Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 41 matches)

Label	Polynomial	Discriminant	Galois group	Class group
9.1.173946175488.1	x^9 - 4x^8 + 8x^7 - 32x^5 + 80x^4 - 104x^3 + 80x^2 - 34x + 8	\( 2^{31}\cdot 3^{4} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.985223153873.1	x^9 - 4x^8 + 17x^6 - 17x^5 - 17x^4 + 34x^3 - 17x + 17	\( 7^{4}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.1680747204608.1	x^9 - 3x^8 + 3x^7 - 11x^6 + 13x^5 - 23x^4 + 14x^3 - 6x^2 + 4x - 4	\( 2^{12}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.33554432000000.1	x^9 - x^8 + 12x^7 - 28x^6 + 50x^5 - 82x^4 + 132x^3 - 84x^2 + 121x - 25	\( 2^{31}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.61334280470528.1	x^9 - 2x^8 + 40x^5 + 16x^4 + 8x^3 - 32x^2 - 98x + 100	\( 2^{31}\cdot 13^{4} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.121721421175625.1	x^9 - x^8 - 4x^7 + 9x^6 + 3x^5 - 39x^4 + 84x^3 - 129x^2 + 215x - 166	\( 5^{4}\cdot 41^{7} \)	$C_3^2:C_8$ (as 9T15)	$[3]$
9.1.218070794717793.1	x^9 - 9x^7 - 21x^6 + 72x^5 + 99x^4 - 99x^3 - 585x^2 + 549x + 166	\( 3^{12}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.218070794717793.2	x^9 - 3x^8 + 6x^7 - 12x^6 + 39x^5 - 33x^4 - 135x^3 + 240x^2 - 102x + 13	\( 3^{12}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.378956381627633.1	x^9 - 3x^8 + 12x^7 - 48x^6 + 122x^5 - 244x^4 + 435x^3 - 605x^2 + 503x - 189	\( 17^{7}\cdot 31^{4} \)	$C_3^2:C_8$ (as 9T15)	$[3]$
9.1.410338673000000.1	x^9 - 4x^8 + 5x^7 - 36x^6 + 139x^5 - 176x^4 + 315x^3 - 1064x^2 + 1496x - 720	\( 2^{6}\cdot 5^{6}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	$[3, 3]$
9.1.410338673000000.2	x^9 + 16x^7 - 3x^6 + 50x^5 - 200x^4 - 61x^3 - 242x^2 + 80x - 7	\( 2^{6}\cdot 5^{6}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	$[3, 3]$
9.1.949294310003793.1	x^9 - 2x^8 - 15x^7 + 31x^6 + 102x^5 - 212x^4 - 319x^3 + 489x^2 + 1318x - 1905	\( 3^{4}\cdot 13^{4}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	$[3]$
9.1.1141260857376768.1	x^9 + 12x^7 - 24x^6 + 18x^5 + 24x^4 - 60x^3 - 72x^2 - 33x - 8	\( 2^{31}\cdot 3^{12} \)	$C_3^2:C_8$ (as 9T15)	$[3, 3]$
9.1.1980626399884457.1	x^9 - x^8 + 6x^7 - 17x^6 + 49x^5 - 73x^4 - 19x^3 - 152x^2 + 304x - 635	\( 13^{6}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	$[3]$
9.1.6904624074435625.1	x^9 - 2x^8 + 2x^7 - 18x^6 + 108x^5 - 434x^4 + 1121x^3 - 1654x^2 + 1920x - 608	\( 5^{4}\cdot 73^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.8268784250602433.1	x^9 - 4x^8 - 9x^7 + 4x^6 + 203x^5 + 401x^4 - 134x^3 - 1999x^2 - 3564x - 2039	\( 17^{7}\cdot 67^{4} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.9.15056675074868288.1	x^9 - 26x^7 - 3x^6 + 236x^5 + 50x^4 - 889x^3 - 302x^2 + 1174x + 629	\( 2^{6}\cdot 113^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.51835034729971712.1	x^9 - 4x^7 - 40x^6 + 62x^5 + 424x^4 + 332x^3 - 56x^2 + x - 8	\( 2^{31}\cdot 17^{6} \)	$C_3^2:C_8$ (as 9T15)	$[3, 3]$ (GRH)
9.1.51835034729971712.2	x^9 - 3x^8 + 8x^7 + 56x^6 - 64x^5 + 384x^4 - 576x^3 + 2528x^2 - 5192x + 3864	\( 2^{31}\cdot 17^{6} \)	$C_3^2:C_8$ (as 9T15)	$[3, 3]$ (GRH)
9.9.57269713922998848.1	x^9 - 3x^8 - 23x^7 + 77x^6 + 78x^5 - 338x^4 - 12x^3 + 348x^2 - 16x - 76	\( 2^{6}\cdot 3^{4}\cdot 73^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.92442129447518208.1	x^9 - 3x^8 - 12x^7 + 36x^6 + 42x^5 - 174x^4 + 60x^3 - 84x^2 + 681x - 715	\( 2^{31}\cdot 3^{16} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.9.92442129447518208.1	x^9 - 36x^7 - 24x^6 + 378x^5 + 360x^4 - 1212x^3 - 1080x^2 + 801x + 136	\( 2^{31}\cdot 3^{16} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.92442129447518208.4	x^9 - 3x^8 + 48x^6 - 108x^5 + 36x^4 + 432x^3 - 720x^2 - 324x + 1164	\( 2^{31}\cdot 3^{16} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.136294246698620625.1	x^9 - 3x^8 - 12x^7 + 60x^6 - 9x^5 - 288x^4 + 54x^3 - 1197x^2 - 1701x - 2448	\( 3^{12}\cdot 5^{4}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.136294246698620625.2	x^9 - 3x^8 - 102x^6 + 612x^5 - 969x^4 + 102x^3 + 306x^2 - 459x - 816	\( 3^{12}\cdot 5^{4}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.9.523587978117420993.1	x^9 - 3x^8 - 60x^7 + 144x^6 + 1008x^5 - 1104x^4 - 5760x^3 - 2112x^2 + 1920x - 256	\( 3^{12}\cdot 7^{4}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.713288035860480000.1	x^9 - 3x^8 + 12x^7 - 84x^6 - 78x^5 + 138x^4 + 3972x^3 - 6012x^2 + 14265x - 49803	\( 2^{31}\cdot 3^{12}\cdot 5^{4} \)	$C_3^2:C_8$ (as 9T15)	$[2]$ (GRH)
9.1.713288035860480000.2	x^9 - 3x^8 + 12x^7 - 36x^6 + 90x^5 + 450x^4 + 804x^3 + 3828x^2 + 11319x - 4357	\( 2^{31}\cdot 3^{12}\cdot 5^{4} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.9.893217975164080128.1	x^9 - 3x^8 - 39x^7 + 63x^6 + 597x^5 - 99x^4 - 3570x^3 - 3330x^2 + 2604x + 2900	\( 2^{12}\cdot 3^{12}\cdot 17^{7} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.9.1905899642487308288.1	x^9 - 3x^8 - 56x^7 + 168x^6 + 896x^5 - 2640x^4 - 3512x^3 + 10344x^2 - 4434x - 698	\( 2^{31}\cdot 31^{6} \)	$C_3^2:C_8$ (as 9T15)	$[3]$ (GRH)
9.9.4423128914083118417.1	x^9 - 4x^8 - 27x^7 + 61x^6 + 168x^5 - 397x^4 - 177x^3 + 919x^2 - 713x + 170	\( 17^{7}\cdot 47^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial
9.1.17832200896512000000.1	x^9 - 12x^7 - 120x^6 + 114x^5 + 1800x^4 + 2652x^3 - 3000x^2 - 38769x - 127400	\( 2^{31}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.9.17832200896512000000.1	x^9 - 3x^8 - 48x^7 + 144x^6 + 744x^5 - 2232x^4 - 4152x^3 + 12696x^2 + 6366x - 20938	\( 2^{31}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.17832200896512000000.2	x^9 - 3x^8 - 12x^7 - 204x^6 - 1206x^5 - 4302x^4 - 11268x^3 - 27396x^2 - 41769x - 40293	\( 2^{31}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.17832200896512000000.3	x^9 - 3x^8 - 12x^7 + 84x^6 + 450x^5 - 486x^4 + 4668x^3 + 5052x^2 + 3081x + 32965	\( 2^{31}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.17832200896512000000.4	x^9 - 3x^8 + 96x^6 + 216x^5 - 3192x^4 + 21720x^3 - 20376x^2 - 175266x + 378966	\( 2^{31}\cdot 3^{12}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.57776330904698880000.1	x^9 - 3x^8 + 48x^6 - 108x^5 + 36x^4 + 432x^3 - 144x^2 - 324x + 1164	\( 2^{31}\cdot 3^{16}\cdot 5^{4} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.57776330904698880000.2	x^9 + 72x^7 - 96x^6 + 1188x^5 - 5472x^4 - 9456x^3 + 31968x^2 + 18594x + 2656	\( 2^{31}\cdot 3^{16}\cdot 5^{4} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)
9.1.1444408272617472000000.1	x^9 - 3x^8 - 48x^7 + 96x^6 + 1392x^5 - 912x^4 - 4992x^3 - 5376x^2 + 61728x - 61792	\( 2^{31}\cdot 3^{16}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	$[2]$ (GRH)
9.1.1444408272617472000000.3	x^9 - 72x^7 - 192x^6 + 4752x^5 + 5040x^4 - 113928x^3 - 172368x^2 + 1513998x + 469664	\( 2^{31}\cdot 3^{16}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	$[3, 3]$ (GRH)
9.1.1444408272617472000000.4	x^9 - 3x^8 + 12x^7 + 348x^6 + 1146x^5 - 12702x^4 + 136548x^3 - 158988x^2 + 117849x + 3432229	\( 2^{31}\cdot 3^{16}\cdot 5^{6} \)	$C_3^2:C_8$ (as 9T15)	Trivial (GRH)