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 706)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.775511104.1	x^9 - 3x^8 + 4x^7 - 5x^6 + 6x^5 - x^4 - 5x^3 + 4x^2 - 2	\( 2^{6}\cdot 59^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1568239201.1	x^9 - x^8 - 3x^6 + 3x^3 + 3x^2 + 5x + 1	\( 199^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.3037332544.1	x^9 - x^8 - 2x^7 - 3x^6 + 2x^5 + 5x^4 + 5x^3 + 6x^2 + 4x + 2	\( 2^{6}\cdot 83^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.4372515625.1	x^9 - x^8 - x^7 - 6x^6 + 6x^5 + 4x^4 + 4x^3 - 5x^2 + 10x + 5	\( 5^{6}\cdot 23^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.8389094464.2	x^9 - 5x^7 - 2x^6 + 9x^5 + 2x^4 - 3x^3 + 6x^2 + 10x + 2	\( 2^{6}\cdot 107^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.12594450625.1	x^9 - 3x^8 + x^7 + 4x^6 - 2x^5 - 6x^4 - 2x^3 + 7x^2 - 5	\( 5^{4}\cdot 67^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.18141126721.1	x^9 - x^8 - 3x^7 - x^6 + 6x^5 - x^4 + 6x^3 - 7x^2 + 2x - 3	\( 367^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.23891266624.1	x^9 - 4x^8 + 5x^7 + 4x^6 - 13x^5 + 4x^4 + 11x^3 - 8x^2 - 8x - 4	\( 2^{6}\cdot 139^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.30821664721.1	x^9 - 2x^7 - 4x^6 + 4x^5 + 10x^4 - x^3 - 8x^2 + 8x + 8	\( 419^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.41764235769.1	x^9 - 3x^8 + 6x^7 - 14x^6 + 9x^5 - 21x^4 + 6x^3 - 12x^2 - 3	\( 3^{10}\cdot 29^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.58120048561.1	x^9 - 2x^8 - 2x^7 + 8x^5 + 6x^4 - 5x^3 - 2x^2 + 4x + 8	\( 491^{4} \)	$D_{9}$ (as 9T3)	$[2]$
9.1.72555348321.1	x^9 - 3x^8 + 5x^7 - 9x^6 - 3x^5 - 3x^4 - 13x^3 + x - 3	\( 3^{4}\cdot 173^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.77133397441.1	x^9 - 3x^8 + 5x^7 - 11x^6 + 14x^5 - 19x^4 + 22x^3 - 19x^2 + 14x - 5	\( 17^{4}\cdot 31^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.100469346961.1	x^9 - 3x^8 + x^7 + 2x^6 + 4x^5 - 16x^4 + 35x^3 - 53x^2 + 43x - 10	\( 563^{4} \)	$D_{9}$ (as 9T3)	$[2]$
9.1.108651322129.1	x^9 - 2x^8 - 4x^7 + x^6 + 14x^5 + 19x^4 - x^3 - 41x^2 - 59x - 27	\( 7^{6}\cdot 31^{4} \)	$D_{9}$ (as 9T3)	$[3]$
9.1.126855644224.1	x^9 - 4x^8 + 9x^7 - 22x^6 + 33x^5 - 46x^4 + 51x^3 - 46x^2 + 26x - 6	\( 2^{6}\cdot 211^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.148718980881.2	x^9 - 6x^7 - 5x^6 + 27x^5 - 3x^4 - 11x^3 - 45x^2 + 60x - 37	\( 3^{12}\cdot 23^{4} \)	$D_{9}$ (as 9T3)	$[3]$
9.1.212558803681.1	x^9 + 2x^7 - 7x^6 + 3x^5 - 7x^4 + 16x^3 + 7x^2 - 13x + 7	\( 7^{4}\cdot 97^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.242137805625.3	x^9 - 6x^6 + 27x^5 - 27x^4 - 12x^3 + 54x^2 - 45x + 15	\( 3^{18}\cdot 5^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.410511866944.1	x^9 - 2x^8 + x^7 + 2x^6 - 17x^5 + 16x^4 - 21x^3 + 14x^2 + 116x + 62	\( 2^{6}\cdot 283^{4} \)	$D_{9}$ (as 9T3)	$[2]$
9.1.458774574241.1	x^9 - 3x^8 + 12x^7 - 27x^6 + 47x^5 - 67x^4 + 71x^3 - 59x^2 + 35x - 25	\( 823^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.490796923761.1	x^9 + 6x^7 - 11x^6 + 9x^5 - 48x^4 + 12x^3 - 99x^2 + 54x - 53	\( 3^{12}\cdot 31^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.495755401801.1	x^9 - 4x^8 + 4x^7 - x^6 + 5x^5 + 40x^4 - 17x^3 - 82x^2 - 38x - 23	\( 11^{6}\cdot 23^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.768231214144.1	x^9 - 3x^8 + 3x^7 - 3x^6 + 22x^5 + 6x^4 - 48x^3 + 12x^2 + 40x - 12	\( 2^{6}\cdot 331^{4} \)	$D_{9}$ (as 9T3)	$[2]$
9.1.845813141761.1	x^9 - 3x^8 + 3x^7 - 2x^6 - 11x^5 + 7x^4 + 30x^3 - 3x^2 + 26x + 1	\( 7^{4}\cdot 137^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.895152515625.1	x^9 - x^8 + 4x^7 - 11x^6 + 11x^5 - 41x^4 + 24x^3 - 60x^2 + 45x - 45	\( 3^{4}\cdot 5^{6}\cdot 29^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.933714431521.1	x^9 - 3x^8 + 5x^7 + 7x^6 - 15x^5 + 8x^4 + 39x^3 - 40x^2 + 6x + 5	\( 983^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1238824650625.1	x^9 - 2x^8 + 11x^7 - 10x^6 + 30x^5 - 28x^4 + 31x^3 - 58x^2 - 40	\( 5^{4}\cdot 211^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1320495160384.1	x^9 - 4x^8 + 4x^7 + 15x^6 - 32x^5 - 46x^4 + 163x^3 - 108x^2 - 18x + 27	\( 2^{6}\cdot 379^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1350739057369.1	x^9 - 4x^8 + 12x^7 - 26x^6 + 32x^5 - 59x^4 - 3x^3 - 176x^2 - 89x - 125	\( 13^{6}\cdot 23^{4} \)	$D_{9}$ (as 9T3)	$[3]$
9.1.1396105301761.1	x^9 - x^8 + 5x^6 - 7x^4 + 39x^3 - 58x^2 + 47x - 27	\( 1087^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1586874322944.5	x^9 + 9x^7 - 6x^6 + 27x^5 - 36x^4 + 27x^3 - 54x^2 - 32	\( 2^{12}\cdot 3^{18} \)	$D_{9}$ (as 9T3)	Trivial
9.9.1624709678881.1	x^9 - 3x^8 - 10x^7 + 38x^6 + 5x^5 - 107x^4 + 58x^3 + 78x^2 - 60x - 1	\( 1129^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1636073786281.1	x^9 - 2x^8 - 10x^7 + 29x^6 + 19x^5 - 98x^4 - 115x^3 + 611x^2 - 705x + 279	\( 11^{6}\cdot 31^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1659523650625.1	x^9 - x^8 - 3x^7 + 16x^5 - 12x^4 - 10x^3 - 13x^2 + 60x - 45	\( 5^{4}\cdot 227^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1826195471424.1	x^9 - x^8 + 5x^6 + 22x^5 + 33x^4 + 43x^3 + 32x^2 + 24x - 6	\( 2^{6}\cdot 3^{4}\cdot 137^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1886733005056.1	x^9 - x^8 - 6x^7 - 8x^6 + 21x^5 + 55x^4 - 24x^3 - 38x^2 - 24x - 104	\( 2^{8}\cdot 293^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.1985193642961.1	x^9 - 2x^8 - 2x^7 + 16x^6 - 6x^5 + 2x^4 + 35x^3 - 36x^2 + 36x - 16	\( 1187^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2048118765625.1	x^9 - 4x^8 + 3x^7 + 9x^6 - 6x^5 + 15x^4 - 18x^3 - 96x^2 + 56x - 16	\( 5^{6}\cdot 107^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2075751918009.1	x^9 - 3x^7 - 8x^6 - 15x^5 - 30x^4 - 12x^3 - 39x^2 - 21	\( 3^{10}\cdot 7^{4}\cdot 11^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2122409008801.1	x^9 - 2x^7 - 3x^6 - 8x^5 - 12x^4 + 25x^3 + 30x^2 + 27x + 27	\( 17^{4}\cdot 71^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2296318960321.1	x^9 - 4x^8 + 4x^7 + 3x^6 + 21x^5 - 24x^4 + 25x^3 + 17x^2 + 7x - 33	\( 1231^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2541865828329.1	x^9 - 9x^6 + 27x^3 - 3	\( 3^{26} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2647805875264.1	x^9 - 3x^8 + 7x^7 - 13x^6 + 16x^5 - 42x^4 + 40x^3 - 40x^2 + 48x - 36	\( 2^{6}\cdot 11^{4}\cdot 41^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2777825555761.1	x^9 - 4x^8 + 5x^7 - 13x^6 + 38x^5 - 55x^4 + 32x^3 - 28x^2 + 64x - 48	\( 1291^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.2812412850625.1	x^9 - 4x^8 + x^7 + 3x^6 + 6x^5 + 25x^4 + 2x^3 + 6x^2 - 10x + 5	\( 5^{4}\cdot 7^{4}\cdot 37^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.3026768337121.1	x^9 - 4x^8 + 6x^7 - 9x^6 + 10x^5 - 11x^4 + 41x^3 - 6x^2 + 26x + 17	\( 1319^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.3082394705625.1	x^9 + 6x^7 - 16x^6 + 15x^5 - 18x^4 + 23x^3 + 9x^2 - 5	\( 3^{10}\cdot 5^{4}\cdot 17^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.3658379210721.1	x^9 - 4x^8 - 2x^7 + 38x^6 - 110x^5 + 221x^4 - 312x^3 + 258x^2 - 126x + 45	\( 3^{4}\cdot 461^{4} \)	$D_{9}$ (as 9T3)	Trivial
9.1.3830635754401.1	x^9 - 3x^8 + 3x^7 + 13x^6 - 21x^5 - 4x^4 + 65x^3 - 56x^2 + 10x - 9	\( 1399^{4} \)	$D_{9}$ (as 9T3)	$[2]$