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 3400)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.7203443945753.1	x^12 - 3x^11 + 4x^10 - 2x^9 + 4x^8 - 13x^7 + 26x^6 - 14x^5 + x^3 + 8x^2 + 4x + 1	\( 11^{2}\cdot 17^{3}\cdot 59^{4} \)	12T221	Trivial
12.4.8928084611072.1	x^12 - 2x^11 - x^10 + 6x^9 - 4x^8 - 6x^7 + 13x^6 + 4x^5 - 16x^4 - 6x^3 + x^2 - 2x - 1	\( 2^{12}\cdot 11^{4}\cdot 53^{3} \)	12T221	Trivial
12.2.9055290581307.1	x^12 - x^11 - x^9 + 2x^8 + 3x^7 - 7x^6 + 3x^5 + 2x^4 - x^3 - x + 1	\( -\,3^{3}\cdot 761^{4} \)	12T221	Trivial
12.2.9055290581307.2	x^12 - 4x^10 - 4x^9 + x^8 + 3x^7 + 3x^6 + 3x^5 + x^4 - 4x^3 - 4x^2 + 1	\( -\,3^{3}\cdot 761^{4} \)	12T221	Trivial
12.0.14436886188032.1	x^12 - 2x^11 + 5x^10 - 10x^9 + 15x^8 - 16x^7 + 17x^6 - 12x^5 + 12x^4 + 8x^2 + 2x + 2	\( 2^{12}\cdot 7^{2}\cdot 11^{4}\cdot 17^{3} \)	12T221	Trivial
12.4.15240344215808.1	x^12 - 8x^10 + 29x^8 - 67x^6 + 95x^4 - 66x^2 + 17	\( 2^{8}\cdot 17^{3}\cdot 59^{4} \)	12T221	Trivial
12.6.34687201573827.1	x^12 - x^11 + 5x^9 - 11x^8 - 11x^7 + 19x^6 + 13x^5 - 14x^4 - 6x^3 + 8x^2 + x - 1	\( -\,3^{7}\cdot 11^{2}\cdot 107^{4} \)	12T221	Trivial
12.0.40400838383661.1	x^12 - 2x^11 + 5x^10 - 3x^9 + 5x^8 + 4x^7 + x^6 + 4x^5 + 5x^4 - 3x^3 + 5x^2 - 2x + 1	\( 3^{3}\cdot 7^{3}\cdot 257^{4} \)	12T221	$[2]$
12.4.40400838383661.1	x^12 - 2x^11 + x^10 - 2x^8 + 3x^7 - 5x^6 + 3x^5 - 2x^4 + x^2 - 2x + 1	\( 3^{3}\cdot 7^{3}\cdot 257^{4} \)	12T221	Trivial
12.6.144301640919808.1	x^12 - x^11 - 9x^10 + 11x^9 + 17x^8 - 12x^7 - 25x^6 - 2x^5 + 21x^4 + 11x^3 - 6x^2 - 6x + 1	\( -\,2^{8}\cdot 37^{4}\cdot 67^{3} \)	12T221	Trivial
12.4.150859825037312.1	x^12 - 3x^11 + 3x^10 + 2x^9 - 19x^8 + 13x^7 + 22x^6 - 13x^5 - 19x^4 - 2x^3 + 3x^2 + 3x + 1	\( 2^{14}\cdot 17^{3}\cdot 37^{4} \)	12T221	Trivial
12.4.162167403008000.1	x^12 - 6x^10 - 6x^9 + 16x^8 + 38x^7 + 44x^6 + 28x^5 - 8x^4 - 16x^3 - 12x^2 - 4x + 4	\( 2^{12}\cdot 5^{3}\cdot 13^{2}\cdot 37^{4} \)	12T221	Trivial
12.0.187223706128384.1	x^12 - 4x^11 + 3x^10 + 4x^9 - 4x^8 + 2x^7 + x^6 - 22x^5 + 28x^4 - 22x^3 + 29x^2 - 2x + 5	\( 2^{12}\cdot 29^{3}\cdot 37^{4} \)	12T221	Trivial
12.4.748894824513536.1	x^12 - 2x^11 - 6x^10 + 14x^9 - 9x^8 + 2x^7 - 2x^6 + 2x^5 - 9x^4 + 14x^3 - 6x^2 - 2x + 1	\( 2^{14}\cdot 29^{3}\cdot 37^{4} \)	12T221	Trivial
12.0.981348487528448.1	x^12 + 5x^10 + 11x^8 + 12x^6 + 2x^4 - 2x^2 + 2	\( 2^{35}\cdot 13^{4} \)	12T221	Trivial
12.4.981348487528448.7	x^12 - 5x^10 + 11x^8 - 12x^6 + 2x^4 + 2x^2 + 2	\( 2^{35}\cdot 13^{4} \)	12T221	Trivial
12.8.1010020959591525.1	x^12 - x^11 - 9x^10 + 5x^9 + 26x^8 - 17x^7 - 32x^6 + 39x^5 + 17x^4 - 39x^3 + 12x - 3	\( 3^{3}\cdot 5^{2}\cdot 7^{3}\cdot 257^{4} \)	12T221	Trivial
12.4.1518874382041088.1	x^12 + 7x^8 - 10x^6 + 10x^4 - 8x^2 + 2	\( 2^{31}\cdot 29^{4} \)	12T221	Trivial
12.4.1518874382041088.3	x^12 - 8x^10 + 19x^8 - 14x^6 - 2x^4 + 4x^2 + 2	\( 2^{31}\cdot 29^{4} \)	12T221	Trivial
12.0.1518874382041088.5	x^12 + 8x^10 + 19x^8 + 14x^6 - 2x^4 - 4x^2 + 2	\( 2^{31}\cdot 29^{4} \)	12T221	Trivial
12.0.1518874382041088.13	x^12 + 7x^8 + 10x^6 + 10x^4 + 8x^2 + 2	\( 2^{31}\cdot 29^{4} \)	12T221	Trivial
12.0.1828079220031488.1	x^12 + 3x^10 - 9x^8 + x^6 + 9x^4 - 6x^2 + 2	\( 2^{19}\cdot 3^{20} \)	12T221	Trivial
12.4.1828079220031488.3	x^12 - 3x^10 - 9x^8 - x^6 + 9x^4 + 6x^2 + 2	\( 2^{19}\cdot 3^{20} \)	12T221	Trivial
12.8.1931817080797184.1	x^12 - 3x^11 - 7x^10 + 26x^9 + 12x^8 - 69x^7 - 5x^6 + 50x^5 + 16x^4 + 2x^3 - 8x^2 - 6x - 1	\( 2^{11}\cdot 7^{3}\cdot 229^{4} \)	12T221	Trivial
12.4.3355443200000000.1	x^12 - 4x^10 - 9x^8 - 16x^6 - 22x^4 - 16x^2 + 2	\( 2^{33}\cdot 5^{8} \)	12T221	Trivial
12.4.3355443200000000.2	x^12 + 5x^10 + 4x^8 - 10x^6 - 13x^4 - 5x^2 + 2	\( 2^{33}\cdot 5^{8} \)	12T221	Trivial
12.0.3355443200000000.8	x^12 + 4x^10 - 9x^8 + 16x^6 - 22x^4 + 16x^2 + 2	\( 2^{33}\cdot 5^{8} \)	12T221	Trivial
12.0.3355443200000000.10	x^12 + 7x^10 + 14x^8 + 2x^6 - 17x^4 - 7x^2 + 8	\( 2^{33}\cdot 5^{8} \)	12T221	Trivial
12.4.3749169810374656.1	x^12 + 7x^10 - 8x^9 + x^8 - 26x^7 - 4x^6 + 32x^5 + 8x^4 + 36x^3 - 36x^2 - 16x + 4	\( 2^{22}\cdot 19^{7} \)	12T221	Trivial
12.4.3925393950113792.1	x^12 - 6x^10 + 5x^8 + 10x^4 - 20x^2 + 2	\( 2^{37}\cdot 13^{4} \)	12T221	Trivial
12.0.3925393950113792.5	x^12 + 6x^10 + 5x^8 + 10x^4 + 20x^2 + 2	\( 2^{37}\cdot 13^{4} \)	12T221	Trivial
12.4.3925393950113792.8	x^12 - 6x^10 + 16x^8 - 32x^6 + 30x^4 - 4x^2 + 8	\( 2^{37}\cdot 13^{4} \)	12T221	Trivial
12.0.3925393950113792.10	x^12 + 6x^10 + 16x^8 + 32x^6 + 30x^4 + 4x^2 + 8	\( 2^{37}\cdot 13^{4} \)	12T221	Trivial
12.4.4477795463856128.8	x^12 - 3x^10 + 3x^8 + 6x^4 - 10x^2 + 2	\( 2^{35}\cdot 19^{4} \)	12T221	Trivial
12.0.4477795463856128.19	x^12 + 3x^10 + 3x^8 + 6x^4 + 10x^2 + 2	\( 2^{35}\cdot 19^{4} \)	12T221	Trivial
12.0.5231047633534976.1	x^12 - 2x^10 + 3x^8 + 22x^6 - 33x^4 + 11	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.0.5231047633534976.2	x^12 + 6x^10 + 15x^8 + 26x^6 + 27x^4 + 20x^2 + 11	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.4.5231047633534976.3	x^12 - 7x^8 + 6x^6 + 13x^4 - 26x^2 + 11	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.0.5231047633534976.3	x^12 - 7x^8 - 6x^6 + 13x^4 + 26x^2 + 11	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.0.5231047633534976.4	x^12 + 2x^10 + 6x^8 + 20x^6 + 4x^4 + 32x^2 + 44	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.4.5231047633534976.4	x^12 - 6x^10 + 15x^8 - 26x^6 + 27x^4 - 20x^2 + 11	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.0.5231047633534976.5	x^12 + 6x^10 + 2x^8 - 16x^6 + 16x^4 + 72x^2 + 44	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.4.5231047633534976.5	x^12 + 2x^10 + 3x^8 - 22x^6 - 33x^4 + 11	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.4.5231047633534976.6	x^12 - 10x^10 + 42x^8 - 88x^6 + 88x^4 - 88x^2 + 44	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.0.5231047633534976.6	x^12 + 10x^10 + 42x^8 + 88x^6 + 88x^4 + 88x^2 + 44	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.4.5231047633534976.7	x^12 - 6x^10 + 2x^8 + 16x^6 + 16x^4 - 72x^2 + 44	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.4.5231047633534976.8	x^12 - 2x^10 + 6x^8 - 20x^6 + 4x^4 - 32x^2 + 44	\( 2^{28}\cdot 11^{7} \)	12T221	Trivial
12.0.5777633090469888.3	x^12 + 6x^10 + 3x^8 + 16x^6 + 24x^4 + 12x^2 + 2	\( 2^{27}\cdot 3^{16} \)	12T221	Trivial
12.0.5777633090469888.4	x^12 + 9x^8 + 34x^6 + 54x^4 + 24x^2 + 2	\( 2^{27}\cdot 3^{16} \)	12T221	Trivial
12.0.5777633090469888.5	x^12 - 3x^11 + 3x^10 - 8x^9 + 12x^8 - 24x^7 + 52x^6 - 12x^5 + 33x^4 + 9x^3 + 15x^2 + 4	\( 2^{27}\cdot 3^{16} \)	12T221	Trivial