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
20.4.230921785379186176385189.1	x^20 - 2x^19 + 5x^18 - 10x^17 + 17x^16 - 34x^15 + 32x^14 - 30x^13 + 16x^12 - 9x^11 - 27x^10 + 89x^9 - 18x^8 - 74x^7 + 53x^6 + 24x^5 - 7x^4 + 19x^3 + 4x^2 - 7x - 1	\( 29^{3}\cdot 79^{10} \)	20T418	Trivial (GRH)
20.0.378138159793919664573793.1	x^20 - x^19 - 4x^18 + 4x^17 + 3x^16 - 6x^15 + 13x^14 + 36x^13 - 4x^12 - 82x^11 - 75x^10 + 71x^9 + 199x^8 + 28x^7 - 72x^6 - 113x^5 - 58x^4 + 96x^3 + 87x^2 + 57x + 31	\( 47^{10}\cdot 193^{3} \)	20T418	Trivial (GRH)
20.0.38798116011178581010939904.1	x^20 + 3x^18 - 4x^16 - 7x^14 + 32x^12 + 27x^10 - 100x^8 - 85x^6 + 95x^4 + 116x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 79^{8} \)	20T418	Trivial (GRH)
20.4.38798116011178581010939904.1	x^20 - 7x^18 + 30x^16 - 76x^14 + 136x^12 - 188x^10 + 155x^8 - 158x^6 + 124x^4 - 87x^2 + 29	\( 2^{20}\cdot 29^{3}\cdot 79^{8} \)	20T418	Trivial (GRH)
20.0.6593371018023678808268905753944157.1	x^20 - 3x^19 + 43x^18 - 102x^17 + 794x^16 - 2060x^15 + 9343x^14 - 20615x^13 + 61749x^12 - 111807x^11 + 246498x^10 - 355752x^9 + 559168x^8 - 595790x^7 + 687028x^6 - 502104x^5 + 494386x^4 - 210983x^3 + 231277x^2 - 40869x + 57087	\( 397^{5}\cdot 401^{8} \)	20T418	$[466]$ (GRH)
20.8.6593371018023678808268905753944157.1	x^20 - 2x^19 - 3x^18 + 33x^17 - 130x^16 + 437x^15 - 1067x^14 + 248x^13 + 5896x^12 - 14188x^11 + 21820x^10 - 43599x^9 - 7699x^8 + 97875x^7 - 91977x^6 + 302319x^5 - 49552x^4 - 292478x^3 - 70145x^2 + 111235x + 28367	\( 397^{5}\cdot 401^{8} \)	20T418	Trivial (GRH)
20.0.6593371018023678808268905753944157.2	x^20 - 2x^19 + 16x^18 - 40x^17 + 153x^16 - 409x^15 + 531x^14 - 631x^13 + 1182x^12 - 2207x^11 + 9841x^10 - 31915x^9 + 59913x^8 - 71946x^7 + 315927x^6 - 188012x^5 - 202487x^4 - 100612x^3 + 686038x^2 + 650199x + 329149	\( 397^{5}\cdot 401^{8} \)	20T418	$[2, 194]$ (GRH)
20.8.6593371018023678808268905753944157.2	x^20 - 3x^19 - 19x^18 + 104x^17 + 46x^16 - 816x^15 - 377x^14 + 5750x^13 + 481x^12 - 23572x^11 - 5409x^10 + 29390x^9 + 61815x^8 + 58301x^7 - 79450x^6 - 129539x^5 - 98958x^4 + 12864x^3 + 90298x^2 + 75365x + 16369	\( 397^{5}\cdot 401^{8} \)	20T418	Trivial (GRH)
20.20.226737880652372036160972485949760873.1	x^20 - 10x^19 - 9x^18 + 360x^17 - 507x^16 - 5094x^15 + 11686x^14 + 36343x^13 - 105960x^12 - 139153x^11 + 502333x^10 + 274440x^9 - 1331717x^8 - 195165x^7 + 1954334x^6 - 179722x^5 - 1451928x^4 + 359345x^3 + 409455x^2 - 140766x + 1777	\( 19^{8}\cdot 43^{8}\cdot 193^{2}\cdot 313^{3} \)	20T418	Trivial (GRH)
20.20.40016504277785918139041483312201654625.1	x^20 - x^19 - 38x^18 + 32x^17 + 528x^16 - 350x^15 - 3494x^14 + 1700x^13 + 11599x^12 - 3821x^11 - 18216x^10 + 3821x^9 + 11599x^8 - 1700x^7 - 3494x^6 + 350x^5 + 528x^4 - 32x^3 - 38x^2 + x + 1	\( 3^{4}\cdot 5^{3}\cdot 13^{2}\cdot 37^{3}\cdot 2153^{8} \)	20T418	Trivial (GRH)
20.16.62037027908584793907002134238860573213.1	x^20 - 3x^19 - 39x^18 + 9x^17 + 1015x^16 + 2294x^15 - 23485x^14 - 33051x^13 + 332416x^12 - 18458x^11 - 2365731x^10 + 2808039x^9 + 6845411x^8 - 17537627x^7 + 1944729x^6 + 34047722x^5 - 36550142x^4 - 2338829x^3 + 19149302x^2 - 4012621x - 2235791	\( 97^{2}\cdot 397^{5}\cdot 401^{8} \)	20T418	Trivial (GRH)
20.16.62037027908584793907002134238860573213.2	x^20 - x^19 - 39x^18 + 24x^17 - 111x^16 + 1377x^15 + 24220x^14 - 57435x^13 - 444438x^12 + 883410x^11 + 3747451x^10 - 7378247x^9 - 17234947x^8 + 36901191x^7 + 47314304x^6 - 107472506x^5 - 84282926x^4 + 161726188x^3 + 98536502x^2 - 92415798x - 56933073	\( 97^{2}\cdot 397^{5}\cdot 401^{8} \)	20T418	Trivial (GRH)
20.12.258736313952918709173181777016119099392.1	x^20 - 13x^18 - 4x^16 + 500x^14 - 666x^12 - 5863x^10 + 8866x^8 + 21576x^6 - 25476x^4 - 7173x^2 + 7173	\( 2^{20}\cdot 3^{6}\cdot 401^{8}\cdot 797^{3} \)	20T418	$[2]$ (GRH)
20.12.506486527315275206295314989777123540992.1	x^20 + 8x^18 - 82x^16 - 361x^14 + 2934x^12 + 701x^10 - 26750x^8 + 31719x^6 + 22482x^4 - 35892x^2 + 8973	\( 2^{20}\cdot 3^{6}\cdot 401^{8}\cdot 997^{3} \)	20T418	$[2]$ (GRH)
20.4.20741620697501495518586141242379606163456.1	x^20 + 69x^18 + 1299x^16 + 7251x^14 - 1235x^12 - 115467x^10 - 282527x^8 - 50172x^6 + 489880x^4 + 490677x^2 + 133821	\( 2^{20}\cdot 3^{2}\cdot 401^{8}\cdot 14869^{3} \)	20T418	$[2, 2]$ (GRH)
20.4.159375711952732783794802017883027342884864.1	x^20 + 113x^18 + 4679x^16 + 92642x^14 + 936165x^12 + 4697526x^10 + 10010207x^8 + 4906246x^6 - 2572937x^4 - 880230x^2 + 264069	\( 2^{20}\cdot 3^{2}\cdot 13^{3}\cdot 37^{3}\cdot 61^{3}\cdot 401^{8} \)	20T418	$[2, 2, 2]$ (GRH)