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 all 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.0.22367896927548830134272.2	x^18 - 6x^16 + 25x^14 - 61x^12 + 127x^10 - 170x^8 + 190x^6 - 114x^4 + 45x^2 + 27	\( -\,2^{12}\cdot 3^{9}\cdot 23^{6}\cdot 37^{4} \)	18T775	$[2]$ (GRH)
18.0.22367896927548830134272.3	x^18 + 7x^16 + 26x^14 + 70x^12 + 141x^10 + 216x^8 + 252x^6 + 207x^4 + 108x^2 + 27	\( -\,2^{12}\cdot 3^{9}\cdot 23^{6}\cdot 37^{4} \)	18T775	Trivial (GRH)
18.4.107829099905166366916608.1	x^18 - x^17 + 5x^16 - 12x^15 + 15x^14 - 53x^13 + 72x^12 - 75x^11 + 35x^10 + 56x^9 - 115x^8 + 199x^7 - 139x^6 + 118x^5 - 36x^4 + 24x^3 - 4x^2 + 4x - 2	\( -\,2^{14}\cdot 3^{9}\cdot 19^{4}\cdot 37^{6} \)	18T775	Trivial (GRH)
18.2.534944674718859596398592.1	x^18 - 2x^16 - 19x^14 + 46x^12 + 25x^10 - 36x^8 - 33x^6 - 14x^4 - 10x^2 - 2	\( 2^{33}\cdot 7^{4}\cdot 11^{10} \)	18T775	Trivial (GRH)
18.2.666838663861214566678528.2	x^18 - 4x^17 + 8x^16 - 6x^15 - 2x^14 + 18x^13 - 78x^12 + 176x^11 - 96x^10 - 316x^9 + 556x^8 + 168x^7 - 1640x^6 + 2632x^5 - 2424x^4 + 1472x^3 - 592x^2 + 144x - 16	\( 2^{32}\cdot 11^{4}\cdot 13^{9} \)	18T775	Trivial
18.6.2667354655444858266714112.1	x^18 - 4x^14 - 8x^12 - 72x^10 - 48x^8 + 340x^6 + 320x^4 - 208x^2 - 208	\( 2^{34}\cdot 11^{4}\cdot 13^{9} \)	18T775	Trivial (GRH)
18.4.4613211198083752632778752.1	x^18 - 6x^14 - 10x^13 - 20x^12 + 6x^11 - 24x^10 + 24x^9 - 122x^8 + 172x^7 - 152x^6 + 240x^5 - 204x^4 + 156x^3 - 66x^2 + 84x - 6	\( -\,2^{28}\cdot 3^{13}\cdot 47^{6} \)	18T775	Trivial (GRH)
18.0.162139825386335748213114048.1	x^18 - 3x^17 + 12x^16 - 14x^15 + 39x^14 - 9x^13 + 28x^12 + 54x^11 + 72x^10 + 32x^9 + 72x^8 + 54x^7 + 28x^6 - 9x^5 + 39x^4 - 14x^3 + 12x^2 - 3x + 1	\( -\,2^{6}\cdot 3^{15}\cdot 7^{6}\cdot 107^{6} \)	18T775	$[2]$ (GRH)
18.6.170710697948470929069703168.1	x^18 - x^16 + 6x^14 + 42x^12 - 56x^10 - 184x^8 + 120x^6 + 84x^4 + 65x^2 - 13	\( 2^{40}\cdot 11^{4}\cdot 13^{9} \)	18T775	Trivial (GRH)
18.0.211774465810724242564067328.1	x^18 - 12x^16 + 48x^14 - 32x^12 - 291x^10 + 849x^8 - 792x^6 - 9x^4 + 270x^2 + 27	\( -\,2^{12}\cdot 3^{15}\cdot 7^{4}\cdot 107^{6} \)	18T775	$[2]$ (GRH)
18.10.42617365285248096686111328125.1	x^18 - 9x^17 + 39x^16 - 108x^15 + 101x^14 + 469x^13 - 1499x^12 + 635x^11 + 3091x^10 - 4521x^9 - 74x^8 + 5339x^7 - 4614x^6 - 224x^5 + 2755x^4 - 1833x^3 + 411x^2 + 41x - 25	\( 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.10.504577458849157680066569739857.1	x^18 - 34x^16 - 3x^15 + 272x^14 + 153x^13 - 305x^12 - 119x^11 - 68x^10 + 631x^9 - 68x^8 - 119x^7 - 305x^6 + 153x^5 + 272x^4 - 3x^3 - 34x^2 + 1	\( 17^{9}\cdot 41^{6}\cdot 173^{4} \)	18T775	$[2]$ (GRH)
18.6.1065434132131202417152783203125.1	x^18 - 4x^17 + 8x^16 + 11x^15 - 111x^14 - 37x^13 + 302x^12 + 462x^11 + 1552x^10 - 434x^9 - 7651x^8 - 7930x^7 - 9515x^6 + 2604x^5 + 13021x^4 + 105x^3 + 4750x^2 - 8300x + 2305	\( 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.6.2088250898977156737619455078125.1	x^18 - 6x^17 + 2x^16 - 2x^15 + 175x^14 - 143x^13 - 558x^12 - 398x^11 + 1013x^10 + 2352x^9 + 492x^8 - 2052x^7 - 2339x^6 + 419x^5 + 1098x^4 - 55x^3 - 814x^2 - 340x + 280	\( 5^{9}\cdot 7^{2}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2]$ (GRH)
18.14.2727511378255878187911125000000.1	x^18 - 2x^17 - 35x^16 + 48x^15 + 390x^14 - 529x^13 - 1849x^12 + 3006x^11 + 3478x^10 - 8101x^9 + 1738x^8 + 9833x^7 - 15945x^6 - 4878x^5 + 20348x^4 + 2400x^3 - 8144x^2 - 1984x - 64	\( 2^{6}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.2.2727511378255878187911125000000.1	x^18 + 10x^16 - 57x^14 - 1283x^12 - 7729x^10 - 22982x^8 - 36084x^6 - 27740x^4 - 7875x^2 - 125	\( 2^{6}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2, 2]$ (GRH)
18.6.2727511378255878187911125000000.1	x^18 - 4x^17 + 2x^16 + 20x^15 - 82x^14 + 90x^13 + 63x^12 - 520x^11 + 756x^10 - 461x^9 - 908x^8 + 509x^7 + 860x^6 - 2807x^5 - 90x^4 + 4668x^3 + 2572x^2 + 239x + 5	\( 2^{6}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.14.2727511378255878187911125000000.2	x^18 - 18x^16 + 95x^14 - 40x^12 - 846x^10 + 1351x^8 + 1072x^6 - 1498x^4 + 199x^2 - 5	\( 2^{6}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2]$ (GRH)
18.14.2727511378255878187911125000000.3	x^18 - 4x^17 - 31x^16 + 131x^15 + 253x^14 - 1266x^13 - 539x^12 + 4982x^11 - 610x^10 - 8537x^9 + 1698x^8 + 6938x^7 + 578x^6 - 3085x^5 - 1308x^4 + 295x^3 + 310x^2 + 70x + 5	\( 2^{6}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.10.68187784456396954697778125000000.1	x^18 - 4x^17 - 9x^16 + 102x^15 - 243x^14 - 492x^13 + 2904x^12 - 3320x^11 - 8983x^10 + 27434x^9 - 5389x^8 - 40470x^7 + 66140x^6 - 56554x^5 - 70720x^4 + 137400x^3 - 25425x^2 - 66850x + 6125	\( 2^{6}\cdot 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.14.68187784456396954697778125000000.1	x^18 - 37x^16 + 500x^14 - 3159x^12 + 10030x^10 - 15925x^8 + 10800x^6 - 625x^4 - 1375x^2 - 125	\( 2^{6}\cdot 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.2.68187784456396954697778125000000.1	x^18 - 7x^17 + 17x^16 - 3x^15 - 51x^14 + 44x^13 + 219x^12 - 2249x^11 + 4504x^10 + 3348x^9 - 18636x^8 + 28161x^7 + 36603x^6 - 144289x^5 + 24874x^4 + 92771x^3 - 138990x^2 + 172369x - 78971	\( 2^{6}\cdot 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2, 4]$ (GRH)
18.6.68187784456396954697778125000000.1	x^18 - 8x^17 + 30x^16 - 69x^15 + 146x^14 - 571x^13 + 1542x^12 - 2361x^11 + 1030x^10 + 17642x^9 - 37902x^8 - 55615x^7 + 183579x^6 - 32886x^5 - 140959x^4 - 48530x^3 + 137535x^2 - 15550x + 425	\( 2^{6}\cdot 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2]$ (GRH)
18.10.68187784456396954697778125000000.2	x^18 - 10x^16 - 29x^14 + 585x^12 - 1836x^10 + 805x^8 + 2665x^6 - 625x^4 - 800x^2 - 125	\( 2^{6}\cdot 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2]$ (GRH)
18.10.174560728208376204026312000000000.1	x^18 - 54x^14 - 20x^12 + 511x^10 - 365x^8 - 164x^6 + 115x^4 + 6x^2 - 5	\( 2^{12}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2]$ (GRH)
18.6.174560728208376204026312000000000.1	x^18 + 7x^16 - 89x^14 - 814x^12 - 1150x^10 + 2019x^8 + 3864x^6 + 242x^4 - 650x^2 - 125	\( 2^{12}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.10.174560728208376204026312000000000.2	x^18 - 8x^16 - 311x^14 - 945x^12 + 4219x^10 + 11554x^8 - 4280x^6 - 1784x^4 + 199x^2 - 5	\( 2^{12}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	$[2]$ (GRH)
18.6.174560728208376204026312000000000.2	x^18 + 13x^16 - 113x^14 - 2057x^12 - 5590x^10 + 25747x^8 + 138159x^6 + 158755x^4 + 9965x^2 - 6125	\( 2^{12}\cdot 5^{9}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.18.4364018205209405100657800000000000.1	x^18 - 47x^16 + 838x^14 - 7474x^12 + 36280x^10 - 96835x^8 + 136975x^6 - 94275x^4 + 28750x^2 - 3125	\( 2^{12}\cdot 5^{11}\cdot 139^{4}\cdot 197^{6} \)	18T775	Trivial (GRH)
18.18.37287761096756969806266368000000000.1	x^18 - 53x^16 + 992x^14 - 7932x^12 + 28146x^10 - 49334x^8 + 44136x^6 - 19420x^4 + 3525x^2 - 125	\( 2^{24}\cdot 5^{9}\cdot 53^{4}\cdot 229^{6} \)	18T775	$[2]$ (GRH)