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 900)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.98890751961.1	x^12 - 2x^11 + 2x^10 - 5x^9 + 10x^8 - 15x^7 + 20x^6 - 24x^5 + 25x^4 - 19x^3 + 11x^2 - 4x + 1	\( 3^{6}\cdot 19^{2}\cdot 613^{2} \)	12T203	Trivial
12.0.112797237609.1	x^12 - x^11 - 2x^10 + x^9 + x^8 + 2x^7 + x^6 - 2x^5 + x^4 - x^3 - 2x^2 + x + 1	\( 3^{6}\cdot 7^{2}\cdot 1777^{2} \)	12T203	Trivial
12.4.933397515625.1	x^12 - x^11 - x^9 - x^8 + 2x^7 - x^6 + 2x^5 - x^4 - x^3 - x + 1	\( 5^{6}\cdot 59^{2}\cdot 131^{2} \)	12T203	Trivial
12.4.960645015625.1	x^12 - 3x^11 + 2x^10 + 2x^9 - 4x^8 + x^7 + x^6 + x^5 - 4x^4 + 2x^3 + 2x^2 - 3x + 1	\( 5^{6}\cdot 7841^{2} \)	12T203	Trivial
12.4.1325664390625.1	x^12 - x^11 - 2x^10 + 3x^9 + x^8 - 5x^6 + 9x^4 - 4x^3 - 2x^2 + 2x - 1	\( 5^{6}\cdot 61^{2}\cdot 151^{2} \)	12T203	Trivial
12.4.1372119390625.1	x^12 - 2x^10 - x^9 + x^7 + 4x^6 - 2x^5 - 5x^4 + 3x^3 + 3x^2 - 1	\( 5^{6}\cdot 9371^{2} \)	12T203	Trivial
12.4.2748964000000.1	x^12 + 4x^10 + 5x^8 - x^6 - 7x^4 - 4x^2 + 1	\( 2^{8}\cdot 5^{6}\cdot 829^{2} \)	12T203	Trivial
12.4.2962271265625.1	x^12 - 2x^11 - 2x^10 + x^9 + 11x^8 + 3x^7 - 21x^6 - 3x^5 + 11x^4 - x^3 - 2x^2 + 2x + 1	\( 5^{6}\cdot 7^{4}\cdot 281^{2} \)	12T203	Trivial
12.0.14281868906496.1	x^12 - 3x^10 - 2x^9 + 3x^8 - 6x^7 - 8x^6 + 24x^5 + 36x^4 - 12x^3 - 36x^2 + 12	\( 2^{12}\cdot 3^{20} \)	12T203	Trivial
12.8.19063047515625.1	x^12 - 2x^11 - 5x^10 + 7x^9 + 10x^8 + 2x^7 - 20x^6 - 19x^5 + 20x^4 + 19x^3 - 5x^2 - 6x - 1	\( 3^{4}\cdot 5^{6}\cdot 3881^{2} \)	12T203	Trivial
12.8.34282488765625.1	x^12 - x^11 - 5x^10 + 7x^9 + x^8 - 11x^7 + 19x^6 - 14x^5 - 5x^4 + 30x^3 - 27x^2 + 5x + 1	\( 5^{6}\cdot 31^{2}\cdot 1511^{2} \)	12T203	Trivial
12.4.36352603193344.1	x^12 - 4x^11 + 6x^10 - 4x^9 - 8x^8 + 16x^7 - 8x^6 - 8x^5 + 19x^4 - 4x^3 - 10x^2 + 4x + 2	\( 2^{36}\cdot 23^{2} \)	12T203	Trivial
12.8.38509781640625.1	x^12 - x^11 - 7x^10 + 4x^9 + 8x^8 - 13x^7 + 9x^6 + 21x^5 - 18x^4 - 12x^3 + 8x^2 + 2x - 1	\( 5^{8}\cdot 9929^{2} \)	12T203	Trivial
12.8.39358370640625.1	x^12 - 2x^11 - 8x^10 + 20x^9 + 8x^8 - 38x^7 + 2x^6 + 20x^5 + 3x^4 + x^3 - 6x^2 - x + 1	\( 5^{6}\cdot 31^{2}\cdot 1619^{2} \)	12T203	Trivial
12.0.50096498540544.1	x^12 + 2x^8 + 4x^6 + 9x^4 + 4x^2 + 4	\( 2^{36}\cdot 3^{6} \)	12T203	Trivial
12.0.63403380965376.1	x^12 - 2x^11 + 3x^10 + 2x^9 + 3x^8 + 4x^7 + 10x^6 - 4x^5 + 3x^4 - 2x^3 + 3x^2 + 2x + 1	\( 2^{30}\cdot 3^{10} \)	12T203	Trivial
12.0.89679990882304.2	x^12 - 4x^10 + 14x^8 - 20x^6 + 21x^4 - 8x^2 + 4	\( 2^{30}\cdot 17^{4} \)	12T203	Trivial
12.4.358719963529216.1	x^12 - 8x^10 - 4x^9 + 11x^8 - 8x^7 - 20x^6 + 16x^5 + 10x^4 - 8x^3 + 8x^2 - 8x + 2	\( 2^{32}\cdot 17^{4} \)	12T203	Trivial
12.4.505298607407104.1	x^12 + 6x^10 + 19x^8 + 4x^6 + 3x^4 - 18x^2 + 1	\( 2^{32}\cdot 7^{6} \)	12T203	Trivial
12.4.570630428688384.7	x^12 - 6x^8 - 8x^6 - 3x^4 + 4	\( 2^{30}\cdot 3^{12} \)	12T203	Trivial
12.4.570630428688384.8	x^12 - 6x^11 + 15x^10 - 10x^9 - 39x^8 + 120x^7 - 144x^6 + 48x^5 + 96x^4 - 160x^3 + 120x^2 - 48x + 8	\( 2^{30}\cdot 3^{12} \)	12T203	Trivial
12.0.570630428688384.10	x^12 - 6x^10 + 21x^8 - 36x^6 + 36x^4 + 4	\( 2^{30}\cdot 3^{12} \)	12T203	Trivial
12.4.581641651093504.1	x^12 + 2x^10 + x^8 - 4x^6 - 3x^4 - 2x^2 + 1	\( 2^{40}\cdot 23^{2} \)	12T203	Trivial
12.4.581641651093504.2	x^12 - 10x^8 - 12x^6 + 7x^4 + 12x^2 + 4	\( 2^{40}\cdot 23^{2} \)	12T203	Trivial
12.0.801543976648704.1	x^12 + 2x^10 + 5x^8 + 4x^6 + x^4 - 2x^2 + 1	\( 2^{40}\cdot 3^{6} \)	12T203	Trivial
12.0.801543976648704.4	x^12 + 2x^8 + 4x^6 + 3x^4 + 4x^2 + 4	\( 2^{40}\cdot 3^{6} \)	12T203	Trivial
12.4.991623123042304.4	x^12 - 2x^10 - 2x^8 - 8x^7 - 16x^6 + 8x^5 - x^4 + 16x^3 - 10x^2 - 8x + 4	\( 2^{30}\cdot 31^{4} \)	12T203	Trivial
12.0.1006121858891776.1	x^12 - 2x^10 - 3x^8 + 8x^6 + 8x^4 - 8x^2 + 4	\( 2^{36}\cdot 11^{4} \)	12T203	Trivial
12.4.1201907943079936.1	x^12 - 2x^11 + x^10 - 12x^9 + 16x^8 - 8x^7 + 32x^6 - 24x^5 - 38x^4 + 28x^3 - 6x^2 + 24x - 8	\( 2^{32}\cdot 23^{4} \)	12T203	Trivial
12.4.1201907943079936.4	x^12 - 2x^11 - 3x^10 + 4x^9 - 10x^8 + 20x^7 + 50x^6 - 40x^5 - 65x^4 + 58x^3 + 11x^2 - 20x + 4	\( 2^{32}\cdot 23^{4} \)	12T203	Trivial
12.0.1434879854116864.1	x^12 - 4x^10 + 13x^8 - 28x^6 + 21x^4 + 1	\( 2^{34}\cdot 17^{4} \)	12T203	Trivial
12.0.1434879854116864.2	x^12 - 4x^10 + 13x^8 - 20x^6 + 24x^4 - 8x^2 + 4	\( 2^{34}\cdot 17^{4} \)	12T203	Trivial
12.0.1619844835311616.1	x^12 - 2x^11 - 3x^10 + 12x^9 - 12x^8 + 16x^7 + 52x^6 - 40x^5 + 117x^4 - 18x^3 + 41x^2 + 28x + 8	\( 2^{26}\cdot 17^{6} \)	12T203	Trivial
12.4.1828652958613504.3	x^12 + 3x^10 - 4x^8 - 16x^6 + 7x^4 + 13x^2 + 4	\( 2^{18}\cdot 17^{8} \)	12T203	Trivial
12.4.1828652958613504.4	x^12 - 13x^10 + 45x^8 - 63x^6 + 58x^4 - 40x^2 + 16	\( 2^{18}\cdot 17^{8} \)	12T203	Trivial
12.4.1828652958613504.5	x^12 - 4x^10 + 13x^8 - 26x^6 + 32x^4 - 36x^2 + 16	\( 2^{18}\cdot 17^{8} \)	12T203	Trivial
12.4.2282521714753536.2	x^12 - 6x^11 + 15x^10 - 18x^9 + 3x^8 + 12x^7 - 10x^6 + 12x^5 + 9x^4 - 10x^3 - 15x^2 - 6x - 1	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.0.2282521714753536.8	x^12 - 2x^11 + 13x^10 - 20x^9 + 44x^8 - 36x^7 + 30x^6 - 40x^5 + 47x^4 - 46x^3 + 31x^2 - 12x + 2	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.4.2282521714753536.8	x^12 - 6x^10 + 21x^8 - 56x^6 + 72x^4 - 24x^2 + 4	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.4.2282521714753536.10	x^12 - 18x^8 - 12x^6 + 9x^4 + 12x^2 + 4	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.4.2282521714753536.11	x^12 - 6x^8 - 12x^6 + 9x^4 + 36x^2 + 4	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.0.2282521714753536.22	x^12 - 4x^11 + 4x^10 + 13x^8 - 48x^7 + 64x^6 - 40x^5 + 65x^4 - 148x^3 + 180x^2 - 72x + 9	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.0.2282521714753536.33	x^12 - 6x^8 - 4x^6 + 9x^4 + 12x^2 + 36	\( 2^{32}\cdot 3^{12} \)	12T203	Trivial
12.4.2326566604374016.1	x^12 + 4x^10 - 2x^8 - 24x^6 + 42x^4 - 24x^2 + 4	\( 2^{42}\cdot 23^{2} \)	12T203	Trivial
12.4.2326566604374016.2	x^12 - 8x^10 + 22x^8 - 32x^6 + 30x^4 - 16x^2 + 4	\( 2^{42}\cdot 23^{2} \)	12T203	Trivial
12.4.2326566604374016.3	x^12 - 4x^10 + 6x^8 - 8x^6 + 10x^4 - 8x^2 + 4	\( 2^{42}\cdot 23^{2} \)	12T203	Trivial
12.4.2326566604374016.4	x^12 - 8x^10 + 22x^8 - 18x^4 + 4	\( 2^{42}\cdot 23^{2} \)	12T203	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
12.0.3206175906594816.3	x^12 + 4x^10 + 10x^8 + 16x^6 + 14x^4 + 8x^2 + 4	\( 2^{42}\cdot 3^{6} \)	12T203	Trivial
12.0.3206175906594816.4	x^12 + 8x^10 + 26x^8 + 40x^6 + 34x^4 + 16x^2 + 4	\( 2^{42}\cdot 3^{6} \)	12T203	Trivial