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 1472)

Label	Polynomial	Discriminant	Galois group	Class group
12.4.7071785078125.1	x^12 - 2x^11 - 2x^10 + 5x^9 - 3x^7 - 3x^6 + 6x^5 + 6x^4 - 11x^3 + 2x^2 + 3x - 1	\( 5^{7}\cdot 449^{3} \)	12T238	Trivial
12.6.17476123046875.1	x^12 - 2x^11 - 4x^10 + 10x^9 - 17x^7 + 19x^6 + 8x^5 - 25x^4 + 10x^3 + 6x^2 - 12x + 1	\( -\,5^{11}\cdot 71^{3} \)	12T238	Trivial
12.2.34075783671875.1	x^12 - 4x^11 + 5x^10 - 4x^8 - 5x^7 + 9x^6 - 5x^5 - 4x^4 + 5x^2 - 4x + 1	\( -\,5^{7}\cdot 11^{4}\cdot 31^{3} \)	12T238	Trivial
12.4.39022400000000.1	x^12 - 3x^10 - 6x^9 + 2x^8 + 14x^7 + 9x^6 - 8x^5 - 12x^4 - 2x^3 + 7x^2 - 1	\( 2^{12}\cdot 5^{8}\cdot 29^{3} \)	12T238	Trivial
12.0.42219101953125.1	x^12 - 5x^11 + 17x^10 - 38x^9 + 65x^8 - 78x^7 + 70x^6 - 46x^5 + 34x^4 - 30x^3 + 30x^2 - 20x + 5	\( 3^{2}\cdot 5^{8}\cdot 229^{3} \)	12T238	Trivial
12.0.42219101953125.2	x^12 - 6x^11 + 23x^10 - 59x^9 + 117x^8 - 176x^7 + 213x^6 - 194x^5 + 142x^4 - 76x^3 + 39x^2 - 10x + 5	\( 3^{2}\cdot 5^{8}\cdot 229^{3} \)	12T238	Trivial
12.0.52256867090432.1	x^12 - 4x^11 + 4x^10 + 8x^9 - 24x^8 + 20x^7 + 10x^6 - 36x^5 + 38x^4 - 24x^3 + 12x^2 - 4x + 1	\( 2^{32}\cdot 23^{3} \)	12T238	Trivial
12.4.52256867090432.1	x^12 - 4x^11 + 16x^9 - 14x^8 - 4x^7 - 6x^6 + 12x^5 + 4x^4 - 4x^2 - 4x + 1	\( 2^{32}\cdot 23^{3} \)	12T238	Trivial
12.6.92483331171875.1	x^12 - 3x^11 + 5x^10 + 5x^9 - 35x^8 + 42x^7 + 16x^6 - 73x^5 + 54x^4 - 4x^3 - 15x^2 + 5x + 1	\( -\,5^{7}\cdot 7^{4}\cdot 79^{3} \)	12T238	Trivial
12.6.111793429296875.1	x^12 - 2x^11 - 3x^10 + 4x^9 - 4x^7 + 23x^6 + 4x^5 - 35x^4 - 9x^3 + 12x^2 + 7x + 1	\( -\,5^{8}\cdot 659^{3} \)	12T238	Trivial
12.6.128882566796875.1	x^12 - 3x^11 - x^10 + 11x^9 - 2x^8 - 21x^7 + 4x^6 + 27x^5 - 13x^4 - 13x^3 + 9x^2 + x - 1	\( -\,5^{8}\cdot 691^{3} \)	12T238	Trivial
12.2.133645398046875.1	x^12 - 4x^11 + 11x^10 - 18x^9 + 27x^8 - 31x^7 + 29x^6 - 17x^5 - 12x^4 + 31x^3 - 16x^2 - 5x + 5	\( -\,3^{2}\cdot 5^{8}\cdot 11^{3}\cdot 13^{4} \)	12T238	Trivial
12.4.209027468361728.1	x^12 - 4x^11 - 2x^10 + 20x^9 + 7x^8 - 56x^7 - 24x^6 + 80x^5 + 44x^4 - 48x^3 - 24x^2 + 16x - 2	\( 2^{34}\cdot 23^{3} \)	12T238	Trivial
12.0.209027468361728.1	x^12 - 4x^11 + 8x^9 + 6x^8 + 8x^5 + 17x^4 + 20x^3 + 16x^2 + 8x + 2	\( 2^{34}\cdot 23^{3} \)	12T238	Trivial
12.0.228581619826688.1	x^12 + 7x^10 + 22x^8 + 46x^6 + 64x^4 + 64x^2 + 32	\( 2^{15}\cdot 17^{8} \)	12T238	Trivial
12.2.358719963529216.1	x^12 - 8x^10 - 4x^9 + 16x^8 - 18x^6 + 16x^4 - 4x^3 - 8x^2 + 1	\( -\,2^{32}\cdot 17^{4} \)	12T238	Trivial
12.0.836109873446912.1	x^12 + 2x^10 - 5x^8 - 12x^6 + x^4 + 22x^2 + 23	\( 2^{36}\cdot 23^{3} \)	12T238	Trivial
12.4.836109873446912.1	x^12 - 2x^11 - 3x^10 + 10x^8 + 20x^7 - 22x^6 + 8x^5 - 19x^4 - 18x^3 - 31x^2 - 24x + 16	\( 2^{36}\cdot 23^{3} \)	12T238	Trivial
12.0.836109873446912.2	x^12 - 6x^10 + 11x^8 - 12x^6 + x^4 + 46x^2 + 23	\( 2^{36}\cdot 23^{3} \)	12T238	Trivial
12.4.836109873446912.3	x^12 - 10x^10 + 39x^8 - 76x^6 + 77x^4 - 46x^2 + 23	\( 2^{36}\cdot 23^{3} \)	12T238	Trivial
12.4.836109873446912.4	x^12 - 8x^10 + 30x^8 - 68x^6 + 135x^4 - 180x^2 + 92	\( 2^{36}\cdot 23^{3} \)	12T238	Trivial
12.0.836109873446912.4	x^12 + 2x^10 - 9x^8 + 12x^6 - 51x^4 + 86x^2 + 23	\( 2^{36}\cdot 23^{3} \)	12T238	$[2]$
12.6.1141260857376768.1	x^12 - 6x^10 - 12x^9 + 15x^8 + 60x^7 + 14x^6 - 108x^5 - 99x^4 + 56x^3 + 84x^2 + 24x + 2	\( -\,2^{31}\cdot 3^{12} \)	12T238	Trivial
12.6.1434879854116864.1	x^12 - 4x^11 + 16x^9 - 10x^8 - 16x^7 - 16x^6 + 64x^5 - 23x^4 - 12x^3 - 24x^2 + 24x + 2	\( -\,2^{34}\cdot 17^{4} \)	12T238	Trivial
12.0.1768545125924864.1	x^12 - 4x^11 + 8x^10 - 8x^9 + 2x^8 + 16x^7 - 16x^6 - 8x^5 + 7x^4 + 76x^3 - 28x^2 - 8x + 146	\( 2^{31}\cdot 7^{7} \)	12T238	Trivial
12.6.1983246246084608.1	x^12 - 4x^11 + 4x^10 - 16x^8 + 40x^7 - 16x^6 + 32x^4 + 16x^2 - 8	\( -\,2^{31}\cdot 31^{4} \)	12T238	Trivial
12.2.2282521714753536.3	x^12 - 18x^8 - 4x^6 + 9x^4 - 12x^2 - 4	\( -\,2^{32}\cdot 3^{12} \)	12T238	Trivial
12.2.3040747419921875.1	x^12 - 2x^11 + 8x^10 - 7x^9 + 22x^8 + 16x^7 + 12x^6 + 94x^5 - 48x^4 + 121x^3 - 15x^2 + 88x - 19	\( -\,5^{9}\cdot 19^{3}\cdot 61^{3} \)	12T238	Trivial
12.4.3344439493787648.1	x^12 - 2x^10 - 9x^8 - 12x^6 - 51x^4 - 86x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.0.3344439493787648.1	x^12 - 6x^10 - 3x^8 + 52x^6 - 5x^4 - 46x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	$[2]$
12.4.3344439493787648.2	x^12 - 10x^10 + 41x^8 - 84x^6 + 95x^4 - 74x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.0.3344439493787648.2	x^12 + 6x^10 + 9x^8 + 44x^6 + 63x^4 + 38x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	$[2]$
12.0.3344439493787648.3	x^12 + 10x^10 + 39x^8 + 76x^6 + 77x^4 + 46x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.4.3344439493787648.3	x^12 + 6x^10 + 11x^8 + 12x^6 + x^4 - 46x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.4.3344439493787648.4	x^12 - 6x^10 + 9x^8 - 44x^6 + 63x^4 - 38x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.0.3344439493787648.4	x^12 + 10x^10 + 41x^8 + 84x^6 + 95x^4 + 74x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.0.3344439493787648.5	x^12 + 10x^10 + 55x^8 + 124x^6 + 173x^4 + 110x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.4.3344439493787648.5	x^12 - 2x^10 - 5x^8 + 12x^6 + x^4 - 22x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.4.3344439493787648.6	x^12 + 6x^10 - 3x^8 - 52x^6 - 5x^4 + 46x^2 + 23	\( 2^{38}\cdot 23^{3} \)	12T238	Trivial
12.0.3344439493787648.6	x^12 + 8x^10 + 30x^8 + 68x^6 + 135x^4 + 180x^2 + 92	\( 2^{38}\cdot 23^{3} \)	12T238	$[2]$
12.0.3657305917227008.1	x^12 + x^10 + 2x^8 + 8x^6 + 3x^4 + 15x^2 + 2	\( 2^{19}\cdot 17^{8} \)	12T238	Trivial
12.4.3657305917227008.1	x^12 - 2x^11 + 2x^10 + 6x^9 - 12x^8 + 4x^7 + 5x^6 - 22x^5 + 14x^4 + 28x^3 - 8x^2 - 12x - 2	\( 2^{19}\cdot 17^{8} \)	12T238	Trivial
12.0.3657305917227008.2	x^12 - 6x^10 + 20x^8 - 26x^6 - 29x^4 + 64x^2 + 8	\( 2^{19}\cdot 17^{8} \)	12T238	Trivial
12.4.3657305917227008.3	x^12 + 6x^10 + 20x^8 + 26x^6 - 29x^4 - 64x^2 + 8	\( 2^{19}\cdot 17^{8} \)	12T238	Trivial
12.0.3657305917227008.3	x^12 + 4x^10 + 15x^8 + 36x^6 + 54x^4 + 94x^2 + 32	\( 2^{19}\cdot 17^{8} \)	12T238	Trivial
12.4.3657305917227008.4	x^12 - 2x^11 - 4x^10 + 16x^9 - 8x^8 - 36x^7 + 56x^6 + 12x^5 - 95x^4 + 70x^3 + 34x^2 - 64x + 16	\( 2^{19}\cdot 17^{8} \)	12T238	Trivial
12.2.4565043429507072.17	x^12 + 6x^10 - 3x^8 - 24x^7 - 24x^6 - 24x^5 - 3x^4 + 6x^2 + 1	\( -\,2^{33}\cdot 3^{12} \)	12T238	Trivial
12.6.5739519416467456.1	x^12 - 4x^10 + 6x^8 - 12x^6 + 15x^4 + 8x^2 - 16	\( -\,2^{36}\cdot 17^{4} \)	12T238	Trivial
12.2.5739519416467456.1	x^12 + 6x^10 + 21x^8 + 24x^6 - 24x^4 - 40x^2 - 4	\( -\,2^{36}\cdot 17^{4} \)	12T238	Trivial
12.2.5739519416467456.3	x^12 + 8x^10 + 26x^8 + 36x^6 + 7x^4 - 12x^2 - 4	\( -\,2^{36}\cdot 17^{4} \)	12T238	Trivial