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 16 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.311952203781699456535737041.1	x^20 - 7x^19 + 12x^18 + 20x^17 - 78x^16 + 23x^15 + 190x^14 - 363x^13 + 164x^12 + 813x^11 - 1543x^10 - 569x^9 + 3393x^8 - 1203x^7 - 2549x^6 + 1579x^5 + 527x^4 - 244x^3 + 96x^2 - 90x + 27	\( 17^{7}\cdot 97^{9} \)	20T291	Trivial (GRH)
20.4.537425469704454926749401088.2	x^20 - 7x^18 + 39x^16 - 122x^14 + 329x^12 - 597x^10 + 805x^8 - 1358x^6 + 1871x^4 - 1243x^2 + 277	\( 2^{32}\cdot 277^{7} \)	20T291	Trivial (GRH)
20.0.537425469704454926749401088.3	x^20 + 7x^18 + 39x^16 + 122x^14 + 329x^12 + 597x^10 + 805x^8 + 1358x^6 + 1871x^4 + 1243x^2 + 277	\( 2^{32}\cdot 277^{7} \)	20T291	$[2]$ (GRH)
20.6.1887710546600429943094095872.1	x^20 + 6x^18 - 8x^16 - 67x^14 + 106x^12 + 341x^10 - 697x^8 - 658x^6 + 648x^4 + 823x^2 - 83	\( -\,2^{12}\cdot 19^{8}\cdot 83^{7} \)	20T291	Trivial (GRH)
20.4.8598807515271278827990417408.1	x^20 + 3x^18 - x^16 - 84x^14 - 289x^12 - 333x^10 + 425x^8 + 1816x^6 + 2261x^4 + 1271x^2 + 277	\( 2^{36}\cdot 277^{7} \)	20T291	Trivial (GRH)
20.6.120813474982427516358022135808.1	x^20 - 2x^18 - 23x^16 + 33x^14 + 159x^12 - 240x^10 - 554x^8 + 555x^6 + 1017x^4 - 697x^2 - 332	\( -\,2^{18}\cdot 19^{8}\cdot 83^{7} \)	20T291	Trivial (GRH)
20.2.120813474982427516358022135808.3	x^20 + 4x^18 - 6x^16 - 36x^14 + 2x^12 + 223x^10 + 187x^8 - 968x^6 - 1268x^4 - 556x^2 - 83	\( -\,2^{18}\cdot 19^{8}\cdot 83^{7} \)	20T291	$[2]$ (GRH)
20.2.483253899929710065432088543232.1	x^20 - 6x^18 - 8x^16 + 67x^14 + 106x^12 - 341x^10 - 697x^8 + 658x^6 + 648x^4 - 823x^2 - 83	\( -\,2^{20}\cdot 19^{8}\cdot 83^{7} \)	20T291	$[2]$ (GRH)
20.12.4884750571953738236922117607273.2	x^20 - x^19 - 23x^18 + 17x^17 + 170x^16 - 175x^15 - 542x^14 + 1074x^13 + 1382x^12 - 2458x^11 - 3128x^10 + 2017x^9 + 4456x^8 + 1326x^7 - 1596x^6 - 1480x^5 - 342x^4 + 135x^3 + 96x^2 + 19x + 1	\( 61^{7}\cdot 397^{7} \)	20T291	$[2]$ (GRH)
20.12.18176156878239859979587199616662833.1	x^20 - 9x^19 + 31x^18 - 28x^17 - 95x^16 + 265x^15 - 424x^14 + 1536x^13 - 4689x^12 + 7565x^11 - 5009x^10 - 3632x^9 + 13042x^8 - 16850x^7 + 7966x^6 + 7372x^5 - 9453x^4 + 1370x^3 + 975x^2 + 66x + 1	\( 61^{9}\cdot 397^{7} \)	20T291	Trivial (GRH)
20.8.52952551476471496673213808640000000.1	x^20 + 9x^18 - 22x^16 - 432x^14 - 1223x^12 + 225x^10 + 4393x^8 + 2649x^6 - 2457x^4 - 511x^2 + 160	\( 2^{33}\cdot 5^{7}\cdot 307^{8} \)	20T291	Trivial (GRH)
20.20.5122032215736963025518846392163893248.2	x^20 - 71x^18 + 1978x^16 - 29031x^14 + 247863x^12 - 1262043x^10 + 3740109x^8 - 6000283x^6 + 4599194x^4 - 1262061x^2 + 24217	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T291	$[2]$ (GRH)
20.8.5122032215736963025518846392163893248.3	x^20 + 21x^18 - 84x^16 - 3464x^14 - 12104x^12 + 32150x^10 + 51915x^8 - 62579x^6 - 70554x^4 + 25684x^2 + 24217	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T291	$[2]$ (GRH)
20.0.5122032215736963025518846392163893248.6	x^20 + 71x^18 + 1978x^16 + 29031x^14 + 247863x^12 + 1262043x^10 + 3740109x^8 + 6000283x^6 + 4599194x^4 + 1262061x^2 + 24217	\( 2^{20}\cdot 61^{7}\cdot 397^{7} \)	20T291	$[2, 2, 2, 1482]$ (GRH)
20.0.19059081874757239417955627425241846775808.1	x^20 + 112x^18 + 4632x^16 + 98910x^14 + 1240519x^12 + 9656781x^10 + 47357655x^8 + 143870574x^6 + 256786210x^4 + 240637070x^2 + 90111457	\( 2^{20}\cdot 61^{9}\cdot 397^{7} \)	20T291	$[2, 2, 2, 77548]$ (GRH)
20.20.19059081874757239417955627425241846775808.1	x^20 - 140x^18 + 7064x^16 - 184362x^14 + 2824883x^12 - 26573759x^10 + 152777611x^8 - 507979574x^6 + 847398214x^4 - 491350608x^2 + 90111457	\( 2^{20}\cdot 61^{9}\cdot 397^{7} \)	20T291	Trivial (GRH)