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 36 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.5572562780160000.1	x^16 - 2x^14 - 7x^12 + 4x^10 + 34x^8 + 50x^6 + 32x^4 + 8x^2 + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{4} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.12548716987355136.1	x^16 - 7x^15 + 25x^14 - 56x^13 + 92x^12 - 133x^11 + 194x^10 - 266x^9 + 301x^8 - 266x^7 + 194x^6 - 133x^5 + 92x^4 - 56x^3 + 25x^2 - 7x + 1	\( 2^{12}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.22799473113563136.1	x^16 + 8x^12 - 40x^10 + 50x^8 - 32x^6 + 24x^4 - 8x^2 + 1	\( 2^{48}\cdot 3^{4} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.110979264025334016.1	x^16 - 4x^15 + 6x^14 + x^13 - 18x^12 + 24x^11 + 19x^10 - 119x^9 + 246x^8 - 355x^7 + 409x^6 - 387x^5 + 288x^4 - 154x^3 + 54x^2 - 11x + 1	\( 2^{8}\cdot 3^{12}\cdot 13^{8} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.584325558976905216.1	x^16 - 2x^14 - 4x^12 + 16x^10 - 5x^8 - 28x^6 + 32x^4 - 10x^2 + 1	\( 2^{40}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.703687441776640000.1	x^16 - 4x^12 + 6x^8 + 4x^4 + 1	\( 2^{50}\cdot 5^{4} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.1426576071720960000.3	x^16 - 8x^14 + 23x^12 - 32x^10 + 37x^8 - 40x^6 + 23x^4 - 4x^2 + 1	\( 2^{32}\cdot 3^{12}\cdot 5^{4} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.1459166279268040704.2	x^16 - 4x^14 - 16x^13 + 64x^12 - 64x^11 + 24x^10 - 136x^9 + 374x^8 - 360x^7 + 56x^6 + 128x^5 - 52x^4 - 48x^3 + 48x^2 - 16x + 2	\( 2^{54}\cdot 3^{4} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.1846757322198614016.9	x^16 - 8x^15 + 32x^14 - 80x^13 + 148x^12 - 232x^11 + 316x^10 - 328x^9 + 190x^8 + 56x^7 - 264x^6 + 312x^5 - 184x^4 - 16x^3 + 128x^2 - 104x + 34	\( 2^{48}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.1883091842914980096.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 55x^12 + 34x^11 - 176x^10 + 187x^9 + 52x^8 - 384x^7 + 297x^6 + 282x^5 - 330x^4 - 153x^3 + 108x^2 + 63x + 9	\( 2^{8}\cdot 3^{12}\cdot 7^{12} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.3482851737600000000.1	x^16 - 8x^15 + 26x^14 - 42x^13 + 30x^12 + 2x^11 - 50x^10 + 184x^9 - 140x^8 - 522x^7 + 1272x^6 - 1220x^5 + 621x^4 - 186x^3 + 40x^2 - 8x + 1	\( 2^{24}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.5641101078795050625.1	x^16 - 8x^15 + 28x^14 - 56x^13 + 83x^12 - 134x^11 + 220x^10 - 253x^9 + 196x^8 - 168x^7 + 187x^6 - 144x^5 + 58x^4 - 11x^3 - 2x^2 + 3x + 1	\( 3^{12}\cdot 5^{4}\cdot 19^{8} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.9349208943630483456.2	x^16 - 8x^14 + 14x^12 + 28x^10 - 53x^8 - 124x^6 + 218x^4 - 28x^2 + 1	\( 2^{44}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.28410691590485508096.2	x^16 - 5x^14 + 7x^12 + 37x^10 + 64x^8 + 37x^6 + 7x^4 - 5x^2 + 1	\( 2^{16}\cdot 3^{12}\cdot 13^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.8.50024641296100000000.1	x^16 - x^14 - 16x^12 - 9x^10 + 29x^8 + 9x^6 - 16x^4 + x^2 + 1	\( 2^{8}\cdot 5^{8}\cdot 29^{8} \)	$C_2^2:D_4$ (as 16T43)	Trivial (GRH)
16.0.51399544780206637056.1	x^16 - 8x^15 + 28x^14 - 50x^13 + 59x^12 - 56x^11 + 67x^10 - 148x^9 + 196x^8 - 132x^7 + 235x^6 + 115x^4 - 20x^3 + 7x^2 - 6x + 1	\( 2^{24}\cdot 3^{12}\cdot 7^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$ (GRH)
16.0.118192468620711297024.4	x^16 - 16x^14 + 132x^12 - 472x^10 + 872x^8 - 368x^6 + 184x^4 - 48x^2 + 4	\( 2^{54}\cdot 3^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.8.149587343098087735296.1	x^16 - 8x^14 - 8x^13 + 28x^12 + 24x^11 - 20x^10 + 10x^8 - 112x^7 - 56x^6 + 40x^5 + 56x^4 + 64x^3 + 16x^2 - 8x - 2	\( 2^{48}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T43)	Trivial (GRH)
16.0.149587343098087735296.4	x^16 - 4x^14 + 22x^12 - 76x^10 + 118x^8 - 76x^6 + 22x^4 - 4x^2 + 1	\( 2^{48}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T43)	Trivial
16.0.149587343098087735296.5	x^16 + 4x^14 + 22x^12 + 76x^10 + 118x^8 + 76x^6 + 22x^4 + 4x^2 + 1	\( 2^{48}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T43)	Trivial (GRH)
16.0.149587343098087735296.12	x^16 - 8x^13 + 8x^12 + 24x^11 + 60x^10 - 72x^8 - 128x^7 + 24x^6 + 240x^5 + 396x^4 + 344x^3 + 204x^2 + 80x + 25	\( 2^{48}\cdot 3^{12} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.439804651110400000000.6	x^16 - 4x^12 + 214x^8 - 700x^4 + 625	\( 2^{50}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.482071511786234904576.3	x^16 - 2x^15 - 4x^14 + 14x^13 - x^12 - 58x^11 + 111x^10 + 30x^9 - 269x^8 + 78x^7 + 354x^6 - 394x^5 + 485x^4 - 742x^3 + 518x^2 - 140x + 28	\( 2^{16}\cdot 3^{12}\cdot 7^{12} \)	$C_2^2:D_4$ (as 16T43)	$[2]$
16.0.891610044825600000000.17	x^16 - 4x^14 - 28x^12 + 164x^10 + 1366x^8 + 3520x^6 + 4325x^4 + 2500x^2 + 625	\( 2^{32}\cdot 3^{12}\cdot 5^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2]$ (GRH)
16.0.2176782336000000000000.4	x^16 - 14x^14 + 83x^12 - 290x^10 + 781x^8 - 1720x^6 + 2012x^4 + 32x^2 + 16	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_2^2:D_4$ (as 16T43)	$[4]$
16.0.2176782336000000000000.6	x^16 + 10x^14 - 2x^13 + 40x^12 + 30x^11 + 34x^10 + 150x^9 + 85x^8 + 122x^7 + 280x^6 + 220x^5 + 206x^4 + 280x^3 + 280x^2 + 160x + 40	\( 2^{24}\cdot 3^{12}\cdot 5^{12} \)	$C_2^2:D_4$ (as 16T43)	$[4]$ (GRH)
16.0.3525688174246906640625.2	x^16 - 8x^15 + 16x^14 + 28x^13 - 100x^12 - 128x^11 + 478x^10 + 404x^9 - 1586x^8 - 348x^7 + 2548x^6 - 300x^5 - 1715x^4 + 484x^3 + 358x^2 - 132x + 49	\( 3^{12}\cdot 5^{8}\cdot 19^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2, 2]$ (GRH)
16.0.7273137047164290072576.1	x^16 - 6x^15 + 14x^14 - 12x^13 - 15x^12 + 54x^11 - 76x^10 + 84x^9 + 4x^8 - 258x^7 + 468x^6 - 666x^5 + 750x^4 - 180x^3 - 270x^2 + 117	\( 2^{24}\cdot 3^{12}\cdot 13^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2, 2]$
16.0.64831935119745600000000.1	x^16 + 5x^14 + 17x^12 + 70x^10 + 266x^8 + 350x^6 + 425x^4 + 625x^2 + 625	\( 2^{12}\cdot 3^{4}\cdot 5^{8}\cdot 29^{8} \)	$C_2^2:D_4$ (as 16T43)	$[10]$
16.0.780855280180961608728576.1	x^16 - 8x^15 + 32x^14 - 84x^13 + 186x^12 - 388x^11 + 724x^10 - 1112x^9 + 1537x^8 - 2028x^7 + 2400x^6 - 2288x^5 + 2904x^4 - 3372x^3 + 2500x^2 - 1004x + 1633	\( 2^{44}\cdot 3^{12}\cdot 17^{4} \)	$C_2^2:D_4$ (as 16T43)	$[2, 10]$ (GRH)
16.16.780855280180961608728576.1	x^16 - 8x^15 + 8x^14 + 84x^13 - 210x^12 - 196x^11 + 1024x^10 - 368x^9 - 1691x^8 + 1668x^7 + 492x^6 - 1280x^5 + 468x^4 + 60x^3 - 56x^2 + 4x + 1	\( 2^{44}\cdot 3^{12}\cdot 17^{4} \)	$C_2^2:D_4$ (as 16T43)	Trivial (GRH)
16.0.3488168408344511962890625.1	x^16 - 4x^15 + 29x^14 - 84x^13 + 302x^12 - 590x^11 + 1255x^10 - 1527x^9 + 2108x^8 - 1523x^7 + 1555x^6 - 147x^5 + 271x^4 + 245x^3 + 410x^2 + 255x + 45	\( 5^{12}\cdot 13^{4}\cdot 29^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2, 4]$ (GRH)
16.0.3488168408344511962890625.2	x^16 - 5x^15 + 16x^14 - 31x^13 + 85x^12 - 182x^11 + 605x^10 - 1411x^9 + 3417x^8 - 6374x^7 + 8857x^6 - 10495x^5 + 7504x^4 - 5933x^3 + 4037x^2 + 464x + 1856	\( 5^{12}\cdot 13^{4}\cdot 29^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2, 8]$ (GRH)
16.0.5251386744699393600000000.1	x^16 + 35x^14 + 458x^12 + 2935x^10 + 10018x^8 + 18495x^6 + 17793x^4 + 8100x^2 + 1296	\( 2^{12}\cdot 3^{8}\cdot 5^{8}\cdot 29^{8} \)	$C_2^2:D_4$ (as 16T43)	$[4]$ (GRH)
16.0.7984925229121000000000000.1	x^16 + 31x^14 + 391x^12 + 2571x^10 + 9351x^8 + 18270x^6 + 16840x^4 + 5200x^2 + 400	\( 2^{12}\cdot 5^{12}\cdot 41^{8} \)	$C_2^2:D_4$ (as 16T43)	$[2, 8]$ (GRH)
16.16.7984925229121000000000000.1	x^16 - 4x^15 - 23x^14 + 98x^13 + 159x^12 - 730x^11 - 588x^10 + 2329x^9 + 1577x^8 - 3229x^7 - 2545x^6 + 1352x^5 + 1425x^4 + 76x^3 - 129x^2 - 15x + 1	\( 2^{12}\cdot 5^{12}\cdot 41^{8} \)	$C_2^2:D_4$ (as 16T43)	Trivial (GRH)