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 102)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.56689952000.1	x^12 - 5x^11 + 13x^10 - 25x^9 + 39x^8 - 50x^7 + 53x^6 - 48x^5 + 37x^4 - 23x^3 + 12x^2 - 4x + 1	\( 2^{8}\cdot 5^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.75794375168.1	x^12 - 4x^11 + 9x^10 - 12x^9 + 14x^8 - 19x^7 + 30x^6 - 39x^5 + 37x^4 - 26x^3 + 14x^2 - 5x + 1	\( 2^{9}\cdot 23^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.110937960125.1	x^12 - 2x^11 + 2x^9 + x^8 - 4x^7 + 3x^6 - 4x^5 + 13x^4 - 19x^3 + 15x^2 - 6x + 1	\( 5^{3}\cdot 31^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.255806016192.1	x^12 - 3x^11 + 4x^9 + 4x^8 - 6x^7 - 5x^6 - 2x^5 + 18x^4 - 17x^3 + 11x^2 - 5x + 1	\( 2^{6}\cdot 3^{3}\cdot 23^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.255806016192.2	x^12 - 5x^11 + 11x^10 - 18x^9 + 29x^8 - 36x^7 + 31x^6 - 25x^5 + 19x^4 - 3x^3 - 5x^2 + x + 1	\( 2^{6}\cdot 3^{3}\cdot 23^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.325234848133.1	x^12 - x^11 - x^9 + x^8 - 6x^7 + 9x^6 - 2x^5 + 8x^4 - 19x^3 + 10x^2 + 1	\( 13^{3}\cdot 23^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.454401884672.1	x^12 - x^11 + x^9 + 5x^8 - x^7 - 2x^6 - 6x^5 - 4x^4 + 3x^3 + 7x^2 + 4x + 1	\( 2^{9}\cdot 31^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.940369969152.1	x^12 - 3x^10 + 9x^6 + 12x^4 + 9x^2 + 3	\( 2^{16}\cdot 3^{15} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.1259948825856.1	x^12 - 3x^11 + 6x^10 - 12x^9 + 9x^8 + 12x^7 - 27x^6 + 18x^5 + 3x^4 - 18x^3 + 18x^2 - 9x + 3	\( 2^{8}\cdot 3^{15}\cdot 7^{3} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.1505468192000.1	x^12 - 3x^11 + 3x^10 - 3x^9 + 5x^8 - 4x^7 + 7x^6 - 16x^5 + 21x^4 - 13x^3 + 4x^2 - 2x + 1	\( 2^{8}\cdot 5^{3}\cdot 19^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.2690094820608.1	x^12 - 2x^9 + 20x^6 + 8x^3 + 16	\( 2^{8}\cdot 3^{14}\cdot 13^{3} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.3134727585792.1	x^12 - 4x^11 + 11x^10 - 16x^9 + 14x^8 - 2x^7 + x^6 + 10x^4 + 16x^3 + 15x^2 + 6x + 1	\( 2^{16}\cdot 3^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.3134727585792.2	x^12 - 4x^11 + 9x^10 - 20x^9 + 42x^8 - 66x^7 + 93x^6 - 130x^5 + 142x^4 - 114x^3 + 81x^2 - 44x + 11	\( 2^{16}\cdot 3^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.4850840010752.3	x^12 + 5x^10 + 14x^8 + 25x^6 + 28x^4 + 20x^2 + 8	\( 2^{15}\cdot 23^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.5272566705125.1	x^12 - 2x^11 + 3x^10 + 2x^9 - 10x^8 + 8x^7 + 2x^6 - 19x^5 + 23x^4 - 15x^3 + 10x^2 - 3x + 1	\( 5^{3}\cdot 59^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.14512627712000.1	x^12 - 4x^11 + 7x^10 - 2x^9 - 16x^8 + 20x^7 + x^6 - 40x^5 + 18x^4 + 74x^3 + 49x^2 + 12x + 1	\( 2^{16}\cdot 5^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.16298134440192.1	x^12 - 4x^11 + 15x^10 - 36x^9 + 72x^8 - 124x^7 + 175x^6 - 240x^5 + 296x^4 - 312x^3 + 291x^2 - 180x + 47	\( 2^{8}\cdot 3^{3}\cdot 11^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.6.17734300939008.1	x^12 - 4x^11 + 3x^10 + 4x^9 - 4x^8 + 10x^7 - 41x^6 + 46x^5 + 2x^4 - 34x^3 + 25x^2 - 8x + 1	\( -\,2^{8}\cdot 3^{3}\cdot 37^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.23529800000000.1	x^12 - 2x^11 + 2x^10 - 16x^9 + 44x^8 - 47x^7 + 33x^6 - 37x^5 + 30x^4 - 12x^3 + 9x^2 - 5x + 1	\( 2^{9}\cdot 5^{8}\cdot 7^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.29081720619008.3	x^12 + 4x^10 + 5x^8 + 3x^6 + 10x^4 + 16x^2 + 8	\( 2^{15}\cdot 31^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.32291110337661.2	x^12 - 3x^9 + 9x^6 - 9x^3 + 3	\( 3^{23}\cdot 7^{3} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.41326975008000.1	x^12 - 4x^11 + 2x^10 + 13x^9 - 19x^8 - 12x^7 + 39x^6 - 24x^5 + 41x^4 - 59x^3 - 73x^2 + 77x + 121	\( 2^{8}\cdot 3^{6}\cdot 5^{3}\cdot 11^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.48631121859501.1	x^12 - x^11 - 3x^10 + 8x^9 - x^8 - 42x^7 + 19x^6 + 93x^5 - 105x^4 - 181x^3 + 229x^2 + 435x + 173	\( 3^{3}\cdot 23^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.60183678025728.3	x^12 + 12x^8 - 24x^4 + 12	\( 2^{22}\cdot 3^{15} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.80873772931125.1	x^12 - x^11 + 2x^10 + 2x^9 - 2x^8 + 4x^7 - 49x^6 - 59x^5 + 40x^4 + 51x^3 + 78x^2 + 144x + 72	\( 3^{6}\cdot 5^{3}\cdot 31^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.115273770333632.1	x^12 - 4x^11 + 19x^10 - 38x^9 + 97x^8 - 99x^7 + 201x^6 - 84x^5 + 306x^4 - 68x^3 + 408x^2 - 72x + 216	\( 2^{6}\cdot 23^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.154530459877376.1	x^12 - 4x^11 + 10x^10 - 18x^9 + 36x^8 - 28x^7 - 68x^6 + 168x^5 - 60x^4 - 44x^3 + 24x^2 - 72x + 108	\( 2^{16}\cdot 11^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.6.168147445940224.2	x^12 - 4x^11 - x^10 + 20x^9 - 18x^8 - 6x^7 - 25x^6 + 78x^5 - 48x^4 - 10x^3 + 21x^2 - 8x + 1	\( -\,2^{16}\cdot 37^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.203335691924736.1	x^12 - 4x^11 - 2x^10 + 29x^9 - 29x^8 - 52x^7 + 97x^6 + 8x^5 + 31x^4 - 525x^3 + 987x^2 - 765x + 225	\( 2^{8}\cdot 3^{9}\cdot 7^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[3]$
12.0.385610460475392.3	x^12 + 3	\( 2^{12}\cdot 3^{23} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.6.432162447268608.1	x^12 - 3x^11 - 6x^10 + 16x^9 + 3x^8 + 27x^6 + 3x^4 + 16x^3 - 6x^2 - 3x + 1	\( -\,2^{8}\cdot 3^{15}\cdot 7^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.503884800000000.1	x^12 - 39x^8 + 387x^4 + 243	\( 2^{16}\cdot 3^{9}\cdot 5^{8} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.579030153957549.1	x^12 - 3x^11 + 6x^10 - 3x^9 + 27x^8 - 105x^7 + 216x^6 - 171x^5 + 39x^4 + 90x^3 - 36x^2 + 72x + 48	\( 3^{15}\cdot 7^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[3]$
12.0.922190162669056.1	x^12 - 3x^11 + 21x^10 - 37x^9 + 160x^8 - 176x^7 + 687x^6 - 440x^5 + 1828x^4 - 514x^3 + 2572x^2 - 5x + 1481	\( 2^{9}\cdot 23^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.1692135818282944.1	x^12 - x^11 + 8x^10 + 9x^9 - 20x^8 + 116x^7 - 84x^6 - 4x^5 + 584x^4 - 1080x^3 + 1504x^2 - 1024x + 512	\( 2^{6}\cdot 31^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.2779905883635712.5	x^12 - 4x^11 + 14x^10 - 66x^9 + 204x^8 - 490x^7 + 1018x^6 - 1558x^5 + 1597x^4 - 1010x^3 + 356x^2 - 72x + 18	\( 2^{18}\cdot 13^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[3]$
12.0.3355443200000000.15	x^12 + 44x^8 - 28x^4 + 32	\( 2^{33}\cdot 5^{8} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.12.4539981040386048.1	x^12 - 4x^11 - 9x^10 + 48x^9 + 10x^8 - 186x^7 + 91x^6 + 232x^5 - 210x^4 - 8x^3 + 43x^2 - 6x - 1	\( 2^{16}\cdot 3^{3}\cdot 37^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.4539981040386048.2	x^12 + 17x^10 + 96x^8 + 241x^6 + 288x^4 + 153x^2 + 27	\( 2^{16}\cdot 3^{3}\cdot 37^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.5777633090469888.23	x^12 - 12x^10 + 72x^8 - 224x^6 + 324x^4 + 144x^2 + 32	\( 2^{27}\cdot 3^{16} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial (GRH)
12.12.6082865222079744.1	x^12 - 3x^11 - 11x^10 + 39x^9 + 17x^8 - 120x^7 + 11x^6 + 144x^5 - 25x^4 - 73x^3 + 6x^2 + 12x + 1	\( 2^{8}\cdot 3^{3}\cdot 7^{3}\cdot 37^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.6082865222079744.2	x^12 - 2x^11 + 6x^10 + 3x^9 + 27x^8 + 50x^7 + 133x^6 + 158x^5 + 229x^4 + 209x^3 + 165x^2 + 63x + 27	\( 2^{8}\cdot 3^{3}\cdot 7^{3}\cdot 37^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2]$
12.0.6169767367606272.4	x^12 - 6x^9 + 36x^6 + 36x^3 + 12	\( 2^{16}\cdot 3^{23} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.6169767367606272.9	x^12 + 48	\( 2^{16}\cdot 3^{23} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.9889949432152064.6	x^12 + 44x^8 + 968x^4 + 5324	\( 2^{22}\cdot 11^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.6.12734707780826667.1	x^12 + 6x^10 - 33x^8 - 90x^6 + 177x^4 + 360x^2 - 48	\( -\,3^{15}\cdot 31^{6} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.13537086546263552.2	x^12 - 3x^11 + 30x^10 - 72x^9 + 344x^8 - 646x^7 + 1873x^6 - 2614x^5 + 4920x^4 - 4645x^3 + 5785x^2 - 2825x + 2341	\( 2^{9}\cdot 31^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.21147660961644544.2	x^12 - 4x^11 + 6x^10 - 2x^9 - 24x^8 - 32x^7 + 104x^6 + 16x^5 + 220x^4 + 428x^3 + 560x^2 + 500	\( 2^{16}\cdot 19^{9} \)	$(C_6\times C_2):C_2$ (as 12T15)	$[2, 2]$
12.0.24679069470425088.5	x^12 + 192	\( 2^{18}\cdot 3^{23} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial
12.0.28770761984442368.13	x^12 - 14x^10 + 98x^8 - 576x^6 + 1600x^4 + 640x^2 + 128	\( 2^{27}\cdot 11^{8} \)	$(C_6\times C_2):C_2$ (as 12T15)	Trivial (GRH)