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 )

Label	Polynomial	Discriminant	Galois group	Class group
12.0.14011639427134441.1	x^12 - 4x^10 + 28x^8 - 76x^6 + 200x^4 + 155x^2 + 196	\( 491^{6} \)	$S_4$ (as 12T9)	$[12]$
12.0.33171021564453125.1	x^12 - x^11 + 7x^10 - 6x^9 + 41x^8 - 62x^7 + 266x^6 - 351x^5 + 1513x^4 - 1757x^3 + 2107x^2 - 2058x + 2401	\( 5^{9}\cdot 19^{8} \)	$C_{12}$ (as 12T1)	$[13]$
12.0.39957753600631952.1	x^12 - 2x^11 + 4x^10 - 4x^9 + 4x^8 + 2x^7 - 3x^6 + 4x^5 + 16x^4 - 32x^3 + 64x^2 - 64x + 64	\( 2^{4}\cdot 79^{2}\cdot 2153\cdot 13633^{2} \)	12T293	$[11]$
12.0.42590699184263473.1	x^12 + 3x^10 - x^9 + 12x^8 - 2x^7 + 23x^6 - 4x^5 + 48x^4 - 8x^3 + 48x^2 + 64	\( 89\cdot 107^{2}\cdot 137\cdot 17467^{2} \)	12T293	$[12]$
12.0.52206766144000000.1	x^12 + 25x^10 + 208x^8 + 655x^6 + 741x^4 + 290x^2 + 25	\( 2^{12}\cdot 5^{6}\cdot 13^{8} \)	$C_6\times C_2$ (as 12T2)	$[2, 6]$
12.0.53981860730241024.1	x^12 + 22x^10 + 176x^8 + 624x^6 + 960x^4 + 512x^2 + 64	\( 2^{18}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[12]$
12.0.53981860730241024.3	x^12 + 14x^10 + 140x^8 + 672x^6 + 2352x^4 + 3136x^2 + 3136	\( 2^{18}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[14]$
12.0.53981860730241024.4	x^12 - 2x^11 + x^10 + 4x^9 + 38x^8 - 88x^7 + 174x^6 - 82x^5 + 496x^4 - 844x^3 + 2776x^2 - 2432x + 3361	\( 2^{18}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[14]$
12.0.53981860730241024.5	x^12 - 6x^10 + 36x^8 - 216x^6 + 1296x^4 - 7776x^2 + 46656	\( 2^{18}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[2, 6]$
12.0.53981860730241024.6	x^12 + 6x^10 + 36x^8 + 216x^6 + 1296x^4 + 7776x^2 + 46656	\( 2^{18}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[14]$
12.0.60314363410603073.1	x^12 - x^11 + 3x^10 + 8x^8 - 4x^7 + 23x^6 - 8x^5 + 32x^4 + 48x^2 - 32x + 64	\( 41^{2}\cdot 8513\cdot 64921^{2} \)	12T293	$[12]$
12.0.60814439242268672.1	x^12 + 4x^10 + 10x^8 - 4x^7 + 22x^6 - 8x^5 + 40x^4 + 64x^2 + 64	\( 2^{22}\cdot 31^{2}\cdot 41\cdot 71^{2}\cdot 73 \)	12T260	$[12]$
12.0.61585005599133696.1	x^12 + 6x^10 + 21x^8 + 49x^6 + 84x^4 + 96x^2 + 64	\( 2^{12}\cdot 3^{18}\cdot 197^{2} \)	$C_2^2 \times A_4$ (as 12T25)	$[14]$
12.0.65470184848162816.1	x^12 - 4x^11 + 11x^10 - 24x^9 + 46x^8 - 76x^7 + 114x^6 - 152x^5 + 184x^4 - 192x^3 + 176x^2 - 128x + 64	\( 2^{16}\cdot 151^{2}\cdot 191^{2}\cdot 1201 \)	12T293	$[11]$
12.0.70943728834969600.2	x^12 + 6x^10 + 20x^8 + 46x^6 + 80x^4 + 96x^2 + 64	\( 2^{22}\cdot 5^{2}\cdot 19^{2}\cdot 37^{4} \)	$C_2^2\times S_4$ (as 12T48)	$[12]$
12.0.76212492224515625.1	x^12 - 3x^11 + 8x^10 - 16x^9 + 32x^8 - 51x^7 + 79x^6 - 102x^5 + 128x^4 - 128x^3 + 128x^2 - 96x + 64	\( 5^{6}\cdot 11^{4}\cdot 181^{2}\cdot 10169 \)	12T260	$[11]$
12.0.86703599443555193.1	x^12 - 2x^11 + 7x^10 - 13x^9 + 28x^8 - 43x^7 + 69x^6 - 86x^5 + 112x^4 - 104x^3 + 112x^2 - 64x + 64	\( 11^{2}\cdot 137\cdot 349^{2}\cdot 6553^{2} \)	12T293	$[12]$
12.0.93099004126639569.1	x^12 - 5x^11 + 16x^10 - 39x^9 + 79x^8 - 137x^7 + 207x^6 - 274x^5 + 316x^4 - 312x^3 + 256x^2 - 160x + 64	\( 3^{2}\cdot 3089\cdot 1829963^{2} \)	12T293	$[13]$
12.0.93358894582925968.1	x^12 - 3x^11 + 6x^10 - 7x^9 + 8x^8 - 6x^7 + 9x^6 - 12x^5 + 32x^4 - 56x^3 + 96x^2 - 96x + 64	\( 2^{4}\cdot 2833\cdot 1435141^{2} \)	12T293	$[12]$
12.0.101439097511492601.1	x^12 - x^11 + 18x^10 - 5x^9 + 243x^8 - 98x^7 + 1039x^6 - 210x^5 + 3303x^4 - 1139x^3 + 1366x^2 + 325x + 169	\( 3^{6}\cdot 7^{8}\cdot 17^{6} \)	$C_6\times C_2$ (as 12T2)	$[13]$
12.0.103997395628457984.53	x^12 - 6x^10 + 3x^8 - 8x^6 + 294x^4 + 816x^2 + 100	\( 2^{28}\cdot 3^{18} \)	$C_2 \times S_4$ (as 12T24)	$[12]$
12.0.103997395628457984.64	x^12 + 12x^10 + 48x^8 + 64x^6 - 12x^4 - 48x^2 + 784	\( 2^{28}\cdot 3^{18} \)	$C_2 \times S_4$ (as 12T23)	$[12]$
12.0.103997395628457984.90	x^12 + 6x^10 + 45x^8 + 336x^6 + 1296x^4 + 648x^2 + 324	\( 2^{28}\cdot 3^{18} \)	$C_2\times S_4$ (as 12T21)	$[2, 6]$
12.0.104623783936000000.1	x^12 + 15x^10 + 86x^8 + 239x^6 + 334x^4 + 217x^2 + 49	\( 2^{20}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4} \)	12T158	$[12]$
12.0.106113981554053376.1	x^12 - 3x^11 + 9x^10 - 19x^9 + 38x^8 - 62x^7 + 94x^6 - 124x^5 + 152x^4 - 152x^3 + 144x^2 - 96x + 64	\( 2^{8}\cdot 37^{4}\cdot 281^{2}\cdot 2801 \)	12T250	$[17]$
12.0.109436699097976761.1	x^12 - 14x^9 + 224x^6 - 490x^3 + 343	\( 3^{18}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	$[21]$
12.0.112519142144278528.1	x^12 - 3x^11 + 5x^10 - 4x^9 - x^8 + 13x^7 - 25x^6 + 26x^5 - 4x^4 - 32x^3 + 80x^2 - 96x + 64	\( 2^{16}\cdot 137^{2}\cdot 337\cdot 521^{2} \)	12T293	$[12]$
12.0.112584506495441152.1	x^12 - x^11 + 4x^10 - 4x^9 + 12x^8 - 12x^7 + 28x^6 - 24x^5 + 48x^4 - 32x^3 + 64x^2 - 32x + 64	\( 2^{8}\cdot 673\cdot 808373^{2} \)	12T293	$[12]$
12.0.113033123172146593.1	x^12 - 5x^11 + 15x^10 - 34x^9 + 64x^8 - 104x^7 + 153x^6 - 208x^5 + 256x^4 - 272x^3 + 240x^2 - 160x + 64	\( 13^{2}\cdot 2113\cdot 562613^{2} \)	12T293	$[11]$
12.0.113293705669460577.1	x^12 - x^11 + 4x^10 - 2x^9 + 6x^8 - 4x^7 + 11x^6 - 8x^5 + 24x^4 - 16x^3 + 64x^2 - 32x + 64	\( 3^{2}\cdot 97^{2}\cdot 5737\cdot 15271^{2} \)	12T293	$[11]$
12.0.113973630361636864.1	x^12 + 29x^10 + 284x^8 + 1095x^6 + 1541x^4 + 326x^2 + 1	\( 2^{12}\cdot 7^{8}\cdot 13^{6} \)	$C_6\times C_2$ (as 12T2)	$[2, 6]$
12.0.114172357111328125.1	x^12 - 2x^11 + 13x^10 - 33x^9 + 71x^8 - 184x^7 + 319x^6 - 378x^5 + 1268x^4 - 99x^3 + 2343x^2 + 41x + 1691	\( 5^{9}\cdot 3881^{3} \)	$S_3^2:C_4$ (as 12T80)	$[20]$
12.0.117090537973140032.1	x^12 - 2x^11 + 7x^10 - 13x^9 + 27x^8 - 43x^7 + 67x^6 - 86x^5 + 108x^4 - 104x^3 + 112x^2 - 64x + 64	\( 2^{6}\cdot 7^{2}\cdot 229^{4}\cdot 13577 \)	12T250	$[12]$
12.0.117451023583608832.1	x^12 - 4x^11 + 16x^10 - 38x^9 + 74x^8 - 114x^7 + 248x^6 - 368x^5 + 302x^4 - 142x^3 + 48x^2 - 10x + 1	\( 2^{16}\cdot 13^{11} \)	$C_4:S_4$ (as 12T54)	$[12]$
12.0.119113607154579712.1	x^12 - x^11 + 4x^10 - 2x^9 + 12x^8 - 8x^7 + 30x^6 - 16x^5 + 48x^4 - 16x^3 + 64x^2 - 32x + 64	\( 2^{8}\cdot 3457\cdot 366869^{2} \)	12T293	$[19]$
12.0.125296227979701209.1	x^12 - 3x^11 + 8x^10 - 15x^9 + 29x^8 - 43x^7 + 67x^6 - 86x^5 + 116x^4 - 120x^3 + 128x^2 - 96x + 64	\( 101^{2}\cdot 11369\cdot 32869^{2} \)	12T293	$[15]$
12.0.125854463671248325.1	x^12 - 2x^11 + 17x^10 - 34x^9 + 159x^8 - 305x^7 + 909x^6 - 1493x^5 + 2869x^4 - 3385x^3 + 3910x^2 - 2646x + 1171	\( 5^{2}\cdot 13^{11}\cdot 53^{2} \)	$C_4\times A_4$ (as 12T29)	$[2, 2, 4]$
12.0.131621703842267136.57	x^12 + 12x^10 + 51x^8 + 28x^6 + 69x^4 + 30x^2 + 64	\( 2^{22}\cdot 3^{22} \)	$C_2\times C_2^2:S_4$ (as 12T103)	$[2, 8]$
12.0.131621703842267136.61	x^12 - 24x^6 + 108x^4 - 162x^2 + 81	\( 2^{22}\cdot 3^{22} \)	$C_2\times C_2^2:S_4$ (as 12T103)	$[2, 8]$
12.0.137277082725750313.1	x^12 - 2x^11 + 7x^10 - 12x^9 + 27x^8 - 37x^7 + 65x^6 - 74x^5 + 108x^4 - 96x^3 + 112x^2 - 64x + 64	\( 769^{2}\cdot 3253^{2}\cdot 21937 \)	12T293	$[11]$
12.0.141917814705923001.1	x^12 - 4x^11 + 11x^10 - 25x^9 + 50x^8 - 84x^7 + 125x^6 - 168x^5 + 200x^4 - 200x^3 + 176x^2 - 128x + 64	\( 3^{2}\cdot 449\cdot 5926169^{2} \)	12T293	$[18]$
12.0.142663603866837857.1	x^12 - 2x^11 + 5x^10 - 7x^9 + 16x^8 - 22x^7 + 41x^6 - 44x^5 + 64x^4 - 56x^3 + 80x^2 - 64x + 64	\( 997^{2}\cdot 3709^{2}\cdot 10433 \)	12T293	$[12]$
12.0.144555105949057024.1	x^12 - 6x^10 + 28x^8 + 6x^6 + 28x^4 - 6x^2 + 1	\( 2^{20}\cdot 13^{10} \)	$C_2 \times S_4$ (as 12T23)	$[12]$
12.0.144555105949057024.2	x^12 + 6x^10 + 28x^8 - 6x^6 + 28x^4 + 6x^2 + 1	\( 2^{20}\cdot 13^{10} \)	$C_2 \times S_4$ (as 12T24)	$[2, 6]$
12.0.144555105949057024.3	x^12 + 7x^10 + 28x^8 + 45x^6 + 28x^4 + 7x^2 + 1	\( 2^{20}\cdot 13^{10} \)	$C_2 \times S_4$ (as 12T24)	$[12]$
12.0.144555105949057024.9	x^12 + 11x^10 - 26x^9 + 45x^8 - 156x^7 + 279x^6 - 286x^5 + 538x^4 - 520x^3 + 346x^2 - 364x + 196	\( 2^{20}\cdot 13^{10} \)	$C_2\times S_4$ (as 12T21)	$[2, 6]$
12.0.144555105949057024.10	x^12 - x^11 + 2x^10 - 12x^9 + 28x^8 + 36x^7 + 184x^6 + 264x^5 + 500x^4 + 524x^3 + 584x^2 + 416x + 256	\( 2^{20}\cdot 13^{10} \)	$C_2\times C_4^2:C_3:C_2$ (as 12T95)	$[20]$
12.0.144869678261310016.1	x^12 - x^11 - x^10 - 3x^8 + 3x^7 + 7x^6 + 6x^5 - 12x^4 - 16x^2 - 32x + 64	\( 2^{6}\cdot 7^{6}\cdot 59^{2}\cdot 2351^{2} \)	$S_6\times C_2$ (as 12T219)	$[11]$
12.0.149650075476775025.1	x^12 - 3x^11 + 9x^10 - 18x^9 + 34x^8 - 52x^7 + 81x^6 - 104x^5 + 136x^4 - 144x^3 + 144x^2 - 96x + 64	\( 5^{2}\cdot 59^{2}\cdot 73^{2}\cdot 521\cdot 787^{2} \)	12T293	$[16]$
12.0.152028237544940457.1	x^12 - 2x^11 + 7x^10 - 11x^9 + 26x^8 - 33x^7 + 61x^6 - 66x^5 + 104x^4 - 88x^3 + 112x^2 - 64x + 64	\( 3^{2}\cdot 199^{2}\cdot 2713\cdot 12539^{2} \)	12T293	$[12]$

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