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 18 matches)

Label	Polynomial	Discriminant	Galois group	Class group
14.12.404015475709296875.1	x^14 - 2x^13 - 11x^12 + 19x^11 + 49x^10 - 67x^9 - 111x^8 + 108x^7 + 131x^6 - 78x^5 - 74x^4 + 20x^3 + 16x^2 - x - 1	\( -\,5^{7}\cdot 549979\cdot 9402901 \)	14T61	Trivial
14.12.541778530793046875.1	x^14 - 2x^13 - 5x^12 + 8x^11 + 4x^10 + 15x^9 + 4x^8 - 110x^7 + 29x^6 + 163x^5 - 83x^4 - 68x^3 + 52x^2 - 6x - 1	\( -\,5^{7}\cdot 93739\cdot 73979509 \)	14T61	Trivial
14.12.6641971715742908416.1	x^14 - 9x^12 + 27x^10 - 24x^8 - 21x^6 + 41x^4 - 15x^2 + 1	\( -\,2^{14}\cdot 71^{2}\cdot 283583^{2} \)	14T57	Trivial
14.12.6641971715742908416.2	x^14 - 6x^12 + 4x^10 + 34x^8 - 74x^6 + 52x^4 - 13x^2 + 1	\( -\,2^{14}\cdot 71^{2}\cdot 283583^{2} \)	14T57	Trivial
14.12.8115190831314403328.1	x^14 - 8x^12 + 5x^10 + 88x^8 - 238x^6 + 200x^4 - 39x^2 + 2	\( -\,2^{15}\cdot 3967^{4} \)	14T51	Trivial
14.12.31262584108407674912.1	x^14 - 10x^12 + 28x^10 - x^8 - 84x^6 + 107x^4 - 50x^2 + 8	\( -\,2^{5}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.12.32289619843775952875.1	x^14 - 5x^13 - 5x^12 + 62x^11 - 57x^10 - 201x^9 + 352x^8 + 89x^7 - 402x^6 + 36x^5 + 165x^4 - 15x^3 - 23x^2 + x + 1	\( -\,5^{3}\cdot 7\cdot 577^{6} \)	14T38	Trivial
14.12.34135604022671835136.1	x^14 - 7x^13 + 6x^12 + 53x^11 - 98x^10 - 127x^9 + 309x^8 + 174x^7 - 406x^6 - 232x^5 + 238x^4 + 226x^3 - 48x^2 - 86x - 2	\( -\,2^{22}\cdot 19\cdot 809^{4} \)	14T51	Trivial
14.12.63287654893800867635.1	x^14 - 3x^13 - 13x^12 + 29x^11 + 71x^10 - 77x^9 - 196x^8 + 23x^7 + 220x^6 + 74x^5 - 96x^4 - 55x^3 + 11x^2 + 9x + 1	\( -\,5\cdot 7^{3}\cdot 577^{6} \)	14T38	Trivial
14.12.80696260103205425703.1	x^14 - 5x^13 - 2x^12 + 42x^11 - 27x^10 - 134x^9 + 128x^8 + 204x^7 - 213x^6 - 153x^5 + 151x^4 + 52x^3 - 41x^2 - 7x + 1	\( -\,3\cdot 17^{2}\cdot 93075271168633709 \)	14T63	Trivial
14.12.581373854406075416576.1	x^14 - 2x^13 - 18x^12 + 38x^11 + 102x^10 - 198x^9 - 316x^8 + 396x^7 + 842x^6 - 544x^5 - 1298x^4 + 602x^3 + 808x^2 - 256x - 146	\( -\,2^{16}\cdot 11\cdot 73^{8} \)	14T44	Trivial
14.12.1072914325448572889988.1	x^14 - 4x^13 - 7x^12 + 41x^11 + 10x^10 - 160x^9 + 24x^8 + 298x^7 - 70x^6 - 266x^5 + 47x^4 + 95x^3 - 6x^2 - 8x - 1	\( -\,2^{2}\cdot 3\cdot 89409527120714407499 \)	14T63	Trivial (GRH)
14.12.3382538789271711514624.1	x^14 - 13x^12 + 53x^10 - 45x^8 - 141x^6 + 217x^4 - 57x^2 + 1	\( -\,2^{22}\cdot 73^{8} \)	14T44	Trivial (GRH)
14.12.4001610765876182388736.1	x^14 - 19x^12 + 113x^10 - 213x^8 + 92x^6 + 91x^4 - 80x^2 + 16	\( -\,2^{12}\cdot 149^{4}\cdot 211^{4} \)	14T56	Trivial
14.12.98547323936652881051648.1	x^14 - 3x^12 - 50x^10 + 276x^8 - 516x^6 + 426x^4 - 152x^2 + 17	\( -\,2^{14}\cdot 17\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	Trivial
14.12.98547323936652881051648.2	x^14 - 14x^12 + 55x^10 - 48x^8 - 107x^6 + 198x^4 - 103x^2 + 17	\( -\,2^{14}\cdot 17\cdot 29^{12} \)	$C_2 \wr C_7$ (as 14T29)	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)