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 4996)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.102014357504.1	x^12 - 2x^11 + 2x^10 - 4x^9 + 3x^8 - 2x^7 + 8x^6 + 7x^4 + 2x^3 + x^2 + 2x + 1	\( 2^{12}\cdot 23^{4}\cdot 89 \)	12T227	Trivial
12.2.177788874752.1	x^12 - 4x^9 + 3x^8 - 4x^7 + 11x^6 - 8x^5 + 8x^4 - 14x^3 + 13x^2 - 6x + 1	\( -\,2^{12}\cdot 31^{4}\cdot 47 \)	12T227	Trivial
12.0.244755204809.1	x^12 - 2x^11 + 5x^10 - 7x^9 + 10x^8 - 13x^7 + 13x^6 - 13x^5 + 10x^4 - 7x^3 + 5x^2 - 2x + 1	\( 89\cdot 229^{4} \)	12T227	Trivial
12.2.255609008128.1	x^12 - 2x^11 + 3x^10 - 4x^9 + 7x^8 - 8x^7 - 2x^6 + 18x^5 - 28x^4 + 22x^3 - 11x^2 + 4x - 1	\( -\,2^{12}\cdot 23^{4}\cdot 223 \)	12T227	Trivial
12.2.279198105664.1	x^12 - 5x^10 + 9x^8 - 7x^6 + x^4 + 3x^2 - 1	\( -\,2^{6}\cdot 257^{4} \)	12T227	Trivial
12.2.349257427087.1	x^12 - 4x^11 + 8x^10 - 10x^9 + 9x^8 - 12x^7 + 18x^6 - 18x^5 + 14x^4 - 9x^3 + 5x^2 - 2x - 1	\( -\,127\cdot 229^{4} \)	12T227	Trivial
12.0.358769594368.1	x^12 - 3x^10 - 6x^9 + 2x^8 + 12x^7 + 11x^6 - 4x^5 - 8x^4 - 4x^3 + 4x^2 + 2x + 1	\( 2^{12}\cdot 23^{4}\cdot 313 \)	12T227	Trivial
12.0.541761520757.1	x^12 - 4x^11 + 9x^10 - 15x^9 + 24x^8 - 30x^7 + 31x^6 - 30x^5 + 24x^4 - 15x^3 + 9x^2 - 4x + 1	\( 197\cdot 229^{4} \)	12T227	Trivial
12.4.936468877312.1	x^12 - 5x^10 - 6x^9 + 11x^8 + 20x^7 - 6x^6 - 28x^5 - 6x^4 + 18x^3 + 5x^2 - 4x - 1	\( 2^{12}\cdot 19\cdot 23^{4}\cdot 43 \)	12T227	Trivial
12.4.1184054284288.1	x^12 - 2x^11 - 2x^9 - 2x^8 + 16x^7 + x^6 - 16x^5 - 2x^4 + 2x^3 + 2x + 1	\( 2^{12}\cdot 23^{4}\cdot 1033 \)	12T227	Trivial
12.4.1365453235513.1	x^12 - 2x^10 - 4x^8 - x^7 + 8x^6 - 2x^4 - 2x^3 - x^2 + 3x - 1	\( 257^{4}\cdot 313 \)	12T227	Trivial
12.4.1630784679233.1	x^12 - 3x^11 + 3x^10 + 2x^9 - 7x^8 + x^7 + 5x^6 - x^5 - 7x^4 - 2x^3 + 3x^2 + 3x + 1	\( 229^{4}\cdot 593 \)	12T227	Trivial
12.2.23732412219392.1	x^12 + 6x^10 + 11x^8 + 4x^6 - 4x^4 - 2	\( -\,2^{25}\cdot 29^{4} \)	12T227	Trivial
12.2.23732412219392.2	x^12 + x^10 + 3x^8 + 6x^6 + 8x^4 + 2x^2 - 2	\( -\,2^{25}\cdot 29^{4} \)	12T227	Trivial
12.2.245337121882112.1	x^12 - 6x^10 + 17x^8 - 28x^6 + 38x^4 - 36x^2 - 2	\( -\,2^{33}\cdot 13^{4} \)	12T227	Trivial
12.2.245337121882112.7	x^12 + 6x^10 + 17x^8 + 28x^6 + 38x^4 + 36x^2 - 2	\( -\,2^{33}\cdot 13^{4} \)	12T227	Trivial
12.4.249351637167617.1	x^12 - 3x^11 - x^10 + 4x^9 + x^8 + 3x^7 + 7x^6 + 3x^5 + x^4 + 4x^3 - x^2 - 3x + 1	\( 17\cdot 19^{4}\cdot 103^{4} \)	12T227	Trivial
12.4.249351637167617.2	x^12 - x^11 - 5x^10 - 2x^9 + 6x^8 + 7x^7 + 5x^6 + 7x^5 + 6x^4 - 2x^3 - 5x^2 - x + 1	\( 17\cdot 19^{4}\cdot 103^{4} \)	12T227	Trivial
12.8.360455665221632.1	x^12 - 7x^10 - 2x^9 + 5x^8 - 12x^7 + 7x^6 + 34x^5 - 9x^4 - 24x^3 + 6x^2 + 4x - 1	\( 2^{17}\cdot 229^{4} \)	12T227	Trivial
12.2.379718595510272.3	x^12 - x^10 + 3x^8 - 6x^6 + 8x^4 - 2x^2 - 2	\( -\,2^{29}\cdot 29^{4} \)	12T227	Trivial
12.2.379718595510272.4	x^12 - 6x^10 + 11x^8 - 4x^6 - 4x^4 - 2	\( -\,2^{29}\cdot 29^{4} \)	12T227	Trivial
12.4.379718595510272.1	x^12 + 4x^10 + 9x^8 - 4x^6 - 12x^4 - 4x^2 + 2	\( 2^{29}\cdot 29^{4} \)	12T227	Trivial
12.4.379718595510272.2	x^12 - x^10 - 3x^8 + 2x^6 - 2x^2 + 2	\( 2^{29}\cdot 29^{4} \)	12T227	Trivial
12.0.379718595510272.5	x^12 + x^10 - 3x^8 - 2x^6 + 2x^2 + 2	\( 2^{29}\cdot 29^{4} \)	12T227	Trivial
12.0.379718595510272.6	x^12 - 4x^10 + 9x^8 + 4x^6 - 12x^4 + 4x^2 + 2	\( 2^{29}\cdot 29^{4} \)	12T227	Trivial
12.8.461833821065216.1	x^12 - 6x^11 + 11x^10 - 8x^9 + 21x^8 - 44x^7 - 13x^6 + 102x^5 - 77x^4 + 2x^3 + 26x^2 - 20x + 4	\( 2^{12}\cdot 41\cdot 229^{4} \)	12T227	Trivial
12.6.529419258294272.1	x^12 - 6x^11 + 15x^10 - 20x^9 - 4x^8 + 70x^7 - 137x^6 + 148x^5 - 88x^4 + 18x^3 + 13x^2 - 10x + 2	\( -\,2^{12}\cdot 47\cdot 229^{4} \)	12T227	Trivial
12.6.529419258294272.2	x^12 - 6x^9 - 9x^8 - 16x^7 + 32x^5 + 21x^4 + 2x^3 - 38x^2 + 8x + 4	\( -\,2^{12}\cdot 47\cdot 229^{4} \)	12T227	Trivial
12.2.688239954362368.1	x^12 - 6x^10 + 15x^8 - 40x^4 + 72x^2 - 58	\( -\,2^{25}\cdot 29^{5} \)	12T227	Trivial
12.2.688239954362368.2	x^12 + x^10 - 9x^8 - 2x^6 + 12x^4 + 74x^2 - 58	\( -\,2^{25}\cdot 29^{5} \)	12T227	Trivial
12.2.688239954362368.3	x^12 - 5x^11 + 10x^10 + x^9 - 41x^8 + 70x^7 - 154x^5 + 192x^4 + 14x^3 - 248x^2 + 222x - 58	\( -\,2^{25}\cdot 29^{5} \)	12T227	Trivial
12.2.688239954362368.4	x^12 - 5x^10 - 12x^9 - 4x^8 + 40x^7 + 76x^6 + 48x^5 - 55x^4 - 144x^3 - 141x^2 - 84x - 16	\( -\,2^{25}\cdot 29^{5} \)	12T227	Trivial
12.2.938735575219264.1	x^12 - 5x^11 + 11x^10 - 19x^9 + 35x^8 - 58x^7 + 84x^6 - 116x^5 + 140x^4 - 152x^3 + 176x^2 - 160x + 64	\( -\,2^{6}\cdot 19^{4}\cdot 103^{4} \)	12T227	Trivial
12.6.938735575219264.1	x^12 - 7x^10 + 9x^8 + 17x^6 - 15x^4 - 20x^2 - 4	\( -\,2^{6}\cdot 19^{4}\cdot 103^{4} \)	12T227	Trivial
12.4.981348487528448.3	x^12 - 6x^10 + 9x^8 + 4x^6 - 10x^4 - 4x^2 + 2	\( 2^{35}\cdot 13^{4} \)	12T227	Trivial
12.0.981348487528448.4	x^12 + 6x^10 + 9x^8 - 4x^6 - 10x^4 + 4x^2 + 2	\( 2^{35}\cdot 13^{4} \)	12T227	Trivial
12.6.1023381597392896.2	x^12 - 3x^11 - x^10 + 4x^9 + x^8 + 7x^7 - 2x^6 + 7x^5 + x^4 + 4x^3 - x^2 - 3x + 1	\( -\,2^{12}\cdot 7^{4}\cdot 101^{4} \)	12T227	Trivial
12.2.1367827575897143.1	x^12 - 2x^11 + 4x^10 - 7x^9 + 4x^8 - 5x^7 - x^6 - 10x^5 + 16x^4 - 56x^3 + 64x^2 - 64x + 64	\( -\,23\cdot 2777^{4} \)	12T227	Trivial
12.4.1444408272617472.1	x^12 - 3x^10 + 3x^8 - 6x^6 + 6x^2 + 2	\( 2^{25}\cdot 3^{16} \)	12T227	Trivial
12.0.1444408272617472.3	x^12 + 9x^10 + 39x^8 + 90x^6 + 108x^4 + 54x^2 + 2	\( 2^{25}\cdot 3^{16} \)	12T227	Trivial
12.2.1518874382041088.1	x^12 + 6x^10 + 10x^8 - 18x^4 - 20x^2 - 8	\( -\,2^{31}\cdot 29^{4} \)	12T227	Trivial
12.2.1518874382041088.2	x^12 + 4x^10 - 2x^8 - 20x^6 + 14x^4 - 8x^2 - 8	\( -\,2^{31}\cdot 29^{4} \)	12T227	Trivial
12.2.1518874382041088.7	x^12 - 4x^10 - 2x^8 + 20x^6 + 14x^4 + 8x^2 - 8	\( -\,2^{31}\cdot 29^{4} \)	12T227	Trivial
12.2.1518874382041088.8	x^12 - 6x^10 + 10x^8 - 18x^4 + 20x^2 - 8	\( -\,2^{31}\cdot 29^{4} \)	12T227	Trivial
12.4.1518874382041088.4	x^12 - 6x^10 + 18x^8 - 32x^6 + 38x^4 - 28x^2 + 8	\( 2^{31}\cdot 29^{4} \)	12T227	Trivial
12.4.1518874382041088.6	x^12 - 8x^10 + 22x^8 - 28x^6 + 6x^4 + 8	\( 2^{31}\cdot 29^{4} \)	12T227	Trivial
12.0.1518874382041088.16	x^12 + 8x^10 + 22x^8 + 28x^6 + 6x^4 + 8	\( 2^{31}\cdot 29^{4} \)	12T227	Trivial
12.0.1518874382041088.20	x^12 + 6x^10 + 18x^8 + 32x^6 + 38x^4 + 28x^2 + 8	\( 2^{31}\cdot 29^{4} \)	12T227	Trivial
12.2.1594691292233728.3	x^12 - 4x^11 + 20x^9 - 24x^8 - 20x^7 + 36x^6 - 4x^5 + 21x^4 - 48x^3 + 28x^2 - 8x - 2	\( -\,2^{32}\cdot 13^{5} \)	12T227	Trivial
12.2.1594691292233728.10	x^12 + 2x^10 - 8x^9 - 3x^8 - 4x^7 - 2x^6 + 20x^5 + 15x^4 + 60x^3 - 56x^2 + 40x + 2	\( -\,2^{32}\cdot 13^{5} \)	12T227	Trivial