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 14 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.1105126562500000000.1	x^16 - 5x^15 + 6x^14 + 5x^13 - 3x^12 - 20x^11 - 2x^10 + 25x^9 + 20x^8 - 28x^6 - 30x^5 + 2x^4 + 20x^3 + 14x^2 + 5x + 1	\( 2^{8}\cdot 5^{14}\cdot 29^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial
16.0.4415251562500000000.1	x^16 - 3x^15 + 2x^14 - 4x^13 + x^12 + 67x^11 - 160x^10 + 48x^9 + 334x^8 - 631x^7 + 535x^6 - 261x^5 + 126x^4 - 92x^3 + 48x^2 - 11x + 1	\( 2^{8}\cdot 5^{14}\cdot 41^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2]$
16.8.282912400000000000000.2	x^16 - 4x^15 + 10x^14 - 20x^13 + 15x^12 + 38x^11 - 177x^10 + 370x^9 - 520x^8 + 590x^7 - 442x^6 + 128x^5 + 160x^4 - 150x^3 - 75x^2 - 4x + 1	\( 2^{16}\cdot 5^{14}\cdot 29^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial (GRH)
16.8.1130304400000000000000.1	x^16 - 4x^15 - 7x^14 + 22x^13 + 36x^12 - 4x^11 - 50x^10 - 144x^9 - 176x^8 - 38x^7 + 35x^6 - 32x^5 - 54x^4 - 6x^3 + 17x^2 + 8x + 1	\( 2^{16}\cdot 5^{14}\cdot 41^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial (GRH)
16.0.5976745079881894723584.1	x^16 + 8x^14 + 12x^12 - 24x^10 - 82x^8 - 72x^6 + 108x^4 + 216x^2 + 81	\( 2^{66}\cdot 3^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial
16.8.5976745079881894723584.1	x^16 - 8x^14 + 12x^12 + 24x^10 - 82x^8 + 72x^6 + 108x^4 - 216x^2 + 81	\( 2^{66}\cdot 3^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial (GRH)
16.8.6710886400000000000000.2	x^16 - 10x^14 + 50x^12 - 190x^10 + 555x^8 - 1050x^6 + 1100x^4 - 500x^2 + 25	\( 2^{40}\cdot 5^{14} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial (GRH)
16.0.6710886400000000000000.3	x^16 + 10x^14 + 50x^12 + 190x^10 + 555x^8 + 1050x^6 + 1100x^4 + 500x^2 + 25	\( 2^{40}\cdot 5^{14} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2]$ (GRH)
16.8.4411897179443060791351047777488896.1	x^16 - 8x^15 - 4x^14 + 86x^13 - 3229x^12 + 22238x^11 - 101440x^10 + 213107x^9 + 2019758x^8 - 11819846x^7 + 63839077x^6 - 134418294x^5 + 322248046x^4 - 455135461x^3 - 469772490x^2 + 689350461x + 431493817	\( 2^{12}\cdot 41^{14}\cdot 73^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial (GRH)
16.8.13753742182201431148415117624283136.1	x^16 - 3x^15 - 3x^14 - 44x^13 - 4901x^12 + 18246x^11 - 116329x^10 + 344801x^9 + 8347337x^8 - 18669757x^7 - 94085134x^6 + 117404282x^5 + 283303175x^4 - 52518582x^3 - 226364881x^2 + 2139886400x - 732956425	\( 2^{12}\cdot 41^{14}\cdot 97^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	Trivial (GRH)
16.0.220059874915222898374641881988530176.1	x^16 - 6x^15 + 174x^14 - 652x^13 + 9346x^12 - 30868x^11 + 255841x^10 - 1057485x^9 + 4134399x^8 - 17495412x^7 + 55333563x^6 - 193059815x^5 + 500688278x^4 - 979188614x^3 + 1719758063x^2 - 1515380265x + 4014327025	\( 2^{16}\cdot 41^{14}\cdot 97^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2, 216554]$ (GRH)
16.0.903391827881520588378160364334874624.1	x^16 + 170x^14 + 10982x^12 + 346460x^10 + 5779728x^8 + 52887000x^6 + 261780824x^4 + 642666640x^2 + 602604304	\( 2^{40}\cdot 17^{14}\cdot 47^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2, 2, 2, 6, 2406]$ (GRH)
16.16.903391827881520588378160364334874624.1	x^16 - 102x^14 + 3638x^12 - 56100x^10 + 396304x^8 - 1213800x^6 + 1227672x^4 - 180336x^2 + 4624	\( 2^{40}\cdot 17^{14}\cdot 47^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2]$ (GRH)
16.16.903391827881520588378160364334874624.2	x^16 - 170x^14 + 10982x^12 - 346460x^10 + 5779728x^8 - 52887000x^6 + 261780824x^4 - 642666640x^2 + 602604304	\( 2^{40}\cdot 17^{14}\cdot 47^{4} \)	$C_4.C_2^2:D_4$ (as 16T209)	$[2]$ (GRH)