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 306)

Label	Polynomial	Discriminant	Galois group	Class group
9.5.9829532736.1	x^9 - 3x^8 + 3x^7 + 4x^6 - 12x^5 + 9x^4 + x^3 - 9x^2 + 6x - 1	\( 2^{6}\cdot 3^{12}\cdot 17^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.12278412864.1	x^9 - 3x^8 + 3x^7 - 2x^6 - 3x^5 + 6x^4 - 7x^3 + 6x^2 + 6x + 1	\( 2^{6}\cdot 3^{12}\cdot 19^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.12657150016.1	x^9 - 2x^8 + x^7 + 5x^6 - 23x^5 + 26x^4 + 4x^3 - 21x^2 + 11x - 1	\( 2^{6}\cdot 7^{6}\cdot 41^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.13361279281.1	x^9 - 4x^8 + x^7 + 14x^6 - 11x^5 - 16x^4 + 7x^3 + 9x^2 + 5x + 1	\( 7^{6}\cdot 337^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.16721334721.1	x^9 - 2x^8 - 2x^7 + 8x^6 - 3x^5 - 16x^4 - 6x^3 - 4x^2 - 4x - 1	\( 7^{6}\cdot 13^{2}\cdot 29^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.24794911296.1	x^9 - 3x^6 + 9x^5 - 9x^4 - 27x^3 + 9x + 1	\( 2^{6}\cdot 3^{18} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.46562734656.1	x^9 - 3x^8 + 6x^7 - 9x^6 + 9x^5 - 3x^4 - 19x^3 + 24x^2 - 6x - 1	\( 2^{6}\cdot 3^{12}\cdot 37^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.51870973504.1	x^9 - 4x^8 + 17x^6 - 19x^5 - 5x^4 + 23x^3 - 22x^2 - 5x + 13	\( 2^{6}\cdot 7^{6}\cdot 83^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.62352087616.1	x^9 - x^8 - 5x^7 - 7x^5 - 14x^4 - 35x^3 - 32x^2 - 10x - 1	\( 2^{6}\cdot 7^{8}\cdot 13^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.62352087616.2	x^9 - 2x^8 - 6x^7 + 7x^6 + 7x^5 + 7x^4 - 7x^3 - 8x^2 - 5x - 1	\( 2^{6}\cdot 7^{8}\cdot 13^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.69257922561.1	x^9 - 2x^6 - 18x^5 - 12x^4 + 4x^3 + 6x^2 + 3x - 1	\( 3^{12}\cdot 19^{4} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.70845404224.1	x^9 - 2x^8 - 4x^7 + x^6 + 14x^5 + 19x^4 - 36x^3 - 13x^2 + 25x - 13	\( 2^{6}\cdot 7^{6}\cdot 97^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.77380217929.1	x^9 - x^8 + 4x^7 + x^6 - 4x^5 - 28x^4 - 27x^3 + 8x^2 + 6x - 1	\( 7^{6}\cdot 811^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.85602471241.1	x^9 - 2x^8 + x^7 - 4x^6 + 3x^5 - 4x^4 + 6x^3 + 21x^2 - 14x - 7	\( 7^{6}\cdot 853^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.95540337216.1	x^9 - 3x^8 + 6x^7 - 9x^6 - 3x^5 - 3x^4 + 11x^3 + 6x^2 - 6x + 1	\( 2^{6}\cdot 3^{12}\cdot 53^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.96144645184.1	x^9 - 2x^8 + 3x^7 - x^6 - 2x^5 + 26x^4 - 4x^3 - 56x^2 - 40x - 8	\( 2^{6}\cdot 7^{6}\cdot 113^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.99639341649.1	x^9 - 3x^8 - 3x^7 + 4x^6 - 6x^4 - 11x^3 + 3x^2 + 9x - 3	\( 3^{12}\cdot 433^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.100228594921.1	x^9 - x^8 - x^7 + 7x^6 - 11x^5 - 4x^4 + 10x^3 - 22x^2 + 9x - 1	\( 7^{6}\cdot 13^{2}\cdot 71^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.100228594921.2	x^9 - 2x^8 - 6x^7 + 5x^6 + 19x^5 - 9x^4 - 10x^3 + 21x^2 + 11x - 1	\( 7^{6}\cdot 13^{2}\cdot 71^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.100228594921.3	x^9 - x^8 - 4x^7 + 7x^6 - 9x^5 - 30x^4 + 29x^3 + 63x^2 + 28x + 7	\( 7^{6}\cdot 13^{2}\cdot 71^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.111964521321.1	x^9 - 9x^5 - 9x^4 - 12x^3 - 18x^2 - 9x - 1	\( 3^{18}\cdot 17^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.120918239289.1	x^9 - 3x^8 + 9x^7 - 21x^6 + 18x^5 - 18x^4 + 18x^3 + 9x^2 - 9x - 3	\( 3^{16}\cdot 53^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.122642141209.1	x^9 - 2x^8 - 11x^7 + 28x^6 + 27x^5 - 114x^4 + 31x^3 + 131x^2 - 97x - 1	\( 7^{6}\cdot 1021^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.136971789409.1	x^9 - x^8 - 4x^7 + 7x^6 + 12x^5 - 9x^4 - 27x^3 + 21x - 7	\( 7^{6}\cdot 13^{2}\cdot 83^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.136971789409.2	x^9 - x^8 + 2x^7 + 5x^6 - 22x^5 + 24x^4 - 45x^3 + 8x - 1	\( 7^{6}\cdot 13^{2}\cdot 83^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.139858796529.1	x^9 - 3x^6 - 9x^5 + 18x^4 - 18x^3 + 27x^2 - 18x + 3	\( 3^{18}\cdot 19^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.145478165056.1	x^9 - x^8 + 3x^7 - 6x^6 + 9x^5 + 10x^4 - 27x^3 - 2x^2 + 6x - 1	\( 2^{6}\cdot 7^{6}\cdot 139^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.166322861929.1	x^9 - 2x^8 - 6x^7 + 22x^6 - 20x^5 - 27x^4 + 111x^3 - 162x^2 + 123x - 41	\( 7^{6}\cdot 29^{2}\cdot 41^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.182945253841.1	x^9 - 7x^7 - 3x^6 + 14x^5 + 35x^4 - 32x^3 - 42x^2 + 14x + 13	\( 7^{6}\cdot 29^{2}\cdot 43^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.186880696209.1	x^9 - 3x^8 - 3x^7 + 5x^6 + 9x^5 + 15x^4 + 7x^3 - 18x^2 - 24x - 8	\( 3^{12}\cdot 593^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.187076145529.1	x^9 - 2x^8 + 2x^7 - 6x^6 - 8x^5 + 7x^4 + x^3 + 30x^2 + 45x + 13	\( 7^{6}\cdot 13^{2}\cdot 97^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.187076145529.2	x^9 + 2x^7 - 8x^6 - 22x^5 + 15x^4 - 3x^3 - 16x^2 + 43x + 29	\( 7^{6}\cdot 13^{2}\cdot 97^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.193072360000.1	x^9 - x^8 - 5x^7 + 8x^6 + 12x^5 - 11x^4 - 15x^3 + 3x^2 + 4x - 1	\( 2^{6}\cdot 5^{4}\cdot 13^{6} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.246675128896.1	x^9 - 2x^8 - 5x^7 + 7x^6 + 5x^5 + 10x^4 - 14x^3 + x^2 - 11x + 1	\( 2^{6}\cdot 7^{6}\cdot 181^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.254573729809.1	x^9 - x^8 - 9x^7 + 17x^6 + 8x^5 - 27x^4 + 13x^3 - 30x^2 + 27	\( 7^{6}\cdot 1471^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.262642925169.1	x^9 - 3x^8 - 9x^5 + 21x^4 - 7x^3 + 15x + 1	\( 3^{12}\cdot 19^{2}\cdot 37^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.266560527025.1	x^9 - x^7 - x^6 - 4x^5 + 5x^4 - 5x^3 + 10x^2 - 3x - 1	\( 5^{2}\cdot 13^{6}\cdot 47^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.274734270801.1	x^9 - 3x^8 - 3x^7 + 15x^6 - 12x^5 + 3x^4 + 32x^3 - 69x^2 + 18x + 19	\( 3^{12}\cdot 719^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.278935028449.1	x^9 - 2x^8 - 3x^7 + 5x^6 - 3x^5 + 11x^4 - 7x^3 - 18x^2 + 12x + 11	\( 7^{2}\cdot 11^{2}\cdot 19^{6} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.310284649024.1	x^9 - x^8 - 5x^7 + 14x^5 - 7x^4 + 7x^3 + 17x^2 - 38x - 1	\( 2^{6}\cdot 7^{8}\cdot 29^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.310284649024.2	x^9 - 7x^7 - 7x^6 + 21x^5 - 14x^4 + 35x^2 - 35x + 7	\( 2^{6}\cdot 7^{8}\cdot 29^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.338962662025.1	x^9 - 4x^8 + 6x^7 - 4x^6 - 5x^5 + 18x^4 - 29x^3 + 17x^2 + 6x - 1	\( 5^{2}\cdot 13^{6}\cdot 53^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.365672974681.1	x^9 - 2x^8 - x^7 + 10x^6 + 2x^5 - 10x^4 - 36x^3 - 53x^2 - 14x - 1	\( 7^{6}\cdot 41^{2}\cdot 43^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.374436295744.1	x^9 - 2x^8 - 4x^7 + 15x^6 - 28x^5 + 33x^4 - 36x^3 + x^2 + 11x + 1	\( 2^{6}\cdot 7^{6}\cdot 223^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.384153279601.1	x^9 - 8x^7 - 3x^6 + 40x^5 - 12x^4 - 73x^3 + 44x^2 + 41x - 29	\( 7^{6}\cdot 13^{2}\cdot 139^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.395800782129.1	x^9 - 3x^8 - x^6 + 60x^4 - 71x^3 - 12x^2 + 6x + 1	\( 3^{12}\cdot 863^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.404099233344.1	x^9 - 3x^8 - 6x^7 + 25x^6 - 3x^5 - 57x^4 + 65x^3 + 24x^2 - 66x + 19	\( 2^{6}\cdot 3^{12}\cdot 109^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.414358701849.1	x^9 - 3x^7 - 9x^6 - 6x^5 + 18x^4 + 23x^3 + 9x^2 - 15x - 17	\( 3^{12}\cdot 883^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.419809397329.1	x^9 - 7x^7 - 12x^6 + 14x^5 + 63x^4 + 34x^3 - 77x^2 - 112x - 43	\( 7^{6}\cdot 1889^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial
9.5.431424335241.1	x^9 - 3x^8 - 6x^7 + 21x^6 + 3x^5 - 15x^4 - 37x^3 + 6x^2 + 48x - 17	\( 3^{12}\cdot 17^{2}\cdot 53^{2} \)	$((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ (as 9T25)	Trivial