Global number field search results

Further refine search

Degree	Signature	Galois group	Class number	Class group
Regulator	Num. ramified primes	Ramified primes		Unramified primes
CM field	Discriminant		Root discriminant

Results (displaying all 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
16.0.71677562524821909.1	x^16 - 6x^15 + 19x^14 - 40x^13 + 60x^12 - 63x^11 + 47x^10 - 39x^9 + 64x^8 - 91x^7 + 66x^6 - 5x^5 - 26x^4 + 16x^3 - 3x + 1	\( 3^{8}\cdot 22189^{3} \)	16T1651	Trivial
16.0.71677562524821909.2	x^16 - 6x^15 + 20x^14 - 50x^13 + 93x^12 - 118x^11 + 90x^10 - 30x^9 + 5x^8 - 25x^7 + 35x^6 - 19x^5 - 2x^4 + 13x^3 - 5x^2 - 2x + 1	\( 3^{8}\cdot 22189^{3} \)	16T1651	Trivial
16.4.8195775610914453125.2	x^16 - 7x^15 + 25x^14 - 57x^13 + 87x^12 - 114x^11 + 167x^10 - 231x^9 + 282x^8 - 288x^7 + 208x^6 - 105x^5 + 24x^4 + 9x^3 - 6x^2 + 3x + 1	\( 5^{8}\cdot 27581^{3} \)	16T1651	Trivial
16.4.8195775610914453125.3	x^16 - 7x^15 + 19x^14 - 19x^13 - 34x^12 + 169x^11 - 312x^10 + 252x^9 + 171x^8 - 836x^7 + 1344x^6 - 1335x^5 + 884x^4 - 381x^3 + 94x^2 - 8x - 1	\( 5^{8}\cdot 27581^{3} \)	16T1651	Trivial
16.10.672488745723457421875.1	x^16 - 6x^15 + 10x^14 + 9x^13 - 75x^12 + 132x^11 - 13x^10 - 297x^9 + 296x^8 + 225x^7 - 338x^6 - 122x^5 + 191x^4 + 43x^3 - 72x^2 + 16x - 1	\( -\,5^{8}\cdot 119851^{3} \)	16T1651	Trivial (GRH)
16.10.672488745723457421875.2	x^16 - x^15 - 11x^14 + 6x^13 + 38x^12 - 18x^11 - 51x^10 + 48x^9 + 63x^8 - 27x^7 - 60x^6 - 33x^5 - 23x^4 - 10x^3 + 15x^2 + 5x - 1	\( -\,5^{8}\cdot 119851^{3} \)	16T1651	Trivial (GRH)
16.2.960464752179926171875.2	x^16 - x^15 - 3x^14 + 8x^13 - x^12 + 34x^10 - 5x^9 + 20x^8 + 54x^7 - 28x^6 + 69x^5 + 72x^4 - 22x^3 - 70x^2 + 42x - 19	\( -\,5^{8}\cdot 71^{3}\cdot 1901^{3} \)	16T1651	Trivial
16.2.960464752179926171875.3	x^16 + 3x^14 - 3x^13 - 13x^12 + 14x^11 + 5x^10 + 22x^9 - 133x^8 + 191x^7 - 186x^6 + 258x^5 - 163x^4 + 156x^3 - 399x^2 + 367x - 149	\( -\,5^{8}\cdot 71^{3}\cdot 1901^{3} \)	16T1651	Trivial
16.0.1761575905283218445703125.1	x^16 - x^15 + 12x^14 - 28x^13 + 95x^12 - 280x^11 + 677x^10 - 1543x^9 + 2994x^8 - 4629x^7 + 6754x^6 - 7815x^5 + 7991x^4 - 7966x^3 + 6147x^2 - 3337x + 3089	\( 5^{8}\cdot 1652141^{3} \)	16T1651	$[30]$ (GRH)
16.0.1761575905283218445703125.2	x^16 - 3x^15 + 11x^14 - 5x^13 - 19x^12 + 85x^11 - 24x^10 - 453x^9 + 1367x^8 - 1610x^7 - 165x^6 + 2664x^5 + 4200x^4 - 24189x^3 + 49513x^2 - 47515x + 25771	\( 5^{8}\cdot 1652141^{3} \)	16T1651	$[30]$ (GRH)
16.16.1100984940802011528564453125.1	x^16 - 4x^15 - 48x^14 + 156x^13 + 946x^12 - 2333x^11 - 9304x^10 + 17736x^9 + 46648x^8 - 76303x^7 - 110738x^6 + 184878x^5 + 91541x^4 - 210015x^3 + 21185x^2 + 70000x - 24155	\( 5^{12}\cdot 1652141^{3} \)	16T1651	Trivial (GRH)
16.16.1100984940802011528564453125.2	x^16 - x^15 - 56x^14 + 38x^13 + 1183x^12 - 642x^11 - 12113x^10 + 6644x^9 + 63489x^8 - 41070x^7 - 158038x^6 + 127414x^5 + 130478x^4 - 136791x^3 + 22158x^2 - 910x + 11	\( 5^{12}\cdot 1652141^{3} \)	16T1651	Trivial (GRH)