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 13 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.44078844068554080256.3	x^16 - 4x^15 + 2x^14 + 16x^13 - 16x^12 - 32x^11 + 46x^10 + 124x^9 + 60x^8 + 20x^7 + 276x^6 + 540x^5 + 478x^4 + 228x^3 + 28x^2 - 16x + 2	\( 2^{34}\cdot 37^{6} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.0.176315376274216321024.2	x^16 - 4x^15 + 16x^14 - 32x^13 + 54x^12 - 24x^11 + 66x^10 + 24x^9 + 170x^8 + 100x^7 + 320x^6 + 812x^5 + 1180x^4 + 1056x^3 + 594x^2 + 212x + 41	\( 2^{36}\cdot 37^{6} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.0.942760328706207514624.1	x^16 - 8x^13 - 12x^12 + 44x^11 + 16x^10 - 72x^9 + 94x^8 + 96x^7 - 340x^6 - 224x^5 + 408x^4 + 432x^3 + 152x^2 + 24x + 2	\( 2^{42}\cdot 11^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial
16.0.37787193273718832889856.1	x^16 - 2x^15 + 36x^14 - 74x^13 + 588x^12 - 1188x^11 + 5724x^10 - 10874x^9 + 35612x^8 - 59336x^7 + 138428x^6 - 184906x^5 + 306639x^4 - 290252x^3 + 326644x^2 - 169936x + 114577	\( 2^{24}\cdot 83^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.4.114073999773451109269504.1	x^16 + 4x^14 - 8x^13 + 16x^12 - 20x^11 - 16x^10 - 200x^9 - 614x^8 - 528x^7 - 996x^6 - 32x^5 + 1488x^4 + 1488x^3 + 1072x^2 - 592x - 194	\( 2^{42}\cdot 11^{10} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.4.215671155821681003462656.1	x^16 - 4x^14 - 20x^12 - 36x^10 + 6x^8 + 36x^6 - 20x^4 + 4x^2 + 1	\( 2^{36}\cdot 11^{12} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.0.3512479453921000000000000.1	x^16 - 6x^15 + 39x^14 - 112x^13 + 292x^12 - 10x^11 - 1482x^10 + 6826x^9 - 12036x^8 + 5804x^7 + 35844x^6 - 102864x^5 + 105348x^4 - 10468x^3 - 185116x^2 + 46280x + 233456	\( 2^{12}\cdot 5^{12}\cdot 37^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	$[2, 2]$ (GRH)
16.0.899194740203776000000000000.1	x^16 - 2x^15 + 17x^14 - 90x^13 + 308x^12 - 658x^11 - 1171x^10 + 32208x^9 - 105028x^8 + 6084x^7 + 904173x^6 - 2844928x^5 + 1626709x^4 + 17845836x^3 - 32073644x^2 - 29920920x + 83022676	\( 2^{20}\cdot 5^{12}\cdot 37^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	$[2, 2]$ (GRH)
16.8.2163460585448341410282471424.3	x^16 - 8x^15 + 20x^14 - 36x^13 + 92x^12 + 524x^11 - 4928x^10 + 12816x^9 - 7767x^8 - 7596x^7 + 124248x^6 - 787088x^5 + 1352106x^4 + 983556x^3 - 5330000x^2 + 5566660x - 1893457	\( 2^{44}\cdot 223^{6} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.8.2163460585448341410282471424.4	x^16 - 8x^15 + 20x^14 - 36x^13 - 280x^12 + 1644x^11 - 2588x^10 + 6808x^9 + 19499x^8 - 16092x^7 + 38240x^6 + 132400x^5 + 10452x^4 - 136060x^3 - 114020x^2 - 44556x - 7121	\( 2^{44}\cdot 223^{6} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.0.107586731453760569991937021444096.1	x^16 - 8x^15 + 204x^14 - 1260x^13 + 15852x^12 - 77252x^11 + 610208x^10 - 2252232x^9 + 11890001x^8 - 29764972x^7 + 104949032x^6 - 121487192x^5 + 325754186x^4 - 21775820x^3 + 464127720x^2 + 125219124x + 530507567	\( 2^{44}\cdot 223^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	$[2, 2, 2, 2, 8626]$ (GRH)
16.16.107586731453760569991937021444096.1	x^16 - 8x^15 - 164x^14 + 1260x^13 + 10036x^12 - 73564x^11 - 287260x^10 + 1952144x^9 + 4122561x^8 - 23144124x^7 - 33317060x^6 + 105425840x^5 + 161682534x^4 - 127064324x^3 - 284134756x^2 - 92368028x + 16653503	\( 2^{44}\cdot 223^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)
16.16.24653126142505861351650009503170816.1	x^16 - 128x^14 - 216x^13 + 5406x^12 + 13460x^11 - 101070x^10 - 308454x^9 + 858049x^8 + 3200816x^7 - 2603550x^6 - 15017698x^5 - 2998756x^4 + 24948824x^3 + 20285886x^2 + 2847754x - 502081	\( 2^{8}\cdot 37^{8}\cdot 269^{8} \)	$C_2^3:S_4.C_2$ (as 16T764)	Trivial (GRH)