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 11 matches)

Label	Polynomial	Discriminant	Galois group	Class group
19.1.27217203547650508966391.1	x^19 - x^18 + 2x^17 - 5x^16 + 8x^15 - 14x^14 + 13x^13 - 10x^12 - x^11 + 9x^10 - 18x^9 + 25x^8 - 10x^7 - 4x^6 + 38x^5 - 42x^4 + 37x^3 - 16x^2 + 4x + 1	\( -\,311^{9} \)	$D_{19}$ (as 19T2)	Trivial
19.1.99048986760825351881639.1	x^19 - 2x^18 + 2x^17 - 2x^16 - 3x^15 + 14x^14 - 7x^13 - 22x^12 + 30x^11 - 9x^10 + 5x^9 - 2x^8 - 51x^7 + 90x^6 - 19x^5 - 91x^4 + 113x^3 - 59x^2 + 14x - 1	\( -\,359^{9} \)	$D_{19}$ (as 19T2)	Trivial
19.1.467562425055097089773569879.1	x^19 - 5x^18 + 10x^17 - 5x^16 + 9x^15 - 42x^14 + 51x^13 - 6x^12 - 23x^11 + 4x^10 - 29x^9 + 112x^8 - 63x^7 - 147x^6 + 183x^5 + 15x^4 - 77x^3 - 17x^2 + 37x + 1	\( -\,919^{9} \)	$D_{19}$ (as 19T2)	Trivial
19.1.1733003264116942402576542823.1	x^19 + 9x^17 - 10x^16 + 8x^15 - 45x^14 + 39x^13 + 7x^12 + 42x^11 - 36x^10 - 60x^9 + 9x^8 + 55x^7 + 63x^6 + 15x^5 - 88x^4 - 7x^3 + 27x^2 + 51x + 1	\( -\,1063^{9} \)	$D_{19}$ (as 19T2)	Trivial
19.1.5121210743359411191500170799.1	x^19 - 3x^18 + 17x^17 - 47x^16 + 135x^15 - 310x^14 + 709x^13 - 1319x^12 + 2423x^11 - 3757x^10 + 5497x^9 - 6561x^8 + 7142x^7 - 5699x^6 + 4212x^5 - 1490x^4 + 482x^3 + 408x^2 - 210x + 49	\( -\,11^{9}\cdot 109^{9} \)	$D_{19}$ (as 19T2)	Trivial
19.1.47312447868976594992787109375.1	x^19 - 6x^18 + 18x^17 - 22x^16 - 38x^15 + 219x^14 - 403x^13 + 380x^12 - 536x^11 + 1378x^10 - 1608x^9 + 691x^8 - 1073x^7 + 1881x^6 - 757x^5 + 716x^4 - 1464x^3 + 513x^2 - 10x + 295	\( -\,5^{9}\cdot 307^{9} \)	$D_{19}$ (as 19T2)	Trivial (GRH)
19.1.49578494467761916312526550343.1	x^19 - 9x^18 + 24x^17 - 6x^16 - 42x^15 + 4x^14 + 34x^13 + 74x^12 + 46x^11 - 238x^10 - 49x^9 + 181x^8 + 195x^7 + 116x^6 - 193x^5 - 275x^4 + 106x^3 - 8x^2 + 121x - 1	\( -\,1543^{9} \)	$D_{19}$ (as 19T2)	Trivial (GRH)
19.1.101575284882268140616515967431.1	x^19 - 5x^18 + 11x^17 - 10x^16 + 3x^15 + 3x^14 - 80x^13 + 481x^12 - 1180x^11 + 1220x^10 + 888x^9 - 5070x^8 + 8854x^7 - 9440x^6 + 6893x^5 - 3748x^4 + 2592x^3 - 2790x^2 + 2673x - 1053	\( -\,3^{9}\cdot 557^{9} \)	$D_{19}$ (as 19T2)	Trivial (GRH)
19.1.231310367559550740879663744871.1	x^19 - 6x^18 + 18x^17 - 39x^16 + 73x^15 - 200x^14 + 265x^13 + 305x^12 - 931x^11 + 1905x^10 - 5214x^9 + 10284x^8 - 13343x^7 + 12719x^6 - 8662x^5 + 4443x^4 - 1732x^3 + 614x^2 - 152x + 39	\( -\,1831^{9} \)	$D_{19}$ (as 19T2)	Trivial (GRH)
19.1.33600614943460448322716069311260139.1	x^19 - 38x^17 + 703x^15 - 228x^14 - 7239x^13 + 6384x^12 + 39159x^11 - 64068x^10 - 78147x^9 + 263112x^8 - 144818x^7 - 236892x^6 + 532855x^5 - 695400x^4 + 696844x^3 - 445968x^2 + 229824x - 110592	\( -\,19^{27} \)	$D_{19}$ (as 19T2)	Trivial (GRH)
19.19.222262197774010870252934365204894747669.1	x^19 - 2x^18 - 78x^17 + 264x^16 + 1763x^15 - 8614x^14 - 9209x^13 + 96924x^12 - 60856x^11 - 443620x^10 + 727151x^9 + 587984x^8 - 2232580x^7 + 1188184x^6 + 1637520x^5 - 2688288x^4 + 1618560x^3 - 475264x^2 + 61952x - 2048	\( 18229^{9} \)	$D_{19}$ (as 19T2)	Trivial (GRH)