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 142)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.493455671296.1	x^9 - 2x^8 + 8x^7 - 8x^6 + 20x^5 - 8x^4 + 4x^3 - 24x^2 + 23x - 6	\( 2^{22}\cdot 7^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.672605015625.1	x^9 - 3x^8 + 9x^6 - 9x^5 - 27x^4 + 72x^3 - 81x^2 + 45x - 12	\( 3^{16}\cdot 5^{6} \)	$C_3^2:C_4$ (as 9T9)	Trivial
9.1.2125764000000.5	x^9 - 3x^8 + 3x^7 - 15x^6 + 33x^5 - 3x^4 + 24x^3 + 6x^2 - 4	\( 2^{8}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_4$ (as 9T9)	Trivial
9.1.2229025112064.1	x^9 - 3x^8 + 6x^7 - 18x^6 + 45x^5 - 63x^4 + 72x^3 - 72x^2 + 54x - 18	\( 2^{22}\cdot 3^{12} \)	$C_3^2:C_4$ (as 9T9)	Trivial
9.1.2565164201769.3	x^9 - 3x^8 + 12x^6 - 9x^5 - 27x^4 + 27x^3 + 54x^2 - 27	\( 3^{12}\cdot 13^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.3709075402816.1	x^9 - 2x^8 + 4x^7 - 5x^6 - 2x^5 - 20x^4 + 75x^3 - 36x^2 + 8x - 1	\( 2^{6}\cdot 7^{4}\cdot 17^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.5345344000000.1	x^9 - 4x^8 + x^7 + 16x^6 - 14x^5 - 30x^4 + 15x^3 + 40x^2 + 5x - 50	\( 2^{12}\cdot 5^{6}\cdot 17^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.6175846265625.1	x^9 - 2x^8 + 2x^7 - 2x^6 - 23x^5 + 34x^4 + 60x^2 + 15x + 20	\( 3^{4}\cdot 5^{6}\cdot 47^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.9294114390625.1	x^9 - 4x^8 + 12x^7 - 6x^6 + 19x^5 - 11x^4 + 12x^3 - 21x^2 + 5x + 3	\( 5^{6}\cdot 29^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.9294114390625.2	x^9 - x^8 + 6x^7 - 6x^6 + 11x^5 + 5x^4 - 15x^3 + 50x^2 - 100x + 125	\( 5^{6}\cdot 29^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.9703274840064.1	x^9 - x^8 + 2x^7 - 10x^6 - 11x^5 + 83x^4 - 96x^3 + 24x^2 + 6x + 10	\( 2^{22}\cdot 3^{4}\cdot 13^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.10942526586601.1	x^9 + 2x^7 - 3x^6 + x^5 - x^4 + 64x^3 - x - 1	\( 149^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.12827693806929.1	x^9 - 3x^7 - 15x^6 - 9x^5 - 6x^4 + 102x^3 + 153x^2 + 153x - 85	\( 3^{12}\cdot 17^{6} \)	$C_3^2:C_4$ (as 9T9)	Trivial
9.1.13675204000000.7	x^9 - x^8 - 2x^7 - 10x^6 - 9x^5 + 35x^4 + 42x^3 + 148x^2 + 61x + 105	\( 2^{8}\cdot 5^{6}\cdot 43^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.13867245015625.1	x^9 - x^8 - 5x^7 - 13x^6 + 31x^5 + 11x^4 + 33x^3 - 3x^2 + 5x + 1	\( 5^{6}\cdot 31^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.17909824000000.1	x^9 - x^8 + x^7 + 29x^6 - 29x^5 - 83x^4 + 98x^3 + 42x^2 + 28x + 12	\( 2^{12}\cdot 5^{6}\cdot 23^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.19937341265625.2	x^9 - 3x^8 + 9x^7 - 42x^6 + 81x^5 - 108x^4 + 294x^3 - 492x^2 + 351x - 88	\( 3^{12}\cdot 5^{6}\cdot 7^{4} \)	$C_3^2:C_4$ (as 9T9)	Trivial
9.1.34012224000000.9	x^9 - 3x^8 + 6x^7 - 18x^6 - 9x^5 + 87x^4 - 54x^3 - 18x^2 + 36x + 12	\( 2^{12}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_4$ (as 9T9)	Trivial
9.1.38380503040000.1	x^9 - x^8 + 8x^7 + 8x^6 + 2x^5 + 46x^4 - 168x^3 + 472x^2 - 807x + 791	\( 2^{22}\cdot 5^{4}\cdot 11^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.49680238593241.1	x^9 + 2x^7 - 15x^6 + x^5 - 5x^4 - 16x^3 - 25x - 125	\( 17^{4}\cdot 29^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.69980368892329.1	x^9 - x^8 + 3x^7 - x^6 - 41x^5 - 119x^4 - 213x^3 - 265x^2 - 225x - 125	\( 7^{6}\cdot 29^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.72964670628096.1	x^9 - 9x^7 - 12x^6 + 33x^5 + 144x^4 - 192x^3 - 360x^2 + 684x - 288	\( 2^{8}\cdot 3^{10}\cdot 13^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.78205723560000.2	x^9 - 2x^8 - 2x^7 - 28x^6 - 48x^5 - 76x^4 + 12x^3 - 16x^2 - 32x - 64	\( 2^{6}\cdot 3^{4}\cdot 5^{4}\cdot 17^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.86790185015625.1	x^9 - 3x^8 + 3x^7 - 3x^6 + 23x^5 - 117x^4 + 195x^3 - 195x^2 + 55x - 15	\( 3^{4}\cdot 5^{6}\cdot 7^{4}\cdot 13^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.90785223184384.1	x^9 - 16x^6 - 31x^5 - 40x^4 - 40x^3 - 12x^2 + 9x - 8	\( 2^{12}\cdot 53^{6} \)	$C_3^2:C_4$ (as 9T9)	$[6]$
9.1.101646724000000.1	x^9 - x^8 - 10x^7 + 42x^6 - 69x^5 + 31x^4 + 38x^3 - 8x^2 - 95x + 81	\( 2^{8}\cdot 5^{6}\cdot 71^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.113379904000000.1	x^9 - 2x^8 - 10x^7 + 16x^6 + 51x^5 - 118x^4 - 158x^3 + 76x^2 - 135x - 478	\( 2^{12}\cdot 5^{6}\cdot 11^{6} \)	$C_3^2:C_4$ (as 9T9)	$[9]$
9.1.116507435287321.1	x^9 - x^8 + 5x^7 - 5x^6 + 13x^5 - 20x^4 + 16x^3 + 8x^2 - 16x + 64	\( 13^{6}\cdot 17^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.119110855819264.1	x^9 - 4x^8 + 10x^7 + 4x^6 - 17x^5 + 180x^3 - 128x^2 - 82x + 64	\( 2^{22}\cdot 73^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.121575432515625.1	x^9 - 3x^8 + 6x^7 + 42x^6 - 39x^5 - 78x^4 + 96x^3 - 93x^2 - 99x + 242	\( 3^{12}\cdot 5^{6}\cdot 11^{4} \)	$C_3^2:C_4$ (as 9T9)	Trivial (GRH)
9.1.147442540478464.1	x^9 - 4x^8 + 8x^7 + 16x^6 - 68x^5 + 64x^4 + 304x^3 - 1056x^2 + 1540x - 1008	\( 2^{22}\cdot 7^{4}\cdot 11^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$ (GRH)
9.1.180551034077184.1	x^9 - 3x^8 - 6x^7 + 18x^6 + 3x^5 + 15x^4 + 24x^3 - 264x^2 + 120x + 184	\( 2^{22}\cdot 3^{16} \)	$C_3^2:C_4$ (as 9T9)	Trivial (GRH)
9.1.301855146292441.1	x^9 - x^8 + 10x^7 + 8x^6 + 44x^5 + 10x^4 + 197x^3 + 19x^2 + 153x - 99	\( 7^{6}\cdot 37^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.315635197515625.1	x^9 - 4x^8 + 16x^7 - 44x^6 + x^5 - 22x^4 + 53x^3 - 17x^2 - 27x - 52	\( 5^{6}\cdot 13^{4}\cdot 29^{4} \)	$C_3^2:C_4$ (as 9T9)	$[9]$
9.1.365611723192576.1	x^9 - x^8 - 3x^7 + 23x^6 - 101x^5 + 235x^4 - 284x^3 + 394x^2 - 112x + 196	\( 2^{8}\cdot 7^{4}\cdot 29^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.372726462515625.1	x^9 - 3x^8 - 2x^7 + 2x^6 + 123x^5 - 467x^4 + 675x^3 - 690x^2 + 380x - 115	\( 3^{4}\cdot 5^{6}\cdot 131^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.390971529000000.3	x^9 - 3x^8 + 22x^7 - 30x^6 + 116x^5 + 20x^4 + 198x^3 + 186x^2 + 351x - 45	\( 2^{6}\cdot 3^{4}\cdot 5^{6}\cdot 13^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.432299612577856.1	x^9 - 3x^8 + 20x^7 - 43x^6 + 108x^5 - 139x^4 + 277x^3 - 218x^2 + 62x - 6	\( 2^{6}\cdot 17^{6}\cdot 23^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.472459130015625.1	x^9 - 3x^8 + 3x^7 - 15x^6 - 22x^5 - 53x^4 - x^3 - 394x^2 + 275x - 764	\( 3^{4}\cdot 5^{6}\cdot 139^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$ (GRH)
9.1.549251955015625.1	x^9 - 2x^8 + 18x^7 - 17x^6 + 103x^5 - 123x^4 - 150x^3 - 20x^2 + 125x + 425	\( 5^{6}\cdot 433^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$ (GRH)
9.1.613376203543489.1	x^9 - 3x^8 + 8x^7 - 44x^6 + 78x^5 - 86x^4 + 103x^3 - 67x^2 - 202x - 1092	\( 17^{6}\cdot 71^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$ (GRH)
9.1.632711491215049.1	x^9 - 3x^8 + 16x^7 - 45x^6 - 43x^5 - 17x^4 + 1465x^2 + 2637x + 1172	\( 293^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.659070838140625.1	x^9 - 3x^8 + 7x^7 - 18x^6 + 47x^5 + x^4 - 10x^3 - 220x^2 - 200x - 145	\( 5^{6}\cdot 59^{6} \)	$C_3^2:C_4$ (as 9T9)	$[9]$
9.1.681343481938249.1	x^9 - 2x^8 - 12x^7 - 14x^6 - 63x^5 - 180x^4 - 171x^3 - 51x^2 - 21x - 20	\( 13^{6}\cdot 109^{4} \)	$C_3^2:C_4$ (as 9T9)	$[9]$
9.1.684328805383041.4	x^9 + 18x^7 - 21x^6 + 81x^5 - 63x^4 + 714x^3 - 441x - 343	\( 3^{10}\cdot 7^{4}\cdot 13^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$
9.1.714540961348201.1	x^9 - 5x^7 - 25x^6 + 16x^5 + 114x^4 - 51x^3 - 325x^2 - 636x - 623	\( 13^{6}\cdot 23^{6} \)	$C_3^2:C_4$ (as 9T9)	$[9]$
9.1.729920018089024.1	x^9 - 4x^8 + 8x^7 - 9x^6 - 4x^5 + 12x^4 - 13x^3 - 20x^2 + 100x - 125	\( 2^{6}\cdot 7^{4}\cdot 41^{6} \)	$C_3^2:C_4$ (as 9T9)	$[9]$
9.1.784516629082176.2	x^9 - 2x^8 - 2x^7 + 15x^6 - 24x^5 + 144x^4 - 261x^3 + 378x^2 - 486x + 729	\( 2^{6}\cdot 3^{4}\cdot 73^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$ (GRH)
9.1.790586776890625.1	x^9 - 2x^8 - 4x^7 - 38x^6 + 89x^5 - 29x^4 + 50x^3 - 165x^2 + 55x - 55	\( 5^{6}\cdot 11^{6}\cdot 13^{4} \)	$C_3^2:C_4$ (as 9T9)	$[3]$ (GRH)
9.1.805005849390625.2	x^9 + 17x^7 - 7x^6 + 76x^5 - 59x^4 + 187x^3 - 35x^2 + 79x - 24	\( 5^{6}\cdot 61^{6} \)	$C_3^2:C_4$ (as 9T9)	$[3]$