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 70)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.120573447359765625.1	x^16 - x^15 + x^14 - 2x^13 + 3x^12 - 5x^11 + 4x^10 - 2x^9 + 2x^8 - x^7 + 3x^6 + 5x^5 + 4x^4 + 2x^3 + 6x^2 - 2x + 1	\( 3^{8}\cdot 5^{8}\cdot 19^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.367765683359765625.1	x^16 - 4x^15 + 14x^14 - 38x^13 + 71x^12 - 122x^11 + 165x^10 - 186x^9 + 217x^8 - 174x^7 + 180x^6 - 83x^5 + 71x^4 - 17x^3 + 14x^2 - x + 1	\( 3^{12}\cdot 5^{8}\cdot 11^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.1103215392813809664.1	x^16 - 2x^12 + 9x^10 + 21x^8 + 9x^6 - 2x^4 + 1	\( 2^{16}\cdot 3^{8}\cdot 37^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.1204374553600000000.1	x^16 + x^14 - 2x^12 - x^10 + 8x^8 + 13x^6 + 12x^4 + 8x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 19^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.1658721111359094784.2	x^16 - 8x^14 + 22x^12 - 20x^10 - 13x^8 + 36x^6 - 14x^4 - 12x^2 + 25	\( 2^{36}\cdot 17^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.1741080579875015625.1	x^16 - x^15 + 2x^14 - 7x^13 + 4x^12 - 6x^11 + 11x^10 - 2x^9 + 13x^8 + 2x^7 + 11x^6 + 6x^5 + 4x^4 + 7x^3 + 2x^2 + x + 1	\( 3^{8}\cdot 5^{6}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.1779409740577342041.1	x^16 - 3x^15 + 6x^14 - 3x^13 + 7x^12 - 12x^11 - 3x^10 - 3x^9 + 30x^8 - 42x^7 + 21x^6 + 12x^5 - 11x^4 - 6x^3 + 12x^2 - 6x + 1	\( 3^{8}\cdot 7^{8}\cdot 19^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.1779985907461265625.1	x^16 - 3x^15 + 10x^14 - 13x^13 + 27x^12 - 24x^11 + 52x^10 - 30x^9 + 49x^8 - 32x^7 + 45x^6 - 22x^5 + 22x^4 - 18x^3 + 6x^2 - 6x + 3	\( 3^{12}\cdot 5^{6}\cdot 11^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.2042457877721972736.1	x^16 - 3x^14 + 9x^12 - 2x^11 - 2x^10 + 14x^9 + 2x^8 + 6x^7 + 10x^6 + 2x^5 + 5x^4 + 2x^3 + 5x^2 + 2x + 1	\( 2^{16}\cdot 3^{8}\cdot 41^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.2069703095939497984.1	x^16 - 4x^14 + 8x^12 - 12x^10 + 14x^8 - 28x^6 + 72x^4 - 84x^2 + 49	\( 2^{44}\cdot 7^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.2656950491119878144.1	x^16 - 2x^15 + 2x^14 - 7x^12 + 18x^11 - 22x^10 + 6x^9 + 48x^8 - 60x^7 + 48x^6 + 46x^5 - 59x^4 + 60x^3 + 16x^2 - 20x + 25	\( 2^{24}\cdot 3^{8}\cdot 17^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.3811799284974616576.1	x^16 + 10x^14 + 45x^12 + 106x^10 + 132x^8 + 78x^6 + 13x^4 + 14x^2 + 1	\( 2^{32}\cdot 31^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.6338465731314712576.8	x^16 + 6x^12 + 13x^8 - 16x^4 + 4	\( 2^{40}\cdot 7^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.7731614709228515625.1	x^16 - 5x^15 + 11x^14 - 17x^13 + 46x^11 + 18x^10 - 257x^9 + 481x^8 - 424x^7 + 141x^6 + 26x^5 - 12x^4 - 22x^3 + 20x^2 - 7x + 1	\( 3^{8}\cdot 5^{12}\cdot 13^{6} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.0.13109528905069805649.1	x^16 - x^15 + 10x^14 - 12x^13 + 42x^12 - 50x^11 + 102x^10 - 88x^9 + 153x^8 - 45x^7 + 115x^6 + 37x^5 + 64x^4 + 93x^3 + 42x^2 + 27x + 9	\( 3^{8}\cdot 7^{6}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.17391168553984000000.1	x^16 + 3x^14 + 11x^12 + 28x^10 + 39x^8 + 28x^6 + 11x^4 + 3x^2 + 1	\( 2^{16}\cdot 5^{6}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.17592186044416000000.3	x^16 - 8x^14 + 24x^12 - 48x^10 + 132x^8 - 320x^6 + 456x^4 - 320x^2 + 100	\( 2^{50}\cdot 5^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.25353862925258850304.2	x^16 + 30x^8 + 1	\( 2^{42}\cdot 7^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.4.43527014496875390625.1	x^16 - 4x^14 - 7x^13 + 4x^12 + 46x^11 + 2x^10 - 134x^9 + 38x^8 + 354x^7 - 328x^6 + 24x^5 + 309x^4 - 348x^3 + 116x^2 - 115x - 29	\( 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.43527014496875390625.2	x^16 - 2x^15 + 3x^14 + 4x^13 - 6x^12 + 12x^11 + 44x^10 - 27x^9 - 25x^8 - 12x^7 + 95x^6 + 245x^5 + 378x^4 + 251x^3 + 77x^2 + 12x + 1	\( 3^{8}\cdot 5^{8}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.4.44499647686531640625.1	x^16 - 8x^14 - 9x^13 + 18x^12 + 51x^11 - 29x^10 - 108x^9 - 23x^8 + 171x^7 + 99x^6 - 111x^5 - 84x^4 - 45x^3 + 9x^2 + 18x + 9	\( 3^{12}\cdot 5^{8}\cdot 11^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.44499647686531640625.2	x^16 - 5x^15 + x^14 + 23x^13 - 5x^12 - 65x^11 + 5x^10 + 79x^9 + 52x^8 - 52x^7 - 107x^6 + 43x^5 + 58x^4 - 21x^3 - 6x^2 - 9x + 9	\( 3^{12}\cdot 5^{8}\cdot 11^{8} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.0.47991168245852798976.1	x^16 + x^12 + 5x^8 - 4x^4 + 16	\( 2^{20}\cdot 3^{8}\cdot 17^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.69528462202535765625.1	x^16 - 3x^15 + 3x^14 + 14x^10 - 24x^9 + 9x^8 - 9x^7 + 49x^4 - 21x^3 + 24x^2 - 9x + 9	\( 3^{8}\cdot 5^{6}\cdot 7^{14} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.71374101816491164089.1	x^16 - 7x^14 + 7x^12 + 28x^10 + 23x^8 + 28x^6 + 7x^4 - 7x^2 + 1	\( 3^{6}\cdot 7^{8}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.4.101415451701035401216.1	x^16 - 4x^14 + 2x^12 - 12x^10 + 3x^8 + 76x^6 + 38x^4 + 16x^2 + 1	\( 2^{44}\cdot 7^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.109951162777600000000.2	x^16 - 4x^14 - 2x^12 + 24x^10 + 23x^8 - 72x^6 + 52x^4 - 12x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.4.109951162777600000000.3	x^16 - 4x^14 - 6x^12 + 64x^10 - 141x^8 + 136x^6 - 56x^4 + 4x^2 + 1	\( 2^{48}\cdot 5^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.118192468620711297024.5	x^16 - 4x^14 + 6x^12 - 24x^10 + 66x^8 - 64x^6 + 44x^4 - 16x^2 + 4	\( 2^{54}\cdot 3^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.118192468620711297024.8	x^16 - 8x^14 + 32x^12 - 72x^10 + 104x^8 - 96x^6 + 32x^4 + 16x^2 + 4	\( 2^{54}\cdot 3^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.119842600295694598144.1	x^16 + 6x^14 + 9x^12 + 8x^10 + 60x^8 + 74x^6 + 33x^4 + 8x^2 + 1	\( 2^{34}\cdot 17^{8} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.4.119842600295694598144.3	x^16 - 6x^14 + 9x^12 - 8x^10 + 60x^8 - 74x^6 + 33x^4 - 8x^2 + 1	\( 2^{34}\cdot 17^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.4.145182542873291015625.1	x^16 - 7x^15 + 21x^14 - 30x^13 + x^12 + 84x^11 - 145x^10 + 89x^9 + 42x^8 - 77x^7 - 85x^6 - 3x^5 + 121x^4 + 30x^3 - 66x^2 - 26x + 1	\( 3^{6}\cdot 5^{12}\cdot 13^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.167811319195789492224.1	x^16 - x^14 + 7x^12 + 28x^10 + 11x^8 + 28x^6 + 7x^4 - x^2 + 1	\( 2^{16}\cdot 3^{6}\cdot 37^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.182059119829942534144.2	x^16 - 2x^15 + 2x^14 + 12x^9 + 4x^8 - 4x^7 + 49x^4 - 14x^3 + 2x^2 - 4x + 4	\( 2^{28}\cdot 7^{14} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.0.193134617229266015625.1	x^16 - 6x^14 + 21x^12 - 42x^10 + 84x^8 - 231x^6 + 469x^4 - 510x^2 + 225	\( 3^{6}\cdot 5^{8}\cdot 7^{14} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.210119944214597861376.2	x^16 - 12x^12 + 42x^8 + 28x^4 + 9	\( 2^{58}\cdot 3^{6} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.214585730778164760576.1	x^16 - 3x^15 + 8x^14 - 11x^13 + 17x^12 - 16x^11 + 34x^10 - 30x^9 + 16x^8 - 30x^7 + 34x^6 - 16x^5 + 17x^4 - 11x^3 + 8x^2 - 3x + 1	\( 2^{12}\cdot 3^{8}\cdot 41^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.228946194553787908096.1	x^16 + 3x^14 + x^12 - 26x^10 + 50x^8 - 26x^6 + x^4 + 3x^2 + 1	\( 2^{28}\cdot 31^{8} \)	$C_2\times D_8$ (as 16T29)	$[3]$
16.4.434779213849600000000.1	x^16 - 2x^14 + 17x^12 - 87x^10 + 268x^8 - 701x^6 + 1208x^4 - 1064x^2 + 361	\( 2^{16}\cdot 5^{8}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.434779213849600000000.2	x^16 + 2x^14 - 9x^12 - 4x^10 + 41x^8 - 115x^6 + 149x^4 - 65x^2 + 25	\( 2^{16}\cdot 5^{8}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.0.439804651110400000000.4	x^16 - 8x^14 + 16x^12 + 16x^10 - 28x^8 + 96x^6 + 104x^4 - 32x^2 + 4	\( 2^{50}\cdot 5^{8} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.0.472769874482845188096.1	x^16 + 6x^12 - 16x^10 + 37x^8 - 48x^6 + 58x^4 - 8x^2 + 1	\( 2^{56}\cdot 3^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.472769874482845188096.4	x^16 - 12x^12 + 52x^8 - 48x^4 + 16	\( 2^{56}\cdot 3^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.479370401182778392576.1	x^16 - 4x^15 + 10x^14 - 48x^13 + 158x^12 - 320x^11 + 614x^10 - 1004x^9 + 606x^8 + 804x^7 - 970x^6 - 1328x^5 + 3606x^4 - 3744x^3 + 2362x^2 - 884x + 145	\( 2^{36}\cdot 17^{8} \)	$C_2\times D_8$ (as 16T29)	$[4]$ (GRH)
16.4.642366916348420476801.1	x^16 - 8x^15 + 18x^14 + 14x^13 - 106x^12 + 90x^11 + 136x^10 - 218x^9 - 44x^8 + 186x^7 - 46x^6 + 2x^5 - 84x^4 + 88x^3 - 8x^2 - 21x + 9	\( 3^{8}\cdot 7^{8}\cdot 19^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial
16.0.728236479319770136576.2	x^16 - 2x^14 + 14x^10 + 49x^4 + 26x^2 + 4	\( 2^{30}\cdot 7^{14} \)	$C_2\times D_8$ (as 16T29)	$[2]$
16.4.767858691933644783616.1	x^16 + 4x^14 - 2x^13 - 23x^12 + 82x^11 - 100x^10 + 40x^9 + 217x^8 - 4x^7 + 12x^6 + 102x^5 + 79x^4 - 302x^3 - 556x^2 - 300x - 50	\( 2^{24}\cdot 3^{8}\cdot 17^{8} \)	$C_2\times D_8$ (as 16T29)	Trivial (GRH)
16.0.767858691933644783616.2	x^16 - 8x^15 + 44x^14 - 162x^13 + 457x^12 - 978x^11 + 1646x^10 - 2074x^9 + 1928x^8 - 1024x^7 + 32x^6 + 522x^5 - 375x^4 + 34x^3 + 134x^2 - 102x + 25	\( 2^{24}\cdot 3^{8}\cdot 17^{8} \)	$C_2\times D_8$ (as 16T29)	$[2]$ (GRH)
16.0.915784778215151632384.1	x^16 + 126x^8 + 1	\( 2^{30}\cdot 31^{8} \)	$C_2\times D_8$ (as 16T29)	$[3]$