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 all 38 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.4.169818168100000000.1	x^16 - 4x^14 + 10x^12 - 16x^10 + 5x^8 + 12x^6 - 7x^4 - x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 7^{4}\cdot 29^{4} \)	16T1701	Trivial
16.0.748709478400000000.1	x^16 - 2x^15 + 3x^14 - 2x^13 - 3x^12 + 6x^11 - 8x^10 - 10x^9 + 48x^8 - 90x^7 + 122x^6 - 114x^5 + 83x^4 - 44x^3 + 17x^2 - 4x + 1	\( 2^{26}\cdot 5^{8}\cdot 13^{4} \)	16T1701	Trivial
16.4.887213286400000000.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 69x^12 - 50x^11 + 13x^10 + 12x^9 - 22x^8 + 38x^7 - 49x^6 + 32x^5 - 12x^4 + 8x^3 - 4x^2 + 1	\( 2^{16}\cdot 5^{8}\cdot 7^{2}\cdot 29^{4} \)	16T1701	Trivial
16.4.4536559206400000000.3	x^16 - 8x^15 + 26x^14 - 40x^13 + 14x^12 + 64x^11 - 136x^10 + 92x^9 + 81x^8 - 216x^7 + 188x^6 - 84x^5 + 32x^4 - 24x^3 + 14x^2 - 4x - 1	\( 2^{36}\cdot 5^{8}\cdot 13^{2} \)	16T1701	Trivial (GRH)
16.0.8321090236900000000.1	x^16 + 4x^14 + 5x^12 - 7x^10 - 50x^8 - 49x^6 + 91x^4 + 147x^2 + 49	\( 2^{8}\cdot 5^{8}\cdot 7^{6}\cdot 29^{4} \)	16T1701	Trivial
16.0.9879530825073033216.1	x^16 + x^12 - 2x^10 - 2x^8 + 2x^6 + 10x^4 + 6x^2 + 1	\( 2^{32}\cdot 3^{4}\cdot 73^{4} \)	16T1701	Trivial
16.0.9879530825073033216.2	x^16 - 6x^14 + 17x^12 - 30x^10 + 34x^8 - 24x^6 + 10x^4 - 2x^2 + 1	\( 2^{32}\cdot 3^{4}\cdot 73^{4} \)	16T1701	Trivial
16.0.11979351654400000000.2	x^16 - 6x^14 + 17x^12 - 30x^10 + 43x^8 - 36x^6 + 30x^4 - 12x^2 + 4	\( 2^{30}\cdot 5^{8}\cdot 13^{4} \)	16T1701	Trivial
16.8.20117736678400000000.1	x^16 - 4x^15 + 4x^14 + 14x^13 - 63x^12 + 108x^11 - 7x^10 - 336x^9 + 600x^8 - 274x^7 - 441x^6 + 744x^5 - 474x^4 + 138x^3 - 6x^2 - 6x + 1	\( 2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 97^{2} \)	16T1701	Trivial (GRH)
16.8.20117736678400000000.2	x^16 - 2x^15 - 4x^14 + 15x^12 + 24x^11 - 16x^10 - 54x^9 - 36x^8 + 32x^7 + 69x^6 + 26x^5 - 31x^4 - 38x^3 - 4x^2 + 6x + 1	\( 2^{16}\cdot 5^{8}\cdot 17^{4}\cdot 97^{2} \)	16T1701	Trivial (GRH)
16.4.72584947302400000000.3	x^16 - 6x^14 - 4x^13 + 4x^12 + 16x^11 + 40x^10 - 40x^9 - 113x^8 + 32x^7 + 156x^6 - 144x^5 + 88x^4 - 88x^3 + 50x^2 - 12x + 1	\( 2^{40}\cdot 5^{8}\cdot 13^{2} \)	16T1701	Trivial (GRH)
16.0.1644750202470400000000.1	x^16 + 8x^14 + 39x^12 + 122x^10 + 227x^8 + 244x^6 + 144x^4 + 40x^2 + 4	\( 2^{26}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial
16.4.1644750202470400000000.1	x^16 + 4x^14 + 6x^12 + 14x^10 + 27x^8 + 2x^6 - 54x^4 - 20x^2 + 4	\( 2^{26}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial
16.8.1644750202470400000000.1	x^16 - 8x^14 + 39x^12 - 122x^10 + 227x^8 - 244x^6 + 144x^4 - 40x^2 + 4	\( 2^{26}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.4.1644750202470400000000.2	x^16 - 4x^14 + 6x^12 - 14x^10 + 27x^8 - 2x^6 - 54x^4 + 20x^2 + 4	\( 2^{26}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.8.1644750202470400000000.2	x^16 - 6x^14 + 16x^12 - 31x^10 + 37x^8 - 8x^6 - 14x^4 + 4	\( 2^{26}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.4.2130199100646400000000.2	x^16 - 8x^15 + 44x^14 - 168x^13 + 505x^12 - 1210x^11 + 2365x^10 - 3784x^9 + 4913x^8 - 5110x^7 + 4081x^6 - 2328x^5 + 752x^4 + 46x^3 - 175x^2 + 76x - 11	\( 2^{16}\cdot 5^{8}\cdot 7^{6}\cdot 29^{4} \)	16T1701	Trivial (GRH)
16.0.5150140589670400000000.1	x^16 - 2x^15 + 4x^14 - 6x^13 + 38x^12 - 116x^11 + 318x^10 - 542x^9 + 495x^8 - 296x^7 + 70x^6 + 1122x^5 - 3122x^4 + 2030x^3 + 2886x^2 - 5340x + 2801	\( 2^{24}\cdot 5^{8}\cdot 17^{4}\cdot 97^{2} \)	16T1701	$[2]$ (GRH)
16.0.5150140589670400000000.2	x^16 - 8x^15 + 44x^14 - 158x^13 + 449x^12 - 950x^11 + 1622x^10 - 2028x^9 + 1863x^8 - 824x^7 - 376x^6 + 1112x^5 - 871x^4 + 202x^3 + 200x^2 - 126x + 29	\( 2^{24}\cdot 5^{8}\cdot 17^{4}\cdot 97^{2} \)	16T1701	$[2]$ (GRH)
16.12.105264012958105600000000.1	x^16 - 40x^12 + 116x^10 - 67x^8 - 60x^6 + 64x^4 - 16x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.4.105264012958105600000000.1	x^16 - 40x^12 - 116x^10 - 67x^8 + 60x^6 + 64x^4 + 16x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.12.105264012958105600000000.2	x^16 - 6x^14 - 19x^12 + 90x^10 + 25x^8 - 360x^6 + 396x^4 - 144x^2 + 16	\( 2^{32}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.8.105264012958105600000000.3	x^16 + 10x^14 + 15x^12 - 62x^10 - 52x^8 + 110x^6 + 11x^4 - 18x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.8.105264012958105600000000.4	x^16 - 10x^14 + 15x^12 + 62x^10 - 52x^8 - 110x^6 + 11x^4 + 18x^2 + 1	\( 2^{32}\cdot 5^{8}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.0.149170955649433600000000.1	x^16 - 6x^15 + 19x^14 - 32x^13 - 18x^12 + 254x^11 - 741x^10 + 1116x^9 - 105x^8 - 2688x^7 + 6769x^6 - 10634x^5 + 11148x^4 - 7042x^3 + 3189x^2 - 750x + 125	\( 2^{20}\cdot 5^{8}\cdot 41^{4}\cdot 359^{2} \)	16T1701	Trivial (GRH)
16.0.149170955649433600000000.2	x^16 + 4x^14 - 18x^13 + 24x^12 - 114x^11 + 191x^10 - 185x^9 + 587x^8 - 388x^7 + 1057x^6 + 465x^5 - 594x^4 + 240x^3 - 1391x^2 - 765x + 1205	\( 2^{20}\cdot 5^{8}\cdot 41^{4}\cdot 359^{2} \)	16T1701	Trivial (GRH)
16.8.265688012523201557135616.1	x^16 - 4x^14 - 45x^12 + 164x^10 + 237x^8 - 724x^6 - 31x^4 + 18x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 7^{8}\cdot 11^{4}\cdot 37^{4} \)	16T1701	Trivial (GRH)
16.8.265688012523201557135616.2	x^16 - 3x^14 - 10x^12 + 25x^10 + 27x^8 - 53x^6 - 24x^4 + 31x^2 + 1	\( 2^{8}\cdot 3^{8}\cdot 7^{8}\cdot 11^{4}\cdot 37^{4} \)	16T1701	Trivial (GRH)
16.4.562116786825947096088576.1	x^16 - 8x^15 + 16x^14 + 18x^13 - 65x^12 - 56x^11 + 188x^10 + 248x^9 - 1511x^8 + 3646x^7 - 5886x^6 + 6040x^5 - 3632x^4 + 1152x^3 - 288x + 144	\( 2^{16}\cdot 3^{8}\cdot 7^{8}\cdot 11^{2}\cdot 37^{4} \)	16T1701	Trivial (GRH)
16.4.562116786825947096088576.2	x^16 - 8x^15 + 23x^14 - 2x^13 - 130x^12 + 206x^11 + 214x^10 - 780x^9 + 95x^8 + 1522x^7 - 724x^6 - 2070x^5 + 416x^4 + 1596x^3 + 681x^2 + 148x + 37	\( 2^{16}\cdot 3^{8}\cdot 7^{8}\cdot 11^{2}\cdot 37^{4} \)	16T1701	Trivial (GRH)
16.0.486740795918280294400000000.1	x^16 - 4x^14 + 4x^12 + 104x^10 - 177x^8 - 872x^6 + 10644x^4 - 11968x^2 + 4624	\( 2^{36}\cdot 5^{8}\cdot 17^{2}\cdot 89^{4} \)	16T1701	$[2]$ (GRH)
16.0.486740795918280294400000000.2	x^16 + 12x^14 + 60x^12 + 136x^10 + 110x^8 - 92x^6 - 76x^4 - 136x^2 + 289	\( 2^{36}\cdot 5^{8}\cdot 17^{2}\cdot 89^{4} \)	16T1701	$[2]$ (GRH)
16.8.35167022505095751270400000000.1	x^16 - 4x^14 - 90x^12 + 316x^10 + 1252x^8 - 1264x^6 - 1392x^4 + 576x^2 + 64	\( 2^{34}\cdot 5^{8}\cdot 17^{4}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.8.35167022505095751270400000000.2	x^16 + 4x^14 - 90x^12 - 316x^10 + 1252x^8 + 1264x^6 - 1392x^4 - 576x^2 + 64	\( 2^{34}\cdot 5^{8}\cdot 17^{4}\cdot 89^{4} \)	16T1701	Trivial (GRH)
16.0.79230447076976256614400000000.1	x^16 + 32x^14 + 405x^12 + 2595x^10 + 9014x^8 + 17061x^6 + 16797x^4 + 7587x^2 + 1089	\( 2^{28}\cdot 3^{6}\cdot 5^{8}\cdot 1009^{4} \)	16T1701	$[2, 220]$ (GRH)
16.16.79230447076976256614400000000.1	x^16 - 32x^14 + 405x^12 - 2595x^10 + 9014x^8 - 17061x^6 + 16797x^4 - 7587x^2 + 1089	\( 2^{28}\cdot 3^{6}\cdot 5^{8}\cdot 1009^{4} \)	16T1701	Trivial (GRH)
16.0.316921788307905026457600000000.1	x^16 + 24x^14 + 232x^12 + 1152x^10 + 3101x^8 + 4380x^6 + 2886x^4 + 684x^2 + 36	\( 2^{30}\cdot 3^{6}\cdot 5^{8}\cdot 1009^{4} \)	16T1701	$[2, 2, 110]$ (GRH)
16.16.316921788307905026457600000000.1	x^16 - 24x^14 + 232x^12 - 1152x^10 + 3101x^8 - 4380x^6 + 2886x^4 - 684x^2 + 36	\( 2^{30}\cdot 3^{6}\cdot 5^{8}\cdot 1009^{4} \)	16T1701	Trivial (GRH)