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 matches 1-50 of 1563)

Label	Polynomial	Discriminant	Galois group	Class group
14.0.9095120158391.1	x^14 - 7x^13 + 25x^12 - 59x^11 + 103x^10 - 141x^9 + 159x^8 - 153x^7 + 129x^6 - 95x^5 + 58x^4 - 27x^3 + 10x^2 - 3x + 1	\( -\,71^{7} \)	$D_{7}$ (as 14T2)	Trivial
14.0.9669040949311.1	x^14 - x^13 + 3x^12 - 6x^11 + 5x^10 - 9x^9 + 11x^8 - 7x^7 + 11x^6 - 9x^5 + 5x^4 - 6x^3 + 3x^2 - x + 1	\( -\,19^{2}\cdot 79\cdot 18413^{2} \)	14T57	Trivial
14.0.9866941650479.1	x^14 - 3x^13 + 6x^12 - 11x^11 + 16x^10 - 21x^9 + 25x^8 - 25x^7 + 25x^6 - 21x^5 + 16x^4 - 11x^3 + 6x^2 - 3x + 1	\( -\,167^{2}\cdot 191\cdot 1361^{2} \)	14T57	Trivial
14.0.11856232199187.1	x^14 - x^13 + x^12 - x^10 - x^9 + x^8 - x^7 - x^6 + 3x^5 - 2x^4 + x^3 + x^2 - x + 1	\( -\,3^{7}\cdot 5421231001 \)	14T61	Trivial
14.0.12985240103739.1	x^14 - x^13 + x^12 - 4x^11 + 4x^10 - 2x^9 + 5x^8 - 6x^7 + 2x^6 - 2x^5 + 5x^4 - 2x^3 - x + 1	\( -\,3^{7}\cdot 5937466897 \)	14T61	Trivial
14.0.13048447346663.1	x^14 - x^13 + 2x^12 - 2x^11 + 2x^10 - 2x^9 + x^8 - x^7 + x^6 - 2x^5 + 2x^4 - 2x^3 + 2x^2 - x + 1	\( -\,23\cdot 37^{2}\cdot 20357^{2} \)	14T57	Trivial
14.0.16973485041483.1	x^14 - 2x^13 + 2x^12 - 6x^11 + 8x^10 - 4x^9 + 9x^8 - 11x^7 + 6x^6 - 6x^5 + 5x^4 - 4x^3 + 2x^2 + 1	\( -\,3^{7}\cdot 37^{2}\cdot 2381^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.22139206005899.1	x^14 - 3x^13 + 4x^12 - 2x^11 + x^10 - 4x^9 + 9x^8 - 11x^7 + 9x^6 - 4x^5 + x^4 - 2x^3 + 4x^2 - 3x + 1	\( -\,59\cdot 593^{2}\cdot 1033^{2} \)	14T57	Trivial
14.0.28466647927227.1	x^14 - x^13 + 2x^12 + 3x^11 - x^10 + 4x^9 + 3x^8 + 2x^7 + 2x^4 - 2x^3 - x^2 + 1	\( -\,3^{7}\cdot 114089^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.51902598731283.1	x^14 - 2x^13 + 3x^12 - 6x^11 + 6x^10 - 4x^9 + 3x^8 + x^7 - x^5 + 3x^4 + 3x^2 + x + 1	\( -\,3^{11}\cdot 17117^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.2.52058057626129.1	x^14 - 2x^13 + 3x^12 - 4x^11 + 4x^10 - 4x^9 + 4x^8 - 5x^7 + 4x^6 - 4x^5 + 4x^4 - 4x^3 + 3x^2 - 2x + 1	\( 7215127^{2} \)	14T55	Trivial
14.2.54815765790289.1	x^14 + x^12 - 2x^8 - x^7 - 2x^6 + x^2 + 1	\( 7^{2}\cdot 1057681^{2} \)	14T55	Trivial
14.2.55059380046329.1	x^14 - 4x^13 + 6x^12 - x^11 - 10x^10 + 18x^9 - 18x^8 + 15x^7 - 13x^6 + 11x^5 - 8x^4 + 6x^3 - 3x^2 + 1	\( 277^{2}\cdot 569\cdot 1123^{2} \)	14T57	Trivial
14.0.56316949686099.1	x^14 - 2x^13 + 6x^12 - 11x^11 + 19x^10 - 26x^9 + 33x^8 - 35x^7 + 33x^6 - 26x^5 + 19x^4 - 10x^3 + 6x^2 - x + 1	\( -\,3^{7}\cdot 2953^{3} \)	$D_7 \wr C_2$ (as 14T20)	Trivial
14.2.62662828387597.1	x^14 - x^13 - 3x^12 + 5x^11 + 2x^10 - 11x^9 + 4x^8 + 11x^7 - 11x^6 - 2x^5 + 10x^4 - 4x^3 - 2x^2 + 3x - 1	\( 167^{2}\cdot 1213\cdot 1361^{2} \)	14T57	Trivial
14.2.63097400703125.1	x^14 - 3x^13 + 2x^12 + 4x^11 - 8x^10 + 2x^9 + 8x^8 - 10x^7 + x^6 + 7x^5 - 6x^4 + x^3 + 2x^2 - x + 1	\( 5^{7}\cdot 807646729 \)	14T61	Trivial
14.2.68537510017457.1	x^14 - 4x^13 + 10x^12 - 15x^11 + 11x^10 + 6x^9 - 26x^8 + 35x^7 - 26x^6 + 6x^5 + 11x^4 - 15x^3 + 10x^2 - 4x + 1	\( 13^{4}\cdot 17\cdot 109^{4} \)	14T51	Trivial
14.0.74532401109963.1	x^14 - x^13 + 2x^12 - x^11 + 2x^10 - 2x^9 + 2x^8 - 2x^7 - 3x^5 - x^3 + 2x^2 + x + 1	\( -\,3^{7}\cdot 184607^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.0.76600746490099.1	x^14 - 2x^13 + 6x^12 - 8x^11 + 16x^10 - 17x^9 + 24x^8 - 21x^7 + 24x^6 - 17x^5 + 16x^4 - 8x^3 + 6x^2 - 2x + 1	\( -\,13^{4}\cdot 19\cdot 109^{4} \)	14T51	Trivial
14.2.78352380449344.1	x^14 - 2x^12 + x^10 + 2x^8 - 3x^6 + x^4 - 1	\( 2^{6}\cdot 23^{2}\cdot 73^{2}\cdot 659^{2} \)	14T55	Trivial
14.2.94241555580481.1	x^14 - x^12 - 2x^9 + 3x^7 - 2x^5 - x^2 + 1	\( 43^{2}\cdot 401^{2}\cdot 563^{2} \)	14T55	Trivial
14.2.94724481953125.1	x^14 - x^13 - 2x^12 + 5x^11 + 2x^10 - 9x^9 + 2x^8 + 10x^7 - 6x^6 - 6x^5 + 7x^4 + x^3 - 4x^2 + 1	\( 5^{7}\cdot 199\cdot 6092831 \)	14T61	Trivial
14.2.103886084489093.1	x^14 - 3x^12 - 3x^11 + 6x^10 + 7x^9 - 5x^8 - 12x^7 + 2x^6 + 11x^5 + x^4 - 7x^3 - 2x^2 + 4x - 1	\( 53\cdot 977^{2}\cdot 1433^{2} \)	14T57	Trivial
14.2.116768679686993.1	x^14 - 3x^13 + 7x^12 - 14x^11 + 21x^10 - 29x^9 + 35x^8 - 37x^7 + 35x^6 - 29x^5 + 21x^4 - 14x^3 + 7x^2 - 3x + 1	\( 257\cdot 674057^{2} \)	14T57	Trivial
14.0.118236562059083.1	x^14 - 3x^13 + 2x^12 + 3x^11 - 5x^10 - x^9 + x^8 + 2x^7 + 11x^6 - 13x^5 + 6x^4 - 8x^3 + 4x^2 + 1	\( -\,13\cdot 71^{7} \)	14T38	Trivial
14.2.154291569457229.1	x^14 - x^13 + x^12 - 2x^11 + 2x^10 - 3x^9 + 3x^8 - 3x^7 + 3x^6 - 3x^5 + 2x^4 - 2x^3 + x^2 - x + 1	\( 29\cdot 107^{2}\cdot 21557^{2} \)	14T57	Trivial
14.2.160805685121205.1	x^14 + x^12 - x^9 - x^8 - x^7 - x^6 - x^5 + x^2 + 1	\( 5\cdot 41^{2}\cdot 138319^{2} \)	14T57	Trivial
14.0.172575877556547.1	x^14 - x^13 - x^12 + 2x^10 + x^9 - x^8 - x^7 - x^6 + x^5 + 2x^4 - x^2 - x + 1	\( -\,3^{7}\cdot 280909^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.2.212764932023296.1	x^14 - x^10 + x^8 + x^2 - 1	\( 2^{10}\cdot 455827^{2} \)	14T55	Trivial
14.2.245928712415581.1	x^14 - x^13 + 4x^12 - x^11 + 3x^10 + 3x^9 - 4x^8 + 9x^7 - 16x^6 + 14x^5 - 21x^4 + 10x^3 - 9x^2 + 2x - 1	\( 13^{4}\cdot 61\cdot 109^{4} \)	14T51	Trivial
14.4.250058750499647.1	x^14 - 2x^13 + x^12 - x^11 + x^10 - 4x^9 + 9x^8 - 9x^7 + 9x^6 - 4x^5 + x^4 - x^3 + x^2 - 2x + 1	\( -\,47\cdot 107^{2}\cdot 21557^{2} \)	14T57	Trivial
14.0.263657868936003.1	x^14 + x^12 - 2x^11 - x^10 + 3x^7 - x^4 - 2x^3 + x^2 + 1	\( -\,3^{7}\cdot 103^{2}\cdot 3371^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.4.270118421833507.1	x^14 - x^13 - 3x^12 - x^11 + x^10 + 2x^8 + 7x^7 + 3x^6 + 4x^5 + 9x^4 + 7x^3 + x^2 + 1	\( -\,13^{4}\cdot 67\cdot 109^{4} \)	14T51	Trivial
14.0.280155320935227.1	x^14 - x^13 + 2x^12 - x^11 + 3x^10 - 4x^9 + 3x^8 - 4x^7 + 2x^6 - 4x^5 + 2x^4 + 5x^2 + 2x + 1	\( -\,3^{7}\cdot 71^{6} \)	$D_{14}$ (as 14T3)	Trivial
14.4.297261105546875.1	x^14 - 3x^12 - x^11 + 5x^10 + 3x^9 - 6x^8 - 6x^7 + 3x^6 + 7x^5 - 4x^3 - 2x^2 + x + 1	\( -\,5^{7}\cdot 89\cdot 971\cdot 44029 \)	14T61	Trivial
14.0.318497840669359.1	x^14 - 4x^13 + 8x^12 - 10x^11 + 15x^10 - 28x^9 + 42x^8 - 41x^7 + 32x^6 - 31x^5 + 37x^4 - 35x^3 + 21x^2 - 7x + 1	\( -\,13^{4}\cdot 79\cdot 109^{4} \)	14T51	Trivial
14.2.321952970703125.1	x^14 - 3x^13 + 2x^12 + 3x^11 - 7x^10 + 11x^9 - 25x^8 + 33x^7 - 4x^6 - 56x^5 + 93x^4 - 78x^3 + 38x^2 - 10x + 1	\( 5^{9}\cdot 37^{2}\cdot 347^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.4.334624313614643.1	x^14 - x^13 - 4x^12 + 3x^11 + 3x^10 + 3x^9 + 2x^8 - 12x^7 + x^5 + 2x^4 + 6x^3 - 3x^2 + x - 1	\( -\,13^{4}\cdot 83\cdot 109^{4} \)	14T51	Trivial
14.2.386441371953125.1	x^14 - x^13 - 2x^12 + 4x^11 - 2x^10 - 3x^9 + x^8 + 6x^6 - 11x^5 + 5x^4 - 12x^3 + 24x^2 - 20x + 5	\( 5^{7}\cdot 53^{2}\cdot 1327^{2} \)	$S_7\times C_2$ (as 14T49)	Trivial
14.2.391066968923137.1	x^14 - 4x^13 + 5x^12 + 4x^11 - 14x^10 + 5x^9 + 13x^8 - 9x^7 - 9x^6 + 8x^5 + 4x^4 - 5x^3 + x - 1	\( 13^{4}\cdot 97\cdot 109^{4} \)	14T51	Trivial
14.0.407483719072587.1	x^14 - x^13 + 4x^12 - x^11 + 4x^10 + 2x^9 - 6x^8 + 3x^7 - 6x^6 + 2x^5 + 4x^4 - x^3 + 4x^2 - x + 1	\( -\,3^{15}\cdot 73^{4} \)	$A_7\times C_2$ (as 14T47)	Trivial
14.4.411650990546875.1	x^14 - 3x^12 - 2x^11 + 5x^10 + 4x^9 - 6x^8 - 7x^7 + 7x^6 + 9x^5 - 4x^4 - 6x^3 + 2x^2 + 2x - 1	\( -\,5^{7}\cdot 24851\cdot 212029 \)	14T61	Trivial
14.2.422859037223221.1	x^14 - 2x^13 - 4x^12 + 6x^11 + 10x^10 - 3x^9 - 19x^8 - 6x^7 + 27x^6 - x^5 - 20x^4 + 9x^3 + 4x^2 - 4x + 1	\( 71^{6}\cdot 3301 \)	14T38	Trivial
14.0.445660887761159.1	x^14 - x^13 + 6x^12 - 4x^11 + 12x^10 - 2x^9 + 11x^8 + 3x^7 + 11x^6 - 2x^5 + 12x^4 - 4x^3 + 6x^2 - x + 1	\( -\,7^{2}\cdot 71^{7} \)	14T27	Trivial
14.2.493856488203125.1	x^14 - 2x^13 + 6x^11 - 3x^10 - 8x^9 + 13x^8 + 4x^7 - 16x^6 + 7x^5 + 13x^4 - 11x^3 - 4x^2 + 6x - 1	\( 5^{7}\cdot 43^{6} \)	$D_{14}$ (as 14T3)	Trivial
14.4.498897726810659.1	x^14 - 2x^13 + 3x^11 - 7x^10 + x^9 + 14x^8 - 2x^7 - 13x^6 + 2x^5 + 4x^4 - 4x^3 + 3x + 1	\( -\,11^{3}\cdot 71^{2}\cdot 8623^{2} \)	14T57	Trivial
14.2.508017475013049.1	x^14 - x^11 - x^10 - 4x^9 + x^7 - 4x^5 - x^4 - x^3 + 1	\( 3^{2}\cdot 2741^{4} \)	14T50	Trivial
14.2.511335829405696.1	x^14 + x^12 - 3x^10 - 2x^8 + 5x^6 + 2x^4 - 2x^2 - 1	\( 2^{16}\cdot 19^{2}\cdot 4649^{2} \)	14T55	Trivial
14.2.552331698375977.1	x^14 - 4x^13 + 8x^12 - 10x^11 + 5x^10 + 3x^9 - 10x^8 + 7x^7 - x^6 - 2x^5 + 5x^4 + x^2 + 3x + 1	\( 13^{4}\cdot 109^{4}\cdot 137 \)	14T51	Trivial
14.4.569282687307707.1	x^14 - 2x^13 + x^12 + 6x^11 - 14x^10 + 15x^9 - 4x^8 - 17x^7 + 25x^6 - 19x^5 + 6x^4 + 4x^3 - x^2 - x - 1	\( -\,107^{3}\cdot 21557^{2} \)	14T57	Trivial

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