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 21 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.57833357504222571486483841024.15	x^20 - 10x^18 + 40x^16 - 100x^14 + 187x^12 - 136x^10 + 86x^8 + 60x^6 + 34x^4 + 6x^2 + 1	\( 2^{40}\cdot 47^{10} \)	20T354	$[2]$ (GRH)
20.0.57833357504222571486483841024.16	x^20 + 6x^18 - 2x^16 - 48x^14 + 25x^12 + 188x^10 - 92x^8 - 58x^6 + 446x^4 - 28x^2 + 1	\( 2^{40}\cdot 47^{10} \)	20T354	$[2]$ (GRH)
20.8.87698172752380894993330638209814721.1	x^20 - 9x^19 + 14x^18 + 137x^17 - 688x^16 + 41x^15 + 9718x^14 - 39145x^13 + 72985x^12 - 42593x^11 - 113630x^10 + 305710x^9 - 295677x^8 - 20188x^7 + 374989x^6 - 372623x^5 + 57747x^4 + 123718x^3 - 42509x^2 - 23700x - 1579	\( 13^{8}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.8.87698172752380894993330638209814721.2	x^20 - 10x^19 + 40x^18 - 43x^17 - 285x^16 + 1478x^15 - 2313x^14 - 3790x^13 + 16263x^12 - 20750x^11 - 19144x^10 + 85292x^9 + 9833x^8 - 101024x^7 - 5874x^6 + 43160x^5 - 9896x^4 - 24159x^3 - 7848x^2 - 459x + 81	\( 13^{8}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.8.9725065664601656707693078997523858169.2	x^20 - 10x^19 + 81x^18 - 444x^17 + 1790x^16 - 5548x^15 + 9816x^14 - 386x^13 - 88573x^12 + 389660x^11 - 1075554x^10 + 2168019x^9 - 3014685x^8 + 2689232x^7 - 84219x^6 - 3654387x^5 + 5576020x^4 - 4463930x^3 + 383748x^2 + 1169369x - 318393	\( 67^{6}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.8.9725065664601656707693078997523858169.3	x^20 - 47x^18 - 20x^17 + 880x^16 + 620x^15 - 7588x^14 - 12585x^13 + 3266x^12 + 62063x^11 + 150789x^10 + 164901x^9 + 49942x^8 - 41917x^7 - 175697x^6 - 223475x^5 - 193770x^4 - 134370x^3 - 18264x^2 + 1573x + 169	\( 67^{6}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.8.9725065664601656707693078997523858169.4	x^20 - 7x^19 + 9x^18 + 18x^17 + 194x^16 - 815x^15 - 2303x^14 + 11147x^13 + 5689x^12 - 33639x^11 - 119465x^10 + 188164x^9 + 689018x^8 - 1111514x^7 - 1004331x^6 + 1659063x^5 + 1097938x^4 - 1061865x^3 - 655857x^2 + 417007x - 51613	\( 67^{6}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.8.9725065664601656707693078997523858169.5	x^20 - 4x^19 - 13x^18 - 23x^17 + 564x^16 + 105x^15 - 7868x^14 + 6862x^13 + 44004x^12 - 52424x^11 - 158619x^10 + 215233x^9 + 412926x^8 - 733252x^7 - 339880x^6 + 1148862x^5 - 268349x^4 - 641995x^3 + 461753x^2 - 81127x - 9203	\( 67^{6}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.8.37232500258172018109896537581762379776.1	x^20 + 17x^18 + 144x^16 + 663x^14 + 1462x^12 + 27x^10 - 6636x^8 - 3535x^6 + 2797x^4 - 412x^2 + 16	\( 2^{20}\cdot 1429^{10} \)	20T354	$[2]$ (GRH)
20.8.37232500258172018109896537581762379776.2	x^20 - 4x^18 - 21x^16 + 132x^14 - 335x^12 + 342x^10 - 119x^8 - 174x^6 + 143x^4 - 30x^2 + 1	\( 2^{20}\cdot 1429^{10} \)	20T354	$[2]$ (GRH)
20.4.118207097260900105334736680441689931776.5	x^20 + 46x^18 + 894x^16 + 9696x^14 + 63988x^12 + 254014x^10 + 542069x^8 + 367920x^6 - 572930x^4 - 781124x^2 + 100489	\( 2^{40}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.4.118207097260900105334736680441689931776.6	x^20 + 26x^18 + 180x^16 - 974x^14 - 23466x^12 - 169256x^10 - 659531x^8 - 1461720x^6 - 1630058x^4 - 407026x^2 + 505521	\( 2^{40}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.4.91958199192000549348526667291494680887296.1	x^20 + 20x^18 + 472x^16 + 3739x^14 - 166848x^12 - 1218087x^10 - 1963533x^8 - 2590094x^6 + 3022227x^4 + 1909193x^2 + 28561	\( 2^{20}\cdot 13^{8}\cdot 401^{10} \)	20T354	$[4]$ (GRH)
20.4.91958199192000549348526667291494680887296.2	x^20 - 4x^18 - 848x^16 - 5585x^14 + 30623x^12 - 221780x^10 + 621036x^8 + 7550244x^6 + 13941148x^4 + 9414145x^2 + 2313441	\( 2^{20}\cdot 13^{8}\cdot 401^{10} \)	20T354	$[4]$ (GRH)
20.12.120593484045596801425364025023890468434241.3	x^20 - 9x^19 + 278x^17 - 1128x^16 - 2239x^15 + 8210x^14 + 28252x^13 + 158779x^12 + 35603x^11 - 1301137x^10 - 4117047x^9 - 9705219x^8 - 4463541x^7 + 27760434x^6 + 67463449x^5 + 101134914x^4 + 32394489x^3 - 157942374x^2 - 199032963x - 67972159	\( 17^{8}\cdot 401^{12} \)	20T354	$[2]$ (GRH)
20.12.120593484045596801425364025023890468434241.4	x^20 - 4x^19 - 87x^18 + 386x^17 + 606x^16 - 4441x^15 + 22730x^14 - 50132x^13 - 75973x^12 + 311050x^11 - 1435499x^10 + 3989586x^9 - 1868787x^8 - 1812945x^7 + 11293992x^6 - 38500433x^5 + 48646097x^4 - 8351232x^3 - 56039732x^2 + 53460795x - 13691801	\( 17^{8}\cdot 401^{12} \)	20T354	$[2]$ (GRH)
20.16.1563800283933611000253754795880833917433369.2	x^20 - 2x^19 - 91x^18 + 333x^17 + 1633x^16 - 10426x^15 + 23238x^14 + 60961x^13 - 691752x^12 - 47119x^11 + 8648382x^10 - 6567940x^9 - 44331309x^8 + 65430409x^7 + 59962305x^6 - 173123757x^5 + 84377645x^4 + 41764421x^3 - 42339548x^2 + 4785950x + 2050157	\( 67^{6}\cdot 401^{12} \)	20T354	$[2]$ (GRH)
20.0.10197470454325346783925978002907577103417344.3	x^20 + 108x^18 + 4533x^16 + 97918x^14 + 1207868x^12 + 8811908x^10 + 37646333x^8 + 89405526x^6 + 107347793x^4 + 59550806x^2 + 11675889	\( 2^{20}\cdot 67^{6}\cdot 401^{10} \)	20T354	$[2, 2, 2, 157964]$ (GRH)
20.0.10197470454325346783925978002907577103417344.4	x^20 + 108x^18 + 4431x^16 + 87121x^14 + 867257x^12 + 4348596x^10 + 10423069x^8 + 11500599x^6 + 5040417x^4 + 613921x^2 + 4489	\( 2^{20}\cdot 67^{6}\cdot 401^{10} \)	20T354	$[2, 2, 2, 51908]$ (GRH)
20.20.10197470454325346783925978002907577103417344.6	x^20 - 99x^18 + 3553x^16 - 63530x^14 + 639709x^12 - 3828919x^10 + 13769532x^8 - 28837315x^6 + 31952387x^4 - 14240917x^2 + 4489	\( 2^{20}\cdot 67^{6}\cdot 401^{10} \)	20T354	$[2]$ (GRH)
20.20.10197470454325346783925978002907577103417344.7	x^20 - 118x^18 + 5398x^16 - 129549x^14 + 1851209x^12 - 16767252x^10 + 98815778x^8 - 377851190x^6 + 903676128x^4 - 1227311427x^2 + 721835689	\( 2^{20}\cdot 67^{6}\cdot 401^{10} \)	20T354	$[2]$ (GRH)