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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
18.2.894396879913401450496.2	x^18 - 3x^16 - 5x^14 + 22x^12 - 4x^10 - 41x^8 + 35x^6 + x^4 - 6x^2 - 1	\( 2^{30}\cdot 97^{6} \)	18T630	Trivial (GRH)
18.2.12539558025308224000000.1	x^18 + 8x^16 + 29x^14 + 61x^12 + 78x^10 + 59x^8 + 23x^6 + x^4 - 2x^2 - 1	\( 2^{12}\cdot 5^{6}\cdot 241^{6} \)	18T630	Trivial (GRH)
18.2.19679535995229561655296.1	x^18 - 8x^16 + 28x^14 - 54x^12 + 57x^10 - 24x^8 - 10x^6 + 13x^4 - x^2 - 1	\( 2^{12}\cdot 3^{6}\cdot 433^{6} \)	18T630	Trivial (GRH)
18.2.19679535995229561655296.2	x^18 + 4x^16 + 5x^14 + 25x^12 + 73x^10 + 56x^8 - 13x^6 - 7x^4 + 12x^2 - 1	\( 2^{12}\cdot 3^{6}\cdot 433^{6} \)	18T630	Trivial (GRH)
18.6.32461465929201970315264.2	x^18 + 4x^16 - 5x^12 + 4x^10 - 19x^8 + 16x^6 - 19x^4 + 11x^2 - 1	\( 2^{24}\cdot 353^{6} \)	18T630	Trivial (GRH)
18.6.90280878376185850466304.1	x^18 - 6x^16 + 15x^14 - 24x^12 + 27x^10 - 3x^8 - 12x^6 - 18x^4 + 18x^2 - 1	\( 2^{12}\cdot 3^{20}\cdot 43^{6} \)	18T630	Trivial (GRH)
18.6.30676715953012756474564249.2	x^18 - x^17 - 9x^16 + 17x^15 + 54x^14 - 125x^13 - 128x^12 + 519x^11 + 76x^10 - 1072x^9 + 243x^8 + 1196x^7 - 433x^6 - 686x^5 + 210x^4 + 92x^3 - 39x^2 + 27x - 1	\( 13^{6}\cdot 1361^{6} \)	18T630	Trivial (GRH)
18.10.81542670543816541216178176.1	x^18 - 5x^17 + 8x^16 + x^15 - 21x^14 + 7x^13 + 55x^12 - 31x^11 - 48x^10 + 70x^9 - 163x^8 - 20x^7 + 325x^6 - 19x^5 - 202x^4 + 11x^3 + 46x^2 - 6x - 1	\( 2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.14.81542670543816541216178176.1	x^18 - 16x^16 + 92x^14 - 217x^12 + 112x^10 + 273x^8 - 232x^6 - 103x^4 + 27x^2 - 1	\( 2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.6.81542670543816541216178176.2	x^18 + 10x^16 + 19x^14 - 81x^12 - 276x^10 + 12x^8 + 640x^6 + 416x^4 - 64x^2 - 64	\( 2^{18}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.10.928821981663160289790529536.1	x^18 - 2x^17 - 17x^16 + 39x^15 + 100x^14 - 242x^13 - 283x^12 + 690x^11 + 405x^10 - 1061x^9 - 280x^8 + 1042x^7 + 243x^6 - 592x^5 - 285x^4 + 61x^3 + 42x^2 - 16x - 8	\( 2^{12}\cdot 3^{6}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.10.1493196207631454487439212544.1	x^18 - 7x^16 - 6x^15 - 11x^14 + 38x^13 + 212x^12 - 66x^11 - 652x^10 + 302x^9 + 569x^8 - 960x^7 + 143x^6 + 356x^5 - 207x^4 + 346x^3 + 414x^2 + 122x + 11	\( 2^{24}\cdot 2113^{6} \)	18T630	Trivial (GRH)
18.10.1493196207631454487439212544.2	x^18 - 2x^17 - 16x^16 + 44x^15 + 58x^14 - 250x^13 - 79x^12 + 728x^11 + 105x^10 - 1356x^9 - 299x^8 + 1628x^7 + 445x^6 - 1110x^5 - 244x^4 + 376x^3 + 37x^2 - 44x + 5	\( 2^{24}\cdot 2113^{6} \)	18T630	Trivial (GRH)
18.14.1963309820992816414372111936.1	x^18 + x^16 - 64x^14 + 90x^12 + 924x^10 - 3178x^8 + 3763x^6 - 1817x^4 + 304x^2 - 1	\( 2^{6}\cdot 13^{6}\cdot 1361^{6} \)	18T630	Trivial (GRH)
18.10.5218730914804258637835403264.1	x^18 + 9x^16 - 21x^14 - 153x^12 + 253x^10 + 295x^8 - 342x^6 - 186x^4 + 81x^2 - 1	\( 2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.2.5218730914804258637835403264.1	x^18 + 22x^16 + 173x^14 + 545x^12 + 279x^10 - 1788x^8 - 3122x^6 - 1509x^4 - 91x^2 - 1	\( 2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T630	$[2]$ (GRH)
18.6.5218730914804258637835403264.1	x^18 + 7x^16 - 19x^14 - 184x^12 + 13x^10 + 1254x^8 + 623x^6 - 1748x^4 - 1586x^2 - 289	\( 2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.10.5218730914804258637835403264.2	x^18 + 8x^16 - 8x^14 - 143x^12 - 33x^10 + 605x^8 + 397x^6 - 210x^4 + 27x^2 - 1	\( 2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T630	Trivial (GRH)
18.2.5218730914804258637835403264.2	x^18 + 9x^16 - 30x^14 - 580x^12 - 2309x^10 - 3831x^8 - 2803x^6 - 817x^4 - 71x^2 - 1	\( 2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T630	$[2]$ (GRH)
18.6.5218730914804258637835403264.2	x^18 - 6x^16 - 56x^14 - 23x^12 + 342x^10 + 395x^8 - 236x^6 - 245x^4 - 35x^2 - 1	\( 2^{24}\cdot 19^{6}\cdot 137^{6} \)	18T630	$[2]$ (GRH)
18.18.8041717026786576033268170489856.2	x^18 - 28x^16 + 243x^14 - 1019x^12 + 2373x^10 - 3184x^8 + 2379x^6 - 863x^4 + 98x^2 - 1	\( 2^{18}\cdot 13^{6}\cdot 1361^{6} \)	18T630	Trivial (GRH)
18.18.120573559055637591568549157011456.1	x^18 - 38x^16 + 562x^14 - 4207x^12 + 17590x^10 - 42153x^8 + 56046x^6 - 36993x^4 + 9177x^2 - 361	\( 2^{30}\cdot 19^{8}\cdot 137^{6} \)	18T630	Trivial (GRH)