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 3569)

Label	Polynomial	Discriminant	Galois group	Class group
12.12.519708953453125.1	x^12 - x^11 - 12x^10 + 11x^9 + 46x^8 - 33x^7 - 71x^6 + 33x^5 + 46x^4 - 11x^3 - 12x^2 + x + 1	\( 5^{6}\cdot 541\cdot 7841^{2} \)	12T260	Trivial
12.12.551709470703125.1	x^12 - x^11 - 12x^10 + 11x^9 + 54x^8 - 43x^7 - 113x^6 + 71x^5 + 110x^4 - 46x^3 - 40x^2 + 8x + 1	\( 5^{9}\cdot 7^{10} \)	$C_{12}$ (as 12T1)	Trivial
12.12.600281227113989.1	x^12 - 2x^11 - 11x^10 + 23x^9 + 37x^8 - 80x^7 - 53x^6 + 114x^5 + 32x^4 - 64x^3 - 4x^2 + 9x - 1	\( 1709\cdot 592661^{2} \)	12T293	Trivial
12.12.637026957477253.1	x^12 - x^11 - 12x^10 + 8x^9 + 51x^8 - 20x^7 - 89x^6 + 23x^5 + 64x^4 - 13x^3 - 17x^2 + 3x + 1	\( 7^{8}\cdot 181^{2}\cdot 3373 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.12.669346477420869.1	x^12 - x^11 - 12x^10 + 10x^9 + 50x^8 - 34x^7 - 87x^6 + 51x^5 + 61x^4 - 33x^3 - 12x^2 + 8x - 1	\( 3^{3}\cdot 103^{2}\cdot 1327^{3} \)	12T231	Trivial
12.12.696248958578125.1	x^12 - 12x^10 + 51x^8 - 2x^7 - 94x^6 + 12x^5 + 74x^4 - 20x^3 - 19x^2 + 9x - 1	\( 5^{6}\cdot 241\cdot 3329\cdot 55541 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.12.756680642578125.1	x^12 - 12x^10 - x^9 + 54x^8 + 9x^7 - 112x^6 - 27x^5 + 105x^4 + 31x^3 - 36x^2 - 12x + 1	\( 3^{18}\cdot 5^{9} \)	$C_{12}$ (as 12T1)	Trivial
12.12.803483858453125.1	x^12 - 13x^10 + 55x^8 - 2x^7 - 99x^6 + 8x^5 + 76x^4 - 9x^3 - 20x^2 + 3x + 1	\( 5^{6}\cdot 601\cdot 85562341 \)	$S_6\wr C_2$ (as 12T299)	Trivial
12.12.843466573910016.1	x^12 - 11x^10 + 44x^8 - 78x^6 + 60x^4 - 16x^2 + 1	\( 2^{12}\cdot 3^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.12.870852093010133.1	x^12 - x^11 - 13x^10 + 15x^9 + 55x^8 - 70x^7 - 85x^6 + 115x^5 + 40x^4 - 50x^3 - 13x^2 + 4x + 1	\( 13^{10}\cdot 6317 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.12.887040302925757.1	x^12 - x^11 - 11x^10 + 10x^9 + 43x^8 - 33x^7 - 75x^6 + 45x^5 + 58x^4 - 25x^3 - 17x^2 + 5x + 1	\( 79^{2}\cdot 613\cdot 15227^{2} \)	12T293	Trivial
12.12.913378856890625.1	x^12 - x^11 - 18x^10 + 8x^9 + 95x^8 - 14x^7 - 165x^6 + 23x^5 + 110x^4 - 17x^3 - 24x^2 + 2x + 1	\( 5^{6}\cdot 3881^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.12.1037754255015625.1	x^12 - 2x^11 - 12x^10 + 19x^9 + 49x^8 - 57x^7 - 82x^6 + 72x^5 + 53x^4 - 40x^3 - 9x^2 + 8x - 1	\( 5^{6}\cdot 7^{8}\cdot 41\cdot 281 \)	$C_2^5.(C_2\times C_6)$ (as 12T134)	Trivial
12.12.1178849444515625.1	x^12 - 3x^11 - 9x^10 + 30x^9 + 23x^8 - 99x^7 - 11x^6 + 126x^5 - 9x^4 - 63x^3 + 5x^2 + 9x - 1	\( 5^{6}\cdot 3881^{2}\cdot 5009 \)	12T260	Trivial
12.12.1272443408263937.1	x^12 - 2x^11 - 11x^10 + 18x^9 + 37x^8 - 52x^7 - 51x^6 + 58x^5 + 32x^4 - 24x^3 - 9x^2 + 3x + 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 1553 \)	$D_4\wr C_3$ (as 12T222)	Trivial
12.12.1278540355140625.1	x^12 - 2x^11 - 11x^10 + 20x^9 + 43x^8 - 67x^7 - 71x^6 + 90x^5 + 40x^4 - 49x^3 - x^2 + 7x - 1	\( 5^{6}\cdot 29^{3}\cdot 61\cdot 55001 \)	12T274	Trivial
12.12.1306484927252973.1	x^12 - x^11 - 12x^10 + 12x^9 + 53x^8 - 53x^7 - 103x^6 + 103x^5 + 79x^4 - 79x^3 - 12x^2 + 12x + 1	\( 3^{6}\cdot 13^{11} \)	$C_{12}$ (as 12T1)	Trivial
12.12.1356520905953125.1	x^12 - x^11 - 16x^10 + 20x^9 + 60x^8 - 69x^7 - 79x^6 + 88x^5 + 35x^4 - 45x^3 - x^2 + 7x - 1	\( 5^{6}\cdot 11^{4}\cdot 181^{3} \)	$S_3\wr C_2$ (as 12T35)	Trivial
12.12.1377319619634049.1	x^12 - x^11 - 16x^10 + 11x^9 + 83x^8 - 19x^7 - 175x^6 - 27x^5 + 135x^4 + 60x^3 - 13x^2 - 9x - 1	\( 7^{8}\cdot 13^{2}\cdot 29^{2}\cdot 41^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.12.1558117876000000.1	x^12 - 3x^11 - 9x^10 + 25x^9 + 31x^8 - 70x^7 - 47x^6 + 84x^5 + 29x^4 - 43x^3 - 4x^2 + 8x - 1	\( 2^{8}\cdot 5^{6}\cdot 7^{2}\cdot 19^{4}\cdot 61 \)	12T208	Trivial
12.12.1644873805328125.1	x^12 - 5x^11 - 2x^10 + 43x^9 - 35x^8 - 122x^7 + 160x^6 + 120x^5 - 225x^4 - 6x^3 + 90x^2 - 21x + 1	\( 5^{6}\cdot 29^{3}\cdot 311\cdot 13879 \)	12T274	Trivial
12.12.1816178885163041.1	x^12 - 3x^11 - 8x^10 + 25x^9 + 22x^8 - 67x^7 - 30x^6 + 73x^5 + 22x^4 - 31x^3 - 8x^2 + 4x + 1	\( 7^{8}\cdot 71\cdot 281\cdot 15791 \)	12T292	Trivial
12.12.1871944227828125.1	x^12 - 3x^11 - 9x^10 + 30x^9 + 15x^8 - 77x^7 - x^6 + 76x^5 - 10x^4 - 30x^3 + 6x^2 + 4x - 1	\( 5^{6}\cdot 11^{2}\cdot 31^{2}\cdot 101^{3} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.12.1952518144000000.1	x^12 - 4x^11 - 6x^10 + 32x^9 + 12x^8 - 86x^7 - 14x^6 + 92x^5 + 10x^4 - 40x^3 - 5x^2 + 6x + 1	\( 2^{18}\cdot 5^{6}\cdot 271\cdot 1759 \)	12T261	Trivial
12.12.2093934172250000.1	x^12 - 13x^10 - x^9 + 56x^8 + 9x^7 - 102x^6 - 25x^5 + 79x^4 + 28x^3 - 20x^2 - 10x - 1	\( 2^{4}\cdot 5^{6}\cdot 89^{3}\cdot 109^{2} \)	12T167	Trivial
12.12.2154038935140625.1	x^12 - x^11 - 16x^10 + 11x^9 + 79x^8 - 29x^7 - 145x^6 + 25x^5 + 107x^4 - 2x^3 - 27x^2 - 3x + 1	\( 5^{6}\cdot 13^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.12.2196839556078125.1	x^12 - x^11 - 17x^10 + 8x^9 + 79x^8 - 32x^7 - 126x^6 + 37x^5 + 81x^4 - 15x^3 - 19x^2 + 2x + 1	\( 5^{6}\cdot 7^{8}\cdot 29^{3} \)	$D_4 \times C_3$ (as 12T14)	Trivial
12.12.2436167488251136.1	x^12 - 5x^11 - 3x^10 + 49x^9 - 43x^8 - 140x^7 + 211x^6 + 114x^5 - 299x^4 + 37x^3 + 116x^2 - 36x - 1	\( 2^{8}\cdot 37^{6}\cdot 3709 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.12.2474477972015625.1	x^12 - 17x^10 - 11x^9 + 73x^8 + 62x^7 - 102x^6 - 87x^5 + 52x^4 + 43x^3 - 5x^2 - 7x - 1	\( 3^{8}\cdot 5^{6}\cdot 17^{6} \)	$C_6\times S_3$ (as 12T18)	Trivial
12.12.2535525376000000.1	x^12 - 2x^11 - 14x^10 + 22x^9 + 67x^8 - 64x^7 - 138x^6 + 48x^5 + 109x^4 + 6x^3 - 28x^2 - 10x - 1	\( 2^{16}\cdot 5^{6}\cdot 19^{5} \)	$C_3\times C_3:D_4$ (as 12T42)	Trivial
12.12.2811266206890625.1	x^12 - 3x^11 - 9x^10 + 28x^9 + 24x^8 - 87x^7 - 19x^6 + 107x^5 + 2x^4 - 52x^3 + 8x + 1	\( 5^{6}\cdot 11^{2}\cdot 38561^{2} \)	12T203	Trivial
12.12.2950947586890625.1	x^12 - 2x^11 - 16x^10 + 12x^9 + 74x^8 - 10x^7 - 119x^6 - 10x^5 + 74x^4 + 12x^3 - 16x^2 - 2x + 1	\( 5^{6}\cdot 7^{8}\cdot 181^{2} \)	$C_2^2 \times A_4$ (as 12T25)	Trivial
12.12.2992691444000000.1	x^12 - x^11 - 15x^10 + 7x^9 + 83x^8 + 4x^7 - 197x^6 - 104x^5 + 151x^4 + 167x^3 + 52x^2 + 2x - 1	\( 2^{8}\cdot 5^{6}\cdot 19^{4}\cdot 5741 \)	12T208	Trivial
12.12.3185030335661329.1	x^12 - 4x^11 - 6x^10 + 38x^9 + 2x^8 - 134x^7 + 49x^6 + 213x^5 - 104x^4 - 146x^3 + 60x^2 + 33x - 1	\( 17^{2}\cdot 101^{2}\cdot 32869^{2} \)	12T285	Trivial
12.12.3217569633140625.1	x^12 - x^11 - 19x^10 + 18x^9 + 110x^8 - 92x^7 - 218x^6 + 155x^5 + 166x^4 - 88x^3 - 40x^2 + 8x + 1	\( 3^{6}\cdot 5^{6}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.12.3356038763843584.1	x^12 - 11x^10 + 43x^8 - 73x^6 + 53x^4 - 15x^2 + 1	\( 2^{12}\cdot 7^{8}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2\times C_2^4:C_3$ (as 12T90)	Trivial
12.12.3408269910093056.1	x^12 - 2x^11 - 14x^10 + 23x^9 + 65x^8 - 66x^7 - 137x^6 + 40x^5 + 117x^4 + 27x^3 - 19x^2 - 9x - 1	\( 2^{8}\cdot 37^{6}\cdot 5189 \)	$C_2^4:C_3.D_4$ (as 12T135)	Trivial
12.12.3441144995703125.1	x^12 - 3x^11 - 11x^10 + 40x^9 + 23x^8 - 161x^7 + 56x^6 + 208x^5 - 168x^4 - 16x^3 + 34x^2 - 3x - 1	\( 5^{8}\cdot 29^{3}\cdot 601^{2} \)	$D_6\wr C_2$ (as 12T125)	Trivial
12.12.3545107547544689.1	x^12 - 3x^11 - 8x^10 + 25x^9 + 25x^8 - 73x^7 - 42x^6 + 89x^5 + 40x^4 - 39x^3 - 17x^2 + 2x + 1	\( 7^{8}\cdot 1021\cdot 602309 \)	12T292	Trivial
12.12.3783372458265625.1	x^12 - 3x^11 - 13x^10 + 47x^9 + 42x^8 - 249x^7 + 46x^6 + 514x^5 - 361x^4 - 319x^3 + 379x^2 - 80x - 5	\( 5^{6}\cdot 263^{2}\cdot 1871^{2} \)	$S_6\times C_2$ (as 12T219)	Trivial
12.12.3823196224000000.1	x^12 - 11x^10 + 42x^8 - 67x^6 + 45x^4 - 12x^2 + 1	\( 2^{12}\cdot 5^{6}\cdot 59^{2}\cdot 131^{2} \)	12T203	Trivial
12.12.3958882310427733.1	x^12 - 4x^11 - 10x^10 + 53x^9 + 9x^8 - 205x^7 + 105x^6 + 204x^5 - 101x^4 - 90x^3 + 22x^2 + 16x + 1	\( 13^{11}\cdot 47^{2} \)	$C_4\times A_4$ (as 12T29)	Trivial
12.12.3989681137476125.1	x^12 - x^11 - 17x^10 + 13x^9 + 96x^8 - 53x^7 - 212x^6 + 62x^5 + 175x^4 - 15x^3 - 44x^2 - 5x + 1	\( 5^{3}\cdot 7^{8}\cdot 13^{2}\cdot 181^{2} \)	$C_2^5.(C_2\times C_6)$ (as 12T142)	Trivial
12.12.4238977831849489.1	x^12 - 3x^11 - 11x^10 + 30x^9 + 39x^8 - 87x^7 - 59x^6 + 87x^5 + 39x^4 - 30x^3 - 11x^2 + 3x + 1	\( 17^{2}\cdot 19^{4}\cdot 103^{4} \)	$C_2\times C_4^2:C_3:C_2$ (as 12T95)	Trivial
12.12.4239150758955121.1	x^12 - 5x^11 - 3x^10 + 42x^9 - 25x^8 - 102x^7 + 97x^6 + 68x^5 - 70x^4 - 21x^3 + 17x^2 + 3x - 1	\( 8069^{4} \)	$C_4^2:C_3:C_2$ (as 12T62)	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
12.12.4638867626953125.1	x^12 - 6x^11 + 4x^10 + 35x^9 - 55x^8 - 56x^7 + 136x^6 + x^5 - 105x^4 + 40x^3 + 14x^2 - 9x + 1	\( 3^{6}\cdot 5^{11}\cdot 19^{4} \)	$S_3 \times C_4$ (as 12T11)	Trivial
12.12.4663778923828125.1	x^12 - x^11 - 12x^10 + 9x^9 + 53x^8 - 27x^7 - 106x^6 + 34x^5 + 96x^4 - 17x^3 - 32x^2 + 2x + 1	\( 3^{6}\cdot 5^{9}\cdot 29\cdot 179\cdot 631 \)	12T264	Trivial
12.12.4739148267126784.1	x^12 - 12x^10 + 53x^8 - 104x^6 + 86x^4 - 24x^2 + 1	\( 2^{24}\cdot 7^{10} \)	$C_6\times C_2$ (as 12T2)	Trivial
12.12.4839863153265625.1	x^12 - 15x^10 - 2x^9 + 77x^8 + 15x^7 - 157x^6 - 22x^5 + 126x^4 + 13x^3 - 33x^2 - 5x + 1	\( 5^{6}\cdot 53^{2}\cdot 10501^{2} \)	12T236	Trivial