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 24 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.2.312145214074303896.1	x^14 - 6x^13 + 15x^12 - 21x^11 + 5x^10 + 23x^9 - 34x^8 - 3x^7 + 36x^6 - 23x^5 - 21x^4 + 24x^3 + 9x^2 - 16x - 6	\( 2^{3}\cdot 3^{3}\cdot 11^{6}\cdot 13^{8} \)	14T48	Trivial
14.0.936435642222911688.1	x^14 - 4x^13 + 8x^12 - 14x^11 + 29x^10 - 52x^9 + 83x^8 - 97x^7 + 124x^6 - 108x^5 + 108x^4 - 56x^3 + 54x^2 - 13x + 11	\( -\,2^{3}\cdot 3^{4}\cdot 11^{6}\cdot 13^{8} \)	14T48	Trivial
14.0.2844673747342852096.1	x^14 - 7x^12 + 7x^10 + 35x^8 - 49x^6 - 49x^4 + 49x^2 + 49	\( -\,2^{22}\cdot 7^{14} \)	14T48	Trivial
14.2.10300792064452028568.1	x^14 - 3x^13 - 4x^12 + 13x^11 + 21x^10 - 39x^9 - 53x^8 + 47x^7 + 95x^6 - 25x^5 - 71x^4 - 22x^3 + 26x^2 + 7x + 1	\( 2^{3}\cdot 3^{4}\cdot 11^{7}\cdot 13^{8} \)	14T48	Trivial
14.4.463641384052739997867.1	x^14 - 9x^12 - 6x^11 + 36x^10 + 32x^9 - 34x^8 - 54x^7 - 116x^6 - 143x^5 + 192x^4 + 289x^3 + 125x^2 - 24x - 21	\( -\,3\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.8.618188512070319997156.1	x^14 - 6x^12 - 25x^10 + 196x^8 - 313x^6 + 17x^4 + 173x^2 + 4	\( -\,2^{2}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.10.772735640087899996445.1	x^14 - 7x^13 + 6x^12 + 55x^11 - 168x^10 + 169x^9 + 182x^8 - 851x^7 + 1059x^6 - 394x^5 - 318x^4 + 416x^3 - 185x^2 + 35x - 2	\( 5\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.8.1081829896123059995023.1	x^14 - 19x^12 + 87x^10 - 68x^8 - 213x^6 + 142x^4 + 153x^2 + 28	\( -\,7^{9}\cdot 173^{6} \)	14T48	Trivial
14.8.1236377024140639994312.1	x^14 - 11x^12 - 5x^11 + 16x^10 + 106x^9 + 98x^8 - 326x^7 - 1116x^6 + 1552x^5 + 1784x^4 - 3304x^3 + 885x^2 + 579x - 127	\( -\,2^{3}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.6.1236377024140639994312.1	x^14 - x^13 - 13x^12 + 23x^11 - 65x^9 + 139x^8 - 172x^7 + 139x^6 - 65x^5 + 23x^3 - 13x^2 - x + 1	\( 2^{3}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.4.1700018408193379992179.1	x^14 - 7x^13 + 28x^12 - 77x^11 + 136x^10 - 141x^9 + 5x^8 + 265x^7 - 464x^6 + 419x^5 - 140x^4 - 99x^3 + 153x^2 - 79x + 18	\( -\,7^{8}\cdot 11\cdot 173^{6} \)	14T48	Trivial
14.10.1854565536210959991468.1	x^14 - 13x^12 + 45x^10 - 49x^8 - 5x^6 + 24x^4 - 2x^2 - 3	\( 2^{2}\cdot 3\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.6.2627301176298859987913.1	x^14 - x^13 - 6x^12 + 27x^11 + 14x^10 - 164x^9 - 5x^8 + 350x^7 - 449x^6 - 869x^5 + 1045x^4 + 1677x^3 + 77x^2 - 222x - 20	\( 7^{8}\cdot 17\cdot 173^{6} \)	14T48	Trivial
14.8.2936395432334019986491.1	x^14 - 9x^12 - 12x^11 + 10x^10 + 203x^9 - 52x^8 - 740x^7 + 268x^6 + 840x^5 - 361x^4 - 279x^3 + 136x^2 + 21x - 10	\( -\,7^{8}\cdot 19\cdot 173^{6} \)	14T48	Trivial
14.6.3245489688369179985069.1	x^14 - x^13 - 21x^12 - 12x^11 + 82x^10 + 11x^9 - 208x^8 + 80x^7 + 293x^6 - 245x^5 - 135x^4 + 305x^3 - 55x^2 - 90x + 96	\( 3\cdot 7^{9}\cdot 173^{6} \)	14T48	Trivial
14.6.3709131072421919982936.1	x^14 - 16x^12 - 8x^11 + 76x^10 + 118x^9 - 166x^8 - 954x^7 + 565x^6 + 3537x^5 - 3007x^4 - 5201x^3 + 5678x^2 + 1212x - 1089	\( 2^{3}\cdot 3\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial
14.2.108337536740323579501589.1	x^14 - 14x^12 - 2x^11 + 63x^10 - 76x^9 - 315x^8 + 113x^7 - 435x^6 - 2835x^5 - 3410x^4 - 1550x^3 - 507x^2 - 847x - 680	\( 7^{8}\cdot 173^{6}\cdot 701 \)	14T48	Trivial
14.2.108337536740323579501589.2	x^14 + 2x^12 - 12x^11 + 5x^10 - 13x^9 + 17x^8 + 301x^7 + 704x^6 - 845x^5 - 1336x^4 + 2572x^3 - 1061x^2 + 474x - 108	\( 7^{8}\cdot 173^{6}\cdot 701 \)	14T48	Trivial
14.12.633025036360007677087744.1	x^14 - 24x^12 + 194x^10 - 607x^8 + 531x^6 + 127x^4 - 55x^2 + 1	\( -\,2^{12}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial (GRH)
14.12.633025036360007677087744.2	x^14 - 13x^12 + 52x^10 - 49x^8 - 89x^6 + 164x^4 - 65x^2 + 4	\( -\,2^{12}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial (GRH)
14.0.1899075109080023031263232.1	x^14 + 26x^12 + 256x^10 + 1188x^8 + 2658x^6 + 2741x^4 + 1081x^2 + 48	\( -\,2^{12}\cdot 3\cdot 7^{8}\cdot 173^{6} \)	14T48	$[30]$ (GRH)
14.14.3165125181800038385438720.1	x^14 - 20x^12 + 144x^10 - 504x^8 + 936x^6 - 921x^4 + 441x^2 - 80	\( 2^{12}\cdot 5\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial (GRH)
14.0.4431175254520053739614208.1	x^14 + 33x^12 + 357x^10 + 1717x^8 + 3843x^6 + 3555x^4 + 727x^2 + 7	\( -\,2^{12}\cdot 7^{9}\cdot 173^{6} \)	14T48	$[216]$ (GRH)
14.14.5064200290880061416701952.1	x^14 - 27x^12 + 269x^10 - 1286x^8 + 3086x^6 - 3405x^4 + 1265x^2 - 128	\( 2^{15}\cdot 7^{8}\cdot 173^{6} \)	14T48	Trivial (GRH)