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 13554)

Label	Polynomial	Discriminant	Galois group	Class group
9.3.203297472.1	x^9 - 3x^7 - x^6 + 3x^5 + 2x^4 + 4x^3 - x^2 - 5x + 1	\( -\,2^{6}\cdot 3^{3}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.272097792.1	x^9 - 3x^8 + 7x^6 - 3x^5 - 9x^4 + 3x^3 + 6x^2 - 1	\( -\,2^{9}\cdot 3^{12} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.308915776.1	x^9 - x^8 - 2x^7 - x^6 + 5x^5 + x^4 - 5x^3 + 2x^2 + 2x - 1	\( -\,2^{6}\cdot 13^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.707347971.1	x^9 - 2x^6 + 6x^4 - 5x^3 - 12x^2 - 6x - 1	\( -\,3^{12}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.806954491.1	x^9 - 4x^8 + 11x^7 - 23x^6 + 38x^5 - 50x^4 + 46x^3 - 28x^2 + 9x - 1	\( -\,7^{6}\cdot 19^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.918330048.1	x^9 - 3x^8 + 3x^7 - 6x^6 + 12x^5 - 3x^4 - 15x^3 + 15x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{15} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.941192000.1	x^9 - x^7 - 3x^6 + 5x^5 + 2x^4 - 10x^3 - 5x^2 - x - 1	\( -\,2^{6}\cdot 5^{3}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.1162261467.1	x^9 - 3x^6 - 6x^3 - 1	\( -\,3^{19} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.1270238787.1	x^9 - x^8 - 3x^7 + 2x^6 - x^5 - x^4 + 6x^3 - 4x^2 + 3x - 1	\( -\,3^{3}\cdot 19^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.1431435383.1	x^9 - x^8 - 2x^7 + 5x^6 + 9x^5 - 5x^4 - 11x^3 + 6x^2 - 1	\( -\,7^{6}\cdot 23^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.1626379776.1	x^9 - 4x^8 + 4x^7 - x^6 + 5x^5 - 11x^4 + 11x^3 - 6x^2 + x + 1	\( -\,2^{9}\cdot 3^{3}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.1793613375.1	x^9 - 6x^7 - 3x^6 + 9x^5 + 3x^4 - 9x^3 + 3x - 1	\( -\,3^{15}\cdot 5^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.2315685267.2	x^9 - 4x^6 + 3x^3 + 1	\( -\,3^{9}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.2754990144.1	x^9 - 3x^8 + 3x^7 - 6x^5 + 15x^4 - 21x^3 + 15x^2 - 6x + 1	\( -\,2^{6}\cdot 3^{16} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.3504881359.1	x^9 + 5x^7 - 4x^6 + 6x^5 - 4x^4 - 10x^3 - x^2 - 2x + 1	\( -\,7^{6}\cdot 31^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.4251528000.1	x^9 - 3x^8 + 3x^6 + 9x^5 - 21x^4 + 17x^3 - 6x^2 + 1	\( -\,2^{6}\cdot 3^{12}\cdot 5^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.6466042647.5	x^9 - 3x^7 - 2x^6 + 18x^5 - 6x^4 - 24x^3 + 9x^2 - 1	\( -\,3^{12}\cdot 23^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.6588344000.1	x^9 - 4x^8 + 7x^7 + x^6 - 23x^5 + 32x^4 - 22x^3 + 11x^2 - 5x + 1	\( -\,2^{6}\cdot 5^{3}\cdot 7^{7} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.7346640384.1	x^9 + 3x^7 - 3x^6 + 12x^4 - 36x^3 + 36x^2 - 24x + 8	\( -\,2^{9}\cdot 3^{15} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.7529536000.1	x^9 - 3x^7 - 7x^6 + 3x^5 + 14x^4 + 20x^3 - 7x^2 - 21x - 7	\( -\,2^{9}\cdot 5^{3}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.8340725952.1	x^9 - x^7 - 3x^6 + 9x^5 + 2x^4 - 24x^3 - 9x^2 - x - 1	\( -\,2^{6}\cdot 3^{3}\cdot 13^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.10021812416.1	x^9 - x^8 + 3x^7 + 4x^6 + 14x^5 - 3x^4 - 9x^3 + 7x^2 - 2x - 1	\( -\,2^{6}\cdot 7^{6}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.12214672127.1	x^9 - 4x^8 + 5x^7 - 8x^6 + 10x^5 - 8x^4 - 11x^3 + 14x^2 + 8x - 8	\( -\,7^{6}\cdot 47^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.12867859375.1	x^9 - 4x^8 + 3x^7 + 6x^6 - 18x^5 + 26x^4 - 8x^3 - 15x^2 + 14x - 13	\( -\,5^{6}\cdot 7^{7} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.14765025303.1	x^9 + 9x^7 - 6x^6 + 18x^5 - 18x^4 + 12x^3 - 9x^2 + 1	\( -\,3^{16}\cdot 7^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.15832158831.4	x^9 + 6x^7 - 3x^6 + 9x^5 - 3x^4 - 23x^3 - 3x - 1	\( -\,3^{12}\cdot 31^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.16542390592.2	x^9 - 7x^7 - x^6 + 28x^5 + 28x^4 - 16x^3 - 28x^2 + 8	\( -\,2^{6}\cdot 7^{6}\cdot 13^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.9.17515230173.1	x^9 - 4x^8 - 3x^7 + 29x^6 - 26x^5 - 24x^4 + 34x^3 - 2x^2 - 5x + 1	\( 7^{6}\cdot 53^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.19573852375.2	x^9 + 7x^7 - 4x^6 + 14x^5 - 14x^4 + 10x^3 - 7x^2 + 1	\( -\,5^{3}\cdot 7^{6}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.22785532875.2	x^9 + 3x^7 + 9x^5 - 9x^4 + 8x^3 - 18x + 9	\( -\,3^{12}\cdot 5^{3}\cdot 7^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.24087491072.1	x^9 - 7x^7 - x^6 + 29x^5 + 30x^4 - 18x^3 - 35x^2 - 5x + 7	\( -\,2^{9}\cdot 19^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.24162633971.1	x^9 - 4x^8 + 11x^7 - 15x^6 + 12x^5 + 10x^4 - 24x^3 + 22x^2 - 13x + 1	\( -\,7^{6}\cdot 59^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.24162633971.2	x^9 + 10x^7 - 4x^6 + 24x^5 - 8x^4 - 3x^3 - 4x^2 - 4x + 1	\( -\,7^{6}\cdot 59^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.24162633971.3	x^9 + 7x^7 - 8x^6 + 21x^5 - 7x^4 - 9x^3 + 28x^2 - 28x + 8	\( -\,7^{6}\cdot 59^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.24162633971.4	x^9 - 2x^8 + 4x^7 - 6x^6 + 18x^5 + 2x^4 - 13x^3 - 7x^2 - 18x + 13	\( -\,7^{6}\cdot 59^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.27512614111.1	x^9 - 3x^8 + 4x^7 - 10x^6 + 5x^5 + 19x^4 - 49x^3 + 131x^2 - 153x + 47	\( -\,31^{7} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.29595664791.1	x^9 - x^8 + 5x^7 - x^6 - x^5 + 27x^4 - x^3 - 30x^2 + 8	\( -\,3^{3}\cdot 7^{7}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.31524548679.1	x^9 + 6x^7 - 3x^6 + 9x^5 - 3x^4 - 3x^3 - 3x - 1	\( -\,3^{15}\cdot 13^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.32127240704.1	x^9 - 2x^8 - x^7 - x^6 + 11x^5 - 2x^4 - 20x^3 + 19x^2 - 7x + 1	\( -\,2^{9}\cdot 13^{7} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.36992610368.1	x^9 - 2x^8 + x^6 - 15x^5 + 15x^4 - 15x^3 - 12x^2 + 39x - 41	\( -\,2^{6}\cdot 7^{6}\cdot 17^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.38883943647.2	x^9 - 6x^7 - 4x^6 - 9x^5 - 12x^4 - 31x^3 - 54x^2 - 36x - 8	\( -\,3^{13}\cdot 29^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.45270270144.5	x^9 + 3x^7 - 3x^6 + 9x^5 - 6x^4 + 2x^3 - 27x^2 - 15x - 1	\( -\,2^{6}\cdot 3^{12}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.45270270144.6	x^9 + 3x^7 - 5x^6 + 27x^5 - 12x^4 - 20x^3 + 9x^2 - 3x - 1	\( -\,2^{6}\cdot 3^{12}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.45270270144.7	x^9 - 3x^8 + 9x^7 - 12x^6 + 6x^5 + 21x^4 - 37x^3 + 33x^2 - 18x + 3	\( -\,2^{6}\cdot 3^{12}\cdot 11^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.49633171875.1	x^9 - 4x^7 - 3x^6 - 18x^5 + 8x^4 - 24x^3 + 18x^2 - 4x - 1	\( -\,3^{3}\cdot 5^{6}\cdot 7^{6} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.51645087424.1	x^9 + 7x^7 - 11x^6 + 35x^5 - 28x^4 + 24x^3 + 7x^2 - 7x + 1	\( -\,2^{6}\cdot 7^{6}\cdot 19^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.51645087424.2	x^9 - 10x^7 - 8x^6 + 24x^5 + 16x^4 - 52x^3 - 8x^2 + 16x + 8	\( -\,2^{6}\cdot 7^{6}\cdot 19^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.51645087424.3	x^9 - 3x^8 - 2x^7 + 8x^6 - 4x^5 + 22x^4 - 46x^3 + 56x^2 - 69x + 29	\( -\,2^{6}\cdot 7^{6}\cdot 19^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.55175798943.1	x^9 - 6x^7 - 9x^6 + 9x^5 + 9x^4 - x^3 + 27x - 27	\( -\,3^{12}\cdot 47^{3} \)	$S_3\times C_3$ (as 9T4)	Trivial
9.3.57207791296.1	x^9 - x^8 - 5x^7 + 2x^6 + 16x^5 - 7x^4 - 23x^3 + 23x^2 - 8x + 1	\( -\,2^{6}\cdot 19^{7} \)	$S_3\times C_3$ (as 9T4)	Trivial