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 1873)

Label	Polynomial	Discriminant	Galois group	Class group
12.0.60454515625.1	x^12 - x^11 - 2x^10 + 2x^9 + 4x^8 - 3x^7 - 5x^6 + 3x^5 + 5x^4 - x^3 - 3x^2 + 1	\( 5^{6}\cdot 7^{2}\cdot 281^{2} \)	12T236	Trivial
12.0.70127513856.1	x^12 + x^10 - 3x^8 - 3x^6 + 2x^4 + 2x^2 + 1	\( 2^{8}\cdot 3^{6}\cdot 613^{2} \)	12T236	Trivial
12.0.114947443521.1	x^12 - 3x^11 + 3x^10 - x^9 - x^8 + 6x^6 - 13x^5 + 16x^4 - 13x^3 + 8x^2 - 3x + 1	\( 3^{6}\cdot 29^{2}\cdot 433^{2} \)	12T236	Trivial
12.0.171810250000.1	x^12 - 2x^10 - x^9 + 4x^8 + x^7 - 2x^6 + x^5 + 4x^4 - x^3 - 2x^2 + 1	\( 2^{4}\cdot 5^{6}\cdot 829^{2} \)	12T236	Trivial
12.4.882697830400.1	x^12 - 4x^11 + 4x^10 + 4x^9 - 9x^8 + 2x^7 + 4x^6 - 2x^5 - x^4 + 2x^3 + x^2 - 2x - 1	\( 2^{18}\cdot 5^{2}\cdot 367^{2} \)	12T236	Trivial
12.4.1153744515625.1	x^12 - 2x^10 - 2x^9 + x^8 + 4x^6 + 2x^5 - 6x^4 - 3x^3 + x^2 + 2x + 1	\( 5^{6}\cdot 13^{2}\cdot 661^{2} \)	12T236	Trivial
12.4.1506176925696.1	x^12 - 2x^10 - 2x^9 - 4x^8 + 5x^6 - 4x^4 - 2x^3 - 2x^2 + 1	\( 2^{18}\cdot 3^{2}\cdot 17^{2}\cdot 47^{2} \)	12T236	Trivial
12.4.2118116390625.1	x^12 - x^11 - x^10 - x^9 - 2x^8 + 4x^7 - x^6 + 4x^5 - 2x^4 - x^3 - x^2 - x + 1	\( 3^{2}\cdot 5^{6}\cdot 3881^{2} \)	12T236	Trivial
12.4.2198176890625.1	x^12 - x^10 - 3x^9 - 2x^8 + 3x^7 + 6x^6 + 2x^5 - 3x^4 - 5x^3 - 2x^2 + 4x + 1	\( 5^{6}\cdot 29^{2}\cdot 409^{2} \)	12T236	Trivial
12.4.2259706445824.1	x^12 - 2x^10 - 3x^8 - 2x^6 + 2x^4 + 4x^2 + 1	\( 2^{24}\cdot 367^{2} \)	12T236	Trivial
12.4.2621161000000.1	x^12 - x^11 - x^10 + 5x^8 - 7x^7 - 7x^6 + 9x^5 + 5x^4 - 4x^2 + 3x + 1	\( 2^{6}\cdot 5^{6}\cdot 1619^{2} \)	12T236	Trivial
12.0.7860313140625.1	x^12 - x^11 + 2x^10 + 2x^8 + x^7 + x^6 + x^5 + 2x^4 + 2x^2 - x + 1	\( 5^{6}\cdot 11^{2}\cdot 2039^{2} \)	12T236	Trivial
12.0.9088150798336.1	x^12 - 2x^11 + 3x^10 + 2x^9 - 7x^8 + 12x^7 + 2x^6 - 20x^5 + 5x^4 + 10x^3 - 3x^2 - 2x + 1	\( 2^{34}\cdot 23^{2} \)	12T236	Trivial
12.4.11531967015625.1	x^12 - 5x^11 + 7x^10 - x^9 - 2x^8 - 6x^7 + 13x^6 - 6x^5 - 2x^4 - x^3 + 7x^2 - 5x + 1	\( 5^{6}\cdot 7^{2}\cdot 3881^{2} \)	12T236	Trivial
12.0.12524124635136.1	x^12 + 2x^8 - 4x^6 + 9x^4 - 4x^2 + 4	\( 2^{34}\cdot 3^{6} \)	12T236	Trivial
12.0.25699830250000.1	x^12 - x^11 - x^10 + 2x^9 + 4x^8 - x^7 - 4x^6 - x^5 + 4x^4 + 2x^3 - x^2 - x + 1	\( 2^{4}\cdot 5^{6}\cdot 10139^{2} \)	12T236	Trivial
12.4.29260310118400.1	x^12 - 4x^10 - 2x^9 - 4x^7 - 7x^6 - 4x^5 - 2x^3 - 4x^2 + 1	\( 2^{18}\cdot 5^{2}\cdot 2113^{2} \)	12T236	Trivial
12.8.36767438995456.1	x^12 - 4x^11 - 2x^10 + 20x^9 + x^8 - 46x^7 - 2x^6 + 58x^5 + 3x^4 - 34x^3 + x^2 + 6x - 1	\( 2^{18}\cdot 13^{2}\cdot 911^{2} \)	12T236	Trivial
12.4.39773518890625.1	x^12 - x^11 - 4x^10 + 4x^9 + 10x^8 - 8x^7 - 16x^6 + 3x^5 + 21x^4 + 3x^3 - 22x^2 + 9x + 1	\( 5^{6}\cdot 13^{2}\cdot 3881^{2} \)	12T236	Trivial
12.8.44962053890625.1	x^12 - 5x^11 + 4x^10 + 14x^9 - 22x^8 - 7x^7 + 29x^6 - 7x^5 - 22x^4 + 14x^3 + 4x^2 - 5x + 1	\( 3^{2}\cdot 5^{6}\cdot 17881^{2} \)	12T236	Trivial
12.8.59967600015625.1	x^12 - 4x^11 + 4x^10 - 3x^9 + x^8 + 21x^7 - 13x^6 - 21x^5 + x^4 + 3x^3 + 4x^2 + 4x + 1	\( 5^{6}\cdot 41^{2}\cdot 1511^{2} \)	12T236	Trivial
12.8.74906393903104.1	x^12 - 6x^10 + 5x^8 + 10x^6 - 6x^4 - 4x^2 + 1	\( 2^{24}\cdot 2113^{2} \)	12T236	Trivial
12.0.75119246442496.1	x^12 - 4x^11 + 10x^10 - 24x^9 + 40x^8 - 60x^7 + 86x^6 - 80x^5 + 93x^4 - 56x^3 + 32x^2 - 8x + 2	\( 2^{28}\cdot 23^{4} \)	12T236	Trivial
12.8.110271001000000.1	x^12 - 4x^11 + 2x^10 + 14x^9 - 20x^8 - 15x^7 + 28x^6 + 11x^5 - 4x^4 - 9x^3 - 8x^2 + 2x + 1	\( 2^{6}\cdot 5^{6}\cdot 10501^{2} \)	12T236	Trivial
12.8.157744180140625.1	x^12 - 2x^11 - 8x^10 + 23x^9 + 13x^8 - 85x^7 + 35x^6 + 101x^5 - 93x^4 + 5x^3 + 16x^2 - 6x + 1	\( 5^{6}\cdot 13^{2}\cdot 59^{2}\cdot 131^{2} \)	12T236	Trivial
12.0.253613523861504.3	x^12 + 6x^10 + 13x^8 + 8x^6 - 8x^2 + 4	\( 2^{32}\cdot 3^{10} \)	12T236	Trivial
12.0.441084004000000.1	x^12 + 12x^10 + 47x^8 + 79x^6 + 57x^4 + 14x^2 + 1	\( 2^{8}\cdot 5^{6}\cdot 10501^{2} \)	12T236	$[2]$
12.0.570630428688384.7	x^12 - 6x^8 + 8x^6 - 3x^4 + 4	\( 2^{30}\cdot 3^{12} \)	12T236	$[2]$
12.0.570630428688384.15	x^12 + 6x^10 + 9x^8 + 12x^6 + 9x^4 + 18x^2 + 9	\( 2^{30}\cdot 3^{12} \)	12T236	$[2]$
12.0.581641651093504.1	x^12 - 2x^10 + x^8 + 4x^6 - 3x^4 + 2x^2 + 1	\( 2^{40}\cdot 23^{2} \)	12T236	Trivial
12.0.581641651093504.2	x^12 - 10x^8 + 12x^6 + 7x^4 - 12x^2 + 4	\( 2^{40}\cdot 23^{2} \)	12T236	Trivial
12.0.801543976648704.2	x^12 - 2x^10 + 5x^8 - 4x^6 + x^4 + 2x^2 + 1	\( 2^{40}\cdot 3^{6} \)	12T236	Trivial
12.0.801543976648704.3	x^12 + 2x^8 - 4x^6 + 3x^4 - 4x^2 + 4	\( 2^{40}\cdot 3^{6} \)	12T236	Trivial
12.0.914039610015744.8	x^12 - 6x^11 + 9x^10 + 6x^9 - 15x^8 - 6x^7 + x^6 + 6x^5 + 9x^4 + 6x^3 + 15x^2 + 6x + 4	\( 2^{18}\cdot 3^{20} \)	12T236	Trivial
12.0.914039610015744.12	x^12 - 9x^10 + 45x^8 - 120x^6 + 162x^4 - 108x^2 + 36	\( 2^{18}\cdot 3^{20} \)	12T236	Trivial
12.0.1014454095446016.2	x^12 - 6x^11 + 13x^10 - 8x^9 - 8x^8 - 4x^7 + 46x^6 - 48x^5 + 3x^4 + 6x^3 + 27x^2 - 24x + 6	\( 2^{34}\cdot 3^{10} \)	12T236	$[2]$
12.0.1014454095446016.4	x^12 - 2x^11 + 5x^10 - 10x^9 + 9x^8 + 12x^7 - 14x^6 + 4x^5 + 53x^4 - 54x^3 + 55x^2 - 22x + 17	\( 2^{34}\cdot 3^{10} \)	12T236	Trivial
12.0.1201907943079936.1	x^12 - 2x^11 + 7x^10 - 8x^9 + 14x^8 + 4x^7 + 10x^6 - 40x^5 + 79x^4 - 142x^3 + 193x^2 - 112x + 64	\( 2^{32}\cdot 23^{4} \)	12T236	$[2]$
12.0.1619844835311616.3	x^12 - 2x^11 - 3x^10 + 20x^9 - 2x^8 - 68x^7 + 62x^6 + 128x^5 - 115x^4 - 34x^3 + 57x^2 - 68x + 40	\( 2^{26}\cdot 17^{6} \)	12T236	$[2]$
12.0.1828652958613504.2	x^12 - 3x^10 - 4x^8 + 16x^6 + 7x^4 - 13x^2 + 4	\( 2^{18}\cdot 17^{8} \)	12T236	Trivial
12.0.1828652958613504.5	x^12 + 4x^10 + 13x^8 + 26x^6 + 32x^4 + 36x^2 + 16	\( 2^{18}\cdot 17^{8} \)	12T236	Trivial
12.0.2021194429628416.1	x^12 - 6x^10 + 19x^8 - 4x^6 + 3x^4 + 18x^2 + 1	\( 2^{34}\cdot 7^{6} \)	12T236	Trivial
12.0.2282521714753536.2	x^12 + 6x^10 + 9x^8 + 4x^6 + 9x^4 - 6x^2 + 1	\( 2^{32}\cdot 3^{12} \)	12T236	$[2]$
12.0.2282521714753536.7	x^12 + 3x^8 - 8x^6 + 3x^4 + 24x^2 + 1	\( 2^{32}\cdot 3^{12} \)	12T236	$[2]$
12.0.2282521714753536.16	x^12 - 6x^10 + 21x^8 - 32x^6 + 24x^2 + 4	\( 2^{32}\cdot 3^{12} \)	12T236	$[2]$
12.0.2282521714753536.20	x^12 - 4x^11 + 12x^10 - 24x^9 + 31x^8 - 48x^7 + 60x^6 - 56x^5 + 54x^4 - 16x^3 + 32x^2 + 6	\( 2^{32}\cdot 3^{12} \)	12T236	Trivial
12.0.2282521714753536.24	x^12 - 2x^10 + 11x^8 - 12x^6 + 3x^4 + 6x^2 + 9	\( 2^{32}\cdot 3^{12} \)	12T236	Trivial
12.0.2326566604374016.1	x^12 + 8x^10 + 22x^8 - 18x^4 + 4	\( 2^{42}\cdot 23^{2} \)	12T236	Trivial
12.0.2326566604374016.2	x^12 + 4x^10 + 6x^8 + 8x^6 + 10x^4 + 8x^2 + 4	\( 2^{42}\cdot 23^{2} \)	12T236	Trivial
12.0.2326566604374016.3	x^12 + 8x^10 + 22x^8 + 32x^6 + 30x^4 + 16x^2 + 4	\( 2^{42}\cdot 23^{2} \)	12T236	$[2]$