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 22 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.64129954426036731291631616.1	x^20 + 22x^16 + 143x^12 + 253x^8 + 99x^4 + 11	\( 2^{20}\cdot 11^{19} \)	20T130	Trivial
20.0.64129954426036731291631616.2	x^20 - 11x^18 + 55x^16 - 165x^14 + 330x^12 - 462x^10 + 462x^8 - 330x^6 + 165x^4 - 55x^2 + 11	\( 2^{20}\cdot 11^{19} \)	20T130	Trivial
20.0.64129954426036731291631616.3	x^20 + 22x^16 + 121x^12 + 176x^8 + 88x^4 + 11	\( 2^{20}\cdot 11^{19} \)	20T130	Trivial
20.0.15583578925526925703866482688.1	x^20 + 11x^18 + 33x^16 - 66x^14 - 572x^12 - 737x^10 + 2442x^8 + 9801x^6 + 14256x^4 + 9801x^2 + 2673	\( 2^{20}\cdot 3^{5}\cdot 11^{19} \)	20T130	$[2]$
20.10.65669073332261612842630774784.1	x^20 - 2x^19 - 8x^18 + 18x^17 + 38x^16 - 94x^15 - 114x^14 + 322x^13 + 218x^12 - 758x^11 - 242x^10 + 1244x^9 + 31x^8 - 1306x^7 + 260x^6 + 742x^5 - 226x^4 - 180x^3 + 36x^2 + 20x + 1	\( -\,2^{30}\cdot 11^{19} \)	20T130	Trivial (GRH)
20.10.65669073332261612842630774784.2	x^20 - 2x^19 - 8x^18 + 40x^17 - 61x^16 - 72x^15 + 458x^14 - 668x^13 - 233x^12 + 1838x^11 - 1562x^10 - 626x^9 + 933x^8 + 498x^7 + 84x^6 - 820x^5 - 204x^4 + 260x^3 + 80x^2 + 20x + 1	\( -\,2^{30}\cdot 11^{19} \)	20T130	Trivial (GRH)
20.10.65669073332261612842630774784.3	x^20 - 2x^19 - 8x^18 + 18x^17 - 6x^16 + 38x^15 - 70x^14 - 118x^13 + 262x^12 - 120x^11 + 594x^10 - 1176x^9 - 145x^8 + 1466x^7 - 576x^6 - 336x^5 + 258x^4 + 40x^3 - 30x^2 - 2x + 1	\( -\,2^{30}\cdot 11^{19} \)	20T130	Trivial (GRH)
20.10.470525233802978928640000000000.1	x^20 - 2x^18 - 19x^16 + 42x^14 + 54x^12 - 110x^10 - 50x^8 + 71x^6 + 10x^4 - 7x^2 - 1	\( -\,2^{20}\cdot 5^{10}\cdot 11^{16} \)	20T130	Trivial (GRH)
20.12.5175777571832768215040000000000.1	x^20 - 8x^18 - 14x^16 + 194x^14 - 98x^12 - 824x^10 + 407x^8 + 1001x^6 - 33x^4 - 198x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{17} \)	20T130	Trivial (GRH)
20.16.5175777571832768215040000000000.1	x^20 - 15x^18 + 68x^16 + 27x^14 - 1234x^12 + 4465x^10 - 7359x^8 + 5863x^6 - 1903x^4 + 165x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{17} \)	20T130	Trivial (GRH)
20.4.5175777571832768215040000000000.1	x^20 + 15x^18 + 68x^16 - 27x^14 - 1234x^12 - 4465x^10 - 7359x^8 - 5863x^6 - 1903x^4 - 165x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{17} \)	20T130	Trivial (GRH)
20.8.5175777571832768215040000000000.1	x^20 + 8x^18 - 14x^16 - 194x^14 - 98x^12 + 824x^10 + 407x^8 - 1001x^6 - 33x^4 + 198x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{17} \)	20T130	Trivial (GRH)
20.12.5175777571832768215040000000000.2	x^20 - 6x^18 - 34x^16 + 175x^14 + 214x^12 - 1429x^10 + 506x^8 + 2321x^6 - 1287x^4 - 671x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{17} \)	20T130	Trivial (GRH)
20.8.5175777571832768215040000000000.2	x^20 + 6x^18 - 34x^16 - 175x^14 + 214x^12 + 1429x^10 + 506x^8 - 2321x^6 - 1287x^4 + 671x^2 + 11	\( 2^{20}\cdot 5^{10}\cdot 11^{17} \)	20T130	Trivial (GRH)
20.16.18655986742119776375747379200000.1	x^20 - 2x^19 - 26x^18 + 90x^17 + 105x^16 - 908x^15 + 976x^14 + 2760x^13 - 8147x^12 + 3102x^11 + 17040x^10 - 28072x^9 + 2236x^8 + 36118x^7 - 31670x^6 - 5428x^5 + 17475x^4 - 4286x^3 - 2176x^2 + 844x - 43	\( 2^{30}\cdot 5^{5}\cdot 11^{18} \)	20T130	Trivial (GRH)
20.4.18655986742119776375747379200000.1	x^20 - 2x^19 + 10x^18 - 10x^17 - 19x^16 - 44x^15 + 40x^14 - 256x^13 - 1019x^12 - 1170x^11 + 2672x^10 + 4996x^9 - 604x^8 + 1902x^7 + 24450x^6 + 43868x^5 + 48635x^4 + 28394x^3 + 7652x^2 + 1192x + 89	\( 2^{30}\cdot 5^{5}\cdot 11^{18} \)	20T130	Trivial (GRH)
20.10.57952586042902321051693895129329600299008.1	x^20 - 2x^19 + 26x^18 - 316x^17 - 4329x^16 + 8240x^15 - 55794x^14 + 112182x^13 + 2245180x^12 + 4679350x^11 + 20230134x^10 - 62057688x^9 - 335257703x^8 - 341587532x^7 - 317626815x^6 + 4990875340x^5 + 6434665655x^4 - 6571612740x^3 - 8525407341x^2 - 6538575428x - 6758223659	\( -\,2^{20}\cdot 11^{18}\cdot 1583^{5} \)	20T130	Trivial (GRH)
20.10.57952586042902321051693895129329600299008.2	x^20 - 2x^19 + 26x^18 - 250x^17 - 2008x^16 + 4368x^15 - 55563x^14 + 310776x^13 + 1931801x^12 - 2159284x^11 - 6849787x^10 - 40521162x^9 - 170875749x^8 - 37548434x^7 + 350417694x^6 + 1258865740x^5 + 2300571482x^4 - 321339590x^3 - 1107249165x^2 - 5789595834x - 9281006867	\( -\,2^{20}\cdot 11^{18}\cdot 1583^{5} \)	20T130	Trivial (GRH)
20.0.12846961306316291046734327469906326168010752.1	x^20 + 2346x^16 + 1662647x^12 + 449242141x^8 + 48999879259x^4 + 1801152661463	\( 2^{20}\cdot 11^{16}\cdot 23^{15} \)	20T130	$[2, 2, 2, 12]$ (GRH)
20.0.12846961306316291046734327469906326168010752.2	x^20 - 69x^18 + 782x^16 + 17986x^14 - 286189x^12 + 3126919x^10 + 160397561x^8 + 79474844x^6 - 3637093477x^4 + 69306541424x^2 + 606618891407	\( 2^{20}\cdot 11^{16}\cdot 23^{15} \)	20T130	$[2, 2, 2, 12]$ (GRH)
20.0.14653272768072533214308458573932333455360000000000.1	x^20 + 1244x^18 + 664827x^16 + 200221838x^14 + 37413894201x^12 + 4495384753024x^10 + 347651176196668x^8 + 16802127274725302x^6 + 473166172952080318x^4 + 6673646740206221537x^2 + 31142373916142055599	\( 2^{20}\cdot 5^{10}\cdot 11^{16}\cdot 7919^{5} \)	20T130	$[2, 2, 2, 2, 6069812336]$ (GRH)
20.0.14653272768072533214308458573932333455360000000000.2	x^20 + 1482x^18 + 908011x^16 + 302386742x^14 + 60210051505x^12 + 7402326813897x^10 + 558955523693880x^8 + 24949694443593628x^6 + 609669460579370325x^4 + 7161290933362126941x^2 + 31142373916142055599	\( 2^{20}\cdot 5^{10}\cdot 11^{16}\cdot 7919^{5} \)	20T130	$[2, 2, 2, 4, 3136325784]$ (GRH)