$S_{10}$ (as 10T45)	Trivial
10.8.194871376691.1	x^10 - x^9 - 4x^8 + 6x^7 - 12x^5 + 13x^4 + 8x^3 - 11x^2 + 1	\( -\,131\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.202997860307.1	x^10 - 4x^9 - x^8 + 19x^7 - 13x^6 - 24x^5 + 32x^4 + 2x^3 - 18x^2 + 8x - 1	\( -\,11^{8}\cdot 947 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.209857344499.1	x^10 - 5x^9 + 3x^8 + 18x^7 - 24x^6 - 12x^5 + 27x^4 - 3x^3 - 7x^2 + 2x + 1	\( -\,11^{9}\cdot 89 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.212429651071.1	x^10 - 4x^9 + 3x^8 + 4x^7 - 7x^6 + 15x^5 - 19x^4 - 6x^3 + 20x^2 - 9x + 1	\( -\,11^{8}\cdot 991 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.215231953663.1	x^10 - 8x^8 - 2x^7 + 17x^6 + 13x^5 - 7x^4 - 22x^3 - 2x^2 + 10x - 1	\( -\,61^{2}\cdot 367\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.219503494144.1	x^10 - 2x^8 - 5x^6 + 13x^4 - 7x^2 + 1	\( -\,2^{10}\cdot 11^{8} \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.224622731911.1	x^10 - 5x^9 + 4x^8 + 14x^7 - 22x^6 - 4x^5 + 22x^4 - 11x^3 - 4x^2 + 5x - 1	\( -\,151\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.229307067799.1	x^10 - 5x^8 - 5x^7 + 7x^6 + 20x^5 - x^4 - 19x^3 - 3x^2 + 5x + 1	\( -\,17\cdot 23\cdot 61^{2}\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.242473545043.1	x^10 - 4x^9 - x^8 + 20x^7 - 15x^6 - 22x^5 + 26x^4 - 2x^3 - 6x^2 + 5x - 1	\( -\,163\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.243382181935.1	x^10 - 5x^9 + 8x^8 + 2x^7 - 24x^6 + 22x^5 + 14x^4 - 21x^3 + 5x - 1	\( -\,5\cdot 61^{2}\cdot 83\cdot 397^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.255275929283.1	x^10 - 4x^9 + 12x^7 - 3x^6 - 7x^5 - 4x^4 - 4x^3 + 6x^2 + 3x - 1	\( -\,79\cdot 3231340877 \)	$S_{10}$ (as 10T45)	Trivial
10.8.259803148427.1	x^10 - 2x^9 - 5x^8 + 6x^7 + 9x^6 + 2x^5 - 7x^4 - 16x^3 + 3x^2 + 9x - 1	\( -\,61^{2}\cdot 397^{2}\cdot 443 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.278175171307.1	x^10 - x^9 - 7x^8 + 2x^7 + 21x^6 + 2x^5 - 26x^4 - 3x^3 + 11x^2 - 1	\( -\,11\cdot 17\cdot 38569^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.281058542899.1	x^10 - 4x^9 + x^8 + 14x^7 - 19x^6 + 2x^5 + 19x^4 - 30x^3 + 15x^2 + 3x - 1	\( -\,211\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.282739364039.1	x^10 - x^9 - 8x^8 + 4x^7 + 19x^6 - 7x^5 - 13x^4 + 14x^3 + 7x^2 - 4x - 1	\( -\,11^{8}\cdot 1319 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.292645081411.1	x^10 - 9x^8 - 4x^7 + 27x^6 + 20x^5 - 28x^4 - 24x^3 + 8x^2 + 7x + 1	\( -\,61^{2}\cdot 397^{2}\cdot 499 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.297042915007.1	x^10 - x^9 - 7x^8 + 2x^7 + 17x^6 + 7x^5 - 14x^4 - 11x^3 + 5x^2 + 3x - 1	\( -\,223\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.304597739107.1	x^10 - 3x^9 + x^8 + 10x^7 - 15x^6 - 12x^5 + 21x^4 + 4x^3 - 9x^2 + 1	\( -\,19\cdot 863\cdot 18576431 \)	$S_{10}$ (as 10T45)	Trivial
10.8.305304871936.1	x^10 - 4x^8 + 11x^4 - 7x^2 + 1	\( -\,2^{10}\cdot 31^{2}\cdot 557^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.312254702807.1	x^10 - x^9 - 4x^8 - 2x^7 + 17x^5 + 15x^4 - 20x^3 - 15x^2 + 6x + 4	\( -\,47\cdot 81509^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.320795309683.1	x^10 - 5x^8 - 3x^7 - x^6 + 5x^5 + 23x^4 + 8x^3 - 11x^2 - x + 1	\( -\,61^{2}\cdot 397^{2}\cdot 547 \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.323683535187.1	x^10 - 2x^9 - 6x^8 + 14x^7 + 8x^6 - 31x^5 + 31x^3 + x^2 - 12x - 3	\( -\,3^{5}\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.326654461587.1	x^10 - 2x^9 - 3x^8 + 14x^6 + 11x^5 - 27x^4 - 15x^3 + 13x^2 + 8x + 1	\( -\,3\cdot 329977^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.333961580467.1	x^10 - 3x^9 - 5x^8 + 22x^7 - 2x^6 - 45x^5 + 22x^4 + 34x^3 - 18x^2 - 8x + 1	\( -\,17^{2}\cdot 67\cdot 4153^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.343802195227.1	x^10 - 6x^8 - 9x^7 + 3x^6 + 21x^5 + 7x^4 - 15x^3 - 5x^2 + 3x + 1	\( -\,43\cdot 89417^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.346954954943.1	x^10 - 3x^9 - 3x^8 + 13x^7 + x^6 - 13x^5 - 4x^4 - 2x^3 + 12x^2 - 1	\( -\,23\cdot 263^{2}\cdot 467^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.348761899387.1	x^10 - 4x^9 + 18x^7 - 16x^6 - 26x^5 + 35x^4 + 13x^3 - 22x^2 - x + 1	\( -\,11^{8}\cdot 1627 \)	$C_2 \times (C_2^4 : C_5)$ (as 10T14)	Trivial
10.8.355652279403.1	x^10 - x^9 - 8x^8 + 5x^7 + 21x^6 - 6x^5 - 22x^4 - 2x^3 + 10x^2 + 2x - 1	\( -\,3\cdot 89\cdot 36497^{2} \)	$C_2 \wr S_5$ (as 10T39)	Trivial
10.8.356621721875.1	x^10 - 4x^9 + 13x^7 - 5x^6 - 6x^5 - 14x^4 + 8x^3 + 9x^2 - 2x - 1	\( -\,5^{5}\cdot 149\cdot 765899 \)	$S_5^2 \wr C_2$ (as 10T43)	Trivial