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 158)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.563507579133.1	x^12 - 2x^11 - 2x^10 + 7x^9 - 2x^8 - 8x^7 + 10x^6 + 4x^5 - 14x^4 - 3x^3 + 9x^2 + 6x + 3	\( 3^{9}\cdot 31^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.1775882908917.1	x^12 - 3x^11 + 9x^9 - 15x^8 + 6x^7 + 14x^6 - 21x^5 + 24x^4 - 15x^3 + 15x^2 - 3x + 1	\( 3^{14}\cdot 13^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.5376874643456.1	x^12 - 6x^11 + 16x^10 - 24x^9 + 24x^8 - 28x^7 + 38x^6 - 30x^5 + 12x^4 - 8x^3 + 6x^2 + 1	\( 2^{18}\cdot 29^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.2.7695492605307.2	x^12 - 2x^9 + 4x^6 - 3x^3 - 1	\( -\,3^{13}\cdot 13^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.11216568631221.1	x^12 - 2x^11 + 8x^10 - 16x^9 + 24x^8 - 28x^7 + 22x^6 - 5x^5 - 9x^4 + 4x^3 + 5x^2 - 4x + 1	\( 3^{6}\cdot 109^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.12476686493952.1	x^12 - x^11 + 5x^10 - 6x^9 + 7x^8 + x^7 - 8x^6 + x^5 + 7x^4 + 12x^3 + 11x^2 + 5x + 1	\( 2^{8}\cdot 3^{9}\cdot 19^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.2.17468734953123.1	x^12 - 4x^11 + 12x^10 - 26x^9 + 37x^8 - 48x^7 + 43x^6 - 33x^5 + 15x^4 - 13x^3 + 10x^2 - 6x + 1	\( -\,3^{9}\cdot 31^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.19534128475869.1	x^12 - 6x^11 + 24x^10 - 62x^9 + 129x^8 - 201x^7 + 237x^6 - 201x^5 + 129x^4 - 62x^3 + 24x^2 - 6x + 1	\( 3^{19}\cdot 7^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.22872307503104.1	x^12 - 4x^10 - 2x^9 + 12x^8 + 20x^7 + 18x^6 + 16x^5 + 20x^4 + 18x^3 + 12x^2 + 4x + 1	\( 2^{12}\cdot 89^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.2.38982341165056.2	x^12 - 2x^10 + 6x^8 - 6x^4 - 2x^2 - 1	\( -\,2^{16}\cdot 29^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.2.55916310546875.1	x^12 - 4x^11 + 8x^10 - 9x^9 - 2x^8 + 2x^7 + 29x^6 - 39x^5 + x^4 + 2x^3 + 8x^2 + 3x - 9	\( -\,5^{9}\cdot 31^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.76169967501312.1	x^12 - 6x^10 - 6x^8 + 48x^6 + 54x^4 - 18x^2 + 3	\( 2^{16}\cdot 3^{19} \)	$D_{12}$ (as 12T12)	Trivial
12.2.80525500000000.1	x^12 - 3x^11 + 3x^10 + 8x^9 - 9x^8 - x^7 + 14x^6 + 3x^5 + 3x^4 + 24x^3 + 23x^2 + 9x + 1	\( -\,2^{8}\cdot 5^{9}\cdot 11^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.109627439316992.1	x^12 - 6x^11 + 24x^10 - 60x^9 + 108x^8 - 148x^7 + 154x^6 - 110x^5 + 52x^4 - 16x^3 + 18x^2 - 8x + 1	\( 2^{18}\cdot 53^{5} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.114516604000000.1	x^12 - x^10 - 2x^9 - 5x^8 + 12x^7 - 15x^6 + 26x^5 - 8x^4 - 4x^3 - 20x^2 + 16x - 4	\( -\,2^{8}\cdot 5^{6}\cdot 31^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.129223508203125.1	x^12 - 4x^11 + 9x^10 - 17x^9 + 40x^8 - 66x^7 + 136x^6 - 198x^5 + 306x^4 - 280x^3 + 274x^2 - 117x + 73	\( 3^{9}\cdot 5^{8}\cdot 7^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.2.136738899331083.1	x^12 - x^9 + 8x^3 + 1	\( -\,3^{19}\cdot 7^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.221405852729344.1	x^12 - 2x^11 + 10x^10 - 28x^9 + 52x^8 - 106x^7 + 170x^6 - 174x^5 + 176x^4 - 192x^3 + 106x^2 - 18x + 9	\( 2^{18}\cdot 61^{5} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.237057043385088.1	x^12 - 4x^11 + 13x^10 - 32x^9 + 49x^8 - 46x^7 - x^6 + 68x^5 - 122x^4 + 118x^3 - 80x^2 + 32x - 8	\( -\,2^{8}\cdot 3^{9}\cdot 19^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.259729655939201.1	x^12 - 4x^11 + 13x^10 - 20x^9 + 21x^8 + 8x^7 - 49x^6 + 60x^5 - 30x^4 - 18x^3 + 53x^2 - 35x + 25	\( 7^{9}\cdot 23^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.2.304679870005248.1	x^12 - 10x^9 + 36x^6 - 46x^3 + 1	\( -\,2^{18}\cdot 3^{19} \)	$D_{12}$ (as 12T12)	Trivial
12.0.331669996668333.1	x^12 - 3x^11 - 3x^10 + 24x^9 - 12x^8 - 69x^7 + 73x^6 + 99x^5 - 108x^4 - 120x^3 + 63x^2 + 111x + 37	\( 3^{14}\cdot 37^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.344119977181184.10	x^12 - 4x^10 + 16x^8 - 20x^6 + 32x^4 + 4x^2 + 29	\( 2^{24}\cdot 29^{5} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.407535326934363.1	x^12 + x^6 - 27	\( -\,3^{5}\cdot 109^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.2.508908841944064.1	x^12 - x^11 + 2x^10 - 15x^9 + 36x^8 - 49x^7 + 48x^6 - 49x^5 + 36x^4 - 15x^3 + 2x^2 - x + 1	\( -\,2^{10}\cdot 89^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.710002944800000.1	x^12 - x^11 + 7x^10 - 8x^9 + 19x^8 - 35x^7 + 54x^6 - 35x^5 + 19x^4 - 8x^3 + 7x^2 - x + 1	\( 2^{8}\cdot 5^{5}\cdot 31^{6} \)	$D_{12}$ (as 12T12)	$[3]$
12.0.797345646116864.1	x^12 - 6x^10 + 20x^8 - 40x^6 + 61x^4 - 58x^2 + 26	\( 2^{31}\cdot 13^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.797345646116864.2	x^12 - 6x^10 + 16x^8 - 20x^6 + 13x^4 - 22x^2 + 26	\( 2^{31}\cdot 13^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.838860800000000.7	x^12 - 14x^10 + 88x^8 - 308x^6 + 621x^4 - 686x^2 + 338	\( 2^{31}\cdot 5^{8} \)	$D_{12}$ (as 12T12)	Trivial
12.0.885780500000000.1	x^12 - x^11 - 2x^10 + 11x^9 + 4x^8 - 43x^7 + 17x^6 + 66x^5 - 90x^4 - 6x^3 + 100x^2 - 72x + 16	\( 2^{8}\cdot 5^{9}\cdot 11^{6} \)	$D_{12}$ (as 12T12)	$[4]$
12.2.904564557421875.1	x^12 - 5x^11 + 14x^10 - 29x^9 + 46x^8 - 34x^7 + 8x^6 + 35x^5 - 11x^4 + 6x^3 + 12x^2 + 9x - 3	\( -\,3^{9}\cdot 5^{8}\cdot 7^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.2.1452563570950144.1	x^12 - 3x^10 + 5x^8 + 22x^6 - 5x^4 - 3x^2 - 1	\( -\,2^{16}\cdot 53^{6} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.1677721600000000.1	x^12 - 14x^10 + 69x^8 - 84x^6 - 69x^4 - 14x^2 - 1	\( -\,2^{32}\cdot 5^{8} \)	$D_{12}$ (as 12T12)	Trivial
12.0.1733405626953125.1	x^12 - 4x^11 + 12x^10 - 14x^9 - 4x^8 + 37x^7 - 44x^6 - 54x^5 + 268x^4 - 428x^3 + 402x^2 - 252x + 81	\( 5^{9}\cdot 31^{6} \)	$D_{12}$ (as 12T12)	$[4]$
12.2.2494869834563584.6	x^12 - 4x^10 + 23x^8 - 28x^6 + 5x^4 + 8x^2 - 4	\( -\,2^{22}\cdot 29^{6} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.3376439254122496.1	x^12 - 6x^10 + 22x^8 - 44x^6 + 42x^4 - 2x^2 - 9	\( -\,2^{16}\cdot 61^{6} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.4090596625576107.1	x^12 - x^9 + 3x^6 + 31x^3 - 1	\( -\,3^{13}\cdot 37^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.4874877920083968.4	x^12 - 12x^10 + 39x^8 - 12x^6 - 27x^4 + 12	\( 2^{22}\cdot 3^{19} \)	$D_{12}$ (as 12T12)	$[2]$
12.0.5533670223904768.1	x^12 - 4x^10 + 22x^8 - 68x^6 + 100x^4 - 72x^2 + 22	\( 2^{35}\cdot 11^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.5533670223904768.26	x^12 + 4x^10 + 22x^8 + 68x^6 + 100x^4 + 72x^2 + 22	\( 2^{35}\cdot 11^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.2.5973782086601623.1	x^12 - 4x^11 + 14x^10 - 39x^9 + 110x^8 - 239x^7 + 387x^6 - 459x^5 + 353x^4 - 228x^3 + 28x^2 - 50x + 1	\( -\,7^{9}\cdot 23^{6} \)	$D_{12}$ (as 12T12)	Trivial
12.0.6847565144260608.18	x^12 - 6x^10 + 27x^8 - 68x^6 + 84x^4 - 48x^2 + 12	\( 2^{32}\cdot 3^{13} \)	$D_{12}$ (as 12T12)	Trivial
12.0.6847565144260608.23	x^12 + 6x^10 + 27x^8 + 68x^6 + 84x^4 + 48x^2 + 12	\( 2^{32}\cdot 3^{13} \)	$D_{12}$ (as 12T12)	Trivial
12.2.10271347716390912.15	x^12 + 6x^10 - 40x^6 - 51x^4 - 6x^2 - 2	\( -\,2^{31}\cdot 3^{14} \)	$D_{12}$ (as 12T12)	Trivial
12.2.10271347716390912.18	x^12 - 6x^10 + 40x^6 - 51x^4 + 6x^2 - 2	\( -\,2^{31}\cdot 3^{14} \)	$D_{12}$ (as 12T12)	Trivial
12.0.10634764226658304.30	x^12 - 6x^10 + 11x^8 - 4x^6 + 20x^4 - 48x^2 + 76	\( 2^{32}\cdot 19^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.10634764226658304.32	x^12 + 6x^10 + 11x^8 + 4x^6 + 20x^4 + 48x^2 + 76	\( 2^{32}\cdot 19^{5} \)	$D_{12}$ (as 12T12)	Trivial
12.0.18698185645162496.1	x^12 + 22x^8 - 55x^4 + 176	\( 2^{16}\cdot 11^{11} \)	$D_{12}$ (as 12T12)	Trivial
12.2.19499511680335872.3	x^12 - 3x^8 + 72x^4 - 48	\( -\,2^{24}\cdot 3^{19} \)	$D_{12}$ (as 12T12)	$[2]$
12.2.20730986799038464.6	x^12 - 6x^10 + 7x^8 + 12x^6 - 4x^4 - 32x^2 - 4	\( -\,2^{32}\cdot 13^{6} \)	$D_{12}$ (as 12T12)	$[2]$