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 12 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.1245300904083251953125.1	x^20 - x^19 + x^18 - 2x^17 + 2x^16 - 5x^15 + 5x^14 - 4x^13 + 5x^12 - 3x^11 + 12x^10 - 8x^9 + 2x^8 - 6x^7 - x^6 - 10x^5 + 6x^4 + 3x^3 + 2x^2 + x + 1	\( 3^{4}\cdot 5^{17}\cdot 67^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial
20.0.2462968747589111328125.1	x^20 - x^19 - x^16 - 2x^15 + 4x^14 - x^13 + x^12 + x^11 + 4x^10 - 8x^9 + 2x^8 - x^7 - 2x^6 - x^5 + 8x^4 - 5x^3 + 3x^2 - 2x + 1	\( 5^{15}\cdot 13^{4}\cdot 41^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial
20.0.87161254882812500000000.1	x^20 - 5x^17 + 15x^16 - 11x^15 - 10x^14 + 25x^13 - 15x^12 - 10x^11 + 21x^10 - 10x^9 - 15x^8 + 25x^7 - 10x^6 - 11x^5 + 15x^4 - 5x^3 + 1	\( 2^{8}\cdot 5^{23}\cdot 13^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial
20.4.907824359076690673828125.1	x^20 - 7x^19 + 22x^18 - 39x^17 + 42x^16 - 29x^15 + 49x^14 - 142x^13 + 205x^12 - 101x^11 - 130x^10 + 209x^9 + 10x^8 - 173x^7 + 47x^6 + 81x^5 - 27x^4 - 26x^3 + 3x^2 + 5x + 1	\( 3^{10}\cdot 5^{17}\cdot 67^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial
20.0.6383448613601104736328125.1	x^20 + 2x^18 - x^17 + 6x^16 + 10x^15 + 17x^14 + 10x^13 + 37x^12 + 17x^11 - 14x^10 + 19x^8 + 11x^7 - 7x^6 - 2x^5 + 13x^4 + 6x^3 + 3x^2 + 2x + 1	\( 5^{15}\cdot 3803^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial
20.4.253408254667989956596734833.1	x^20 - x^19 + 5x^18 - 5x^17 - 5x^16 + 6x^15 - 132x^14 + 436x^13 - 1129x^12 + 2613x^11 - 4464x^10 + 6829x^9 - 10176x^8 + 12663x^7 - 11903x^6 + 7141x^5 - 1038x^4 - 1531x^3 + 443x^2 + 403x - 169	\( 17^{15}\cdot 97^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial (GRH)
20.12.357012500000000000000000000.1	x^20 - 10x^18 + 35x^16 - 65x^14 + 115x^12 - 235x^10 + 370x^8 - 415x^6 + 290x^4 - 75x^2 + 5	\( 2^{20}\cdot 5^{23}\cdot 13^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial (GRH)
20.0.1008024781832337188720703125.1	x^20 - 5x^19 + 17x^18 - 42x^17 + 108x^16 - 177x^15 + 293x^14 - 301x^13 + 475x^12 - 358x^11 + 945x^10 - 217x^9 + 1380x^8 - 261x^7 + 1006x^6 - 128x^5 + 227x^4 - 67x^3 + 8x^2 + 6x + 1	\( 5^{17}\cdot 6029^{4} \)	$C_4\times S_5$ (as 20T123)	$[2]$
20.0.1085041785093811798095703125.1	x^20 - 5x^19 + 18x^18 - 40x^17 + 79x^16 - 120x^15 + 242x^14 - 345x^13 + 641x^12 - 1005x^11 + 1640x^10 - 1910x^9 + 1900x^8 - 1125x^7 + 660x^6 - 225x^5 + 200x^4 - 75x^3 + 75x^2 + 25	\( 3^{4}\cdot 5^{17}\cdot 23^{4}\cdot 89^{4} \)	$C_4\times S_5$ (as 20T123)	$[2]$
20.12.4147200000000000000000000000.1	x^20 - 10x^19 + 30x^18 + 10x^17 - 215x^16 + 272x^15 + 440x^14 - 1040x^13 - 350x^12 + 1740x^11 + 204x^10 - 1740x^9 - 350x^8 + 1040x^7 + 440x^6 - 272x^5 - 215x^4 - 10x^3 + 30x^2 + 10x + 1	\( 2^{32}\cdot 3^{4}\cdot 5^{23} \)	$C_4\times S_5$ (as 20T123)	Trivial (GRH)
20.20.790995461333388800811767578125.1	x^20 - 5x^19 - 17x^18 + 123x^17 + 30x^16 - 1110x^15 + 927x^14 + 4504x^13 - 6723x^12 - 7662x^11 + 17547x^10 + 2813x^9 - 18435x^8 + 2142x^7 + 8947x^6 - 1585x^5 - 1872x^4 + 343x^3 + 120x^2 - 28x + 1	\( 3^{10}\cdot 5^{17}\cdot 23^{4}\cdot 89^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial (GRH)
20.20.619789164416171417636993408203125.1	x^20 - 3x^19 - 36x^18 + 92x^17 + 519x^16 - 1110x^15 - 3841x^14 + 6814x^13 + 15654x^12 - 23105x^11 - 35526x^10 + 44358x^9 + 44365x^8 - 47573x^7 - 29261x^6 + 27081x^5 + 9352x^4 - 7316x^3 - 1317x^2 + 732x + 61	\( 3^{10}\cdot 5^{15}\cdot 61^{4}\cdot 397^{4} \)	$C_4\times S_5$ (as 20T123)	Trivial (GRH)