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
20.2.11900726940981550744576.1	x^20 - 7x^18 + 28x^16 - 70x^14 + 112x^12 - 118x^10 + 80x^8 - 29x^6 + 2x^4 + 3x^2 - 1	\( -\,2^{10}\cdot 7^{8}\cdot 17^{10} \)	$D_4\times D_5$ (as 20T21)	Trivial
20.0.64568649977367029645312.1	x^20 - 2x^19 + 8x^18 - 16x^17 + 29x^16 - 63x^15 + 88x^14 - 103x^13 + 160x^12 - 175x^11 + 125x^10 - 136x^9 + 143x^8 - 77x^7 + 58x^6 - 77x^5 + 48x^4 - 12x^3 + 5x^2 - 4x + 1	\( 2^{15}\cdot 7^{10}\cdot 17^{8} \)	$D_4\times D_5$ (as 20T21)	Trivial
20.0.380823262111409623826432.1	x^20 - 4x^19 + 8x^18 - 16x^17 + 35x^16 - 58x^15 + 98x^14 - 194x^13 + 339x^12 - 506x^11 + 672x^10 - 748x^9 + 650x^8 - 454x^7 + 336x^6 - 318x^5 + 275x^4 - 164x^3 + 60x^2 - 12x + 1	\( 2^{15}\cdot 7^{8}\cdot 17^{10} \)	$D_4\times D_5$ (as 20T21)	Trivial
20.0.522050086690675147528677.1	x^20 - 2x^19 + 2x^18 - x^17 - 2x^15 - 9x^14 + 3x^12 + x^11 + 22x^9 + 45x^8 + 41x^7 + 29x^6 + 18x^5 + 7x^4 - 2x^3 - 3x^2 + 1	\( 3^{10}\cdot 13^{5}\cdot 47^{8} \)	$D_4\times D_5$ (as 20T21)	Trivial
20.2.583135620108095986484224.1	x^20 - 6x^19 + 17x^18 - 26x^17 + 3x^16 + 99x^15 - 278x^14 + 401x^13 - 222x^12 - 386x^11 + 1130x^10 - 1293x^9 + 290x^8 + 1647x^7 - 3426x^6 + 3993x^5 - 3230x^4 + 1866x^3 - 736x^2 + 176x - 19	\( -\,2^{10}\cdot 7^{10}\cdot 17^{10} \)	$D_4\times D_5$ (as 20T21)	Trivial
20.4.18660339843459071567495168.1	x^20 - 7x^19 + 26x^18 - 74x^17 + 178x^16 - 348x^15 + 530x^14 - 614x^13 + 478x^12 + 34x^11 - 884x^10 + 1523x^9 - 1585x^8 + 1413x^7 - 1104x^6 + 634x^5 - 304x^4 + 151x^3 - 52x^2 + 4x + 1	\( 2^{15}\cdot 7^{10}\cdot 17^{10} \)	$D_4\times D_5$ (as 20T21)	Trivial (GRH)
20.4.389963020402083454798266368.1	x^20 + 8x^18 + 24x^16 + x^14 - 170x^12 - 403x^10 - 340x^8 + 4x^6 + 192x^4 + 128x^2 + 32	\( 2^{25}\cdot 7^{8}\cdot 17^{10} \)	$D_4\times D_5$ (as 20T21)	Trivial (GRH)
20.0.734048038403921797267324928.1	x^20 - 4x^19 + 14x^18 - 14x^17 + 8x^16 + 12x^15 + 27x^14 - 42x^13 + 135x^12 + 10x^11 + 220x^10 + 160x^9 + 322x^8 + 668x^7 + 816x^6 + 644x^5 + 332x^4 + 128x^3 + 35x^2 + 6x + 1	\( 2^{30}\cdot 7^{8}\cdot 17^{9} \)	$D_4\times D_5$ (as 20T21)	Trivial
20.0.14658323082243334363275748982757.1	x^20 - x^19 - 16x^18 + 15x^17 + 140x^16 - 106x^15 - 609x^14 + 388x^13 + 1656x^12 - 814x^11 - 2628x^10 + 827x^9 + 2615x^8 - 246x^7 - 1201x^6 + 121x^5 + 310x^4 - 56x^3 - 21x^2 + 3x + 1	\( 3^{10}\cdot 13^{5}\cdot 401^{8} \)	$D_4\times D_5$ (as 20T21)	$[2, 2]$ (GRH)
20.10.163023866649059818618082021484375.1	x^20 - 9x^19 + 24x^18 + 54x^17 - 631x^16 + 2452x^15 - 5691x^14 + 8318x^13 - 6817x^12 - 504x^11 + 11216x^10 - 22964x^9 + 34562x^8 - 23706x^7 - 24944x^6 + 53552x^5 - 20774x^4 - 13526x^3 + 11231x^2 - 1890x + 45	\( -\,3^{8}\cdot 5^{10}\cdot 239^{9} \)	$D_4\times D_5$ (as 20T21)	Trivial (GRH)
20.10.1051522209829636336015666513671875.1	x^20 - x^19 - 5x^18 + 12x^17 + 38x^16 - 63x^15 - 360x^14 + 471x^13 + 577x^12 - 1603x^11 - 191x^10 + 1926x^9 + 566x^8 - 1116x^7 - 765x^6 + 582x^5 + 79x^4 - 88x^3 + 16x^2 + 6x - 1	\( -\,5^{10}\cdot 11^{5}\cdot 401^{8} \)	$D_4\times D_5$ (as 20T21)	Trivial (GRH)
20.0.2243390479903105373955109683200000.1	x^20 - 2x^19 - 20x^18 + 40x^17 + 247x^16 - 412x^15 - 1048x^14 + 1552x^13 + 3039x^12 - 2670x^11 - 4608x^10 + 2708x^9 + 4444x^8 - 1252x^7 - 1796x^6 + 478x^5 + 405x^4 - 136x^3 - 16x^2 + 6x + 1	\( 2^{30}\cdot 5^{5}\cdot 401^{8} \)	$D_4\times D_5$ (as 20T21)	$[5]$ (GRH)
20.20.133919868380978295718942460439453125.1	x^20 - x^19 - 38x^18 + 29x^17 + 484x^16 - 284x^15 - 2761x^14 + 1136x^13 + 7908x^12 - 2304x^11 - 11892x^10 + 2701x^9 + 9451x^8 - 1736x^7 - 3821x^6 + 509x^5 + 732x^4 - 62x^3 - 55x^2 + 3x + 1	\( 5^{10}\cdot 29^{5}\cdot 401^{8} \)	$D_4\times D_5$ (as 20T21)	Trivial (GRH)
20.0.72825983445554038731855441697381112832.1	x^20 - 9x^19 + 61x^18 - 221x^17 + 822x^16 - 1892x^15 + 5219x^14 - 8472x^13 + 27597x^12 - 48534x^11 + 163342x^10 - 238292x^9 + 523033x^8 - 258674x^7 + 365450x^6 + 574249x^5 + 872126x^4 + 87755x^3 + 1041518x^2 + 1084745x + 1823113	\( 2^{10}\cdot 3^{10}\cdot 7^{5}\cdot 19^{10}\cdot 43^{8} \)	$D_4\times D_5$ (as 20T21)	$[2, 4, 404]$ (GRH)
20.0.170942913995404548367273973760000000000.1	x^20 + 55x^18 + 1286x^16 + 16755x^14 + 134201x^12 + 688496x^10 + 2284561x^8 + 4822473x^6 + 6162421x^4 + 4269541x^2 + 1204799	\( 2^{20}\cdot 3^{8}\cdot 5^{10}\cdot 239^{9} \)	$D_4\times D_5$ (as 20T21)	$[37, 148]$ (GRH)
20.20.170942913995404548367273973760000000000.1	x^20 - 55x^18 + 1286x^16 - 16755x^14 + 134201x^12 - 688496x^10 + 2284561x^8 - 4822473x^6 + 6162421x^4 - 4269541x^2 + 1204799	\( 2^{20}\cdot 3^{8}\cdot 5^{10}\cdot 239^{9} \)	$D_4\times D_5$ (as 20T21)	Trivial (GRH)