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 30 matches)

Label	Polynomial	Discriminant	Galois group	Class group
20.0.66045000696445844586496.2	x^20 + 4x^18 + 2x^16 - 4x^14 + 10x^12 + 21x^10 - 3x^8 + 28x^4 + 20x^2 + 4	\( 2^{24}\cdot 89^{8} \)	20T555	Trivial (GRH)
20.4.643855366856495035580416.1	x^20 - 6x^18 - 8x^17 + 13x^16 + 40x^15 + 14x^14 - 54x^13 - 78x^12 - 12x^11 + 48x^10 + 62x^9 + 44x^8 + 24x^7 - 38x^6 - 62x^5 - 31x^4 + 28x^3 + 14x^2 - 2x - 1	\( 2^{24}\cdot 13^{8}\cdot 19^{6} \)	20T555	Trivial
20.4.906356010836672093618176.1	x^20 - 3x^18 - 5x^16 + 2x^14 + 5x^12 - x^10 + 9x^8 + 30x^6 + 23x^4 + 5x^2 + 1	\( 2^{44}\cdot 61^{6} \)	20T555	Trivial (GRH)
20.4.1421468785090685198113024.2	x^20 + 2x^18 + 5x^14 - 13x^12 - 32x^10 - 27x^8 - 56x^6 - 31x^4 + 28x^2 + 16	\( 2^{8}\cdot 19^{8}\cdot 83^{6} \)	20T555	Trivial (GRH)
20.4.1940164150557599013535744.3	x^20 - x^18 - 11x^16 - 32x^14 - 59x^12 - 73x^10 - 59x^8 - 32x^6 - 11x^4 - x^2 + 1	\( 2^{32}\cdot 277^{6} \)	20T555	Trivial (GRH)
20.8.4226880044572534053535744.1	x^20 - 4x^19 - 4x^18 + 32x^17 - 13x^16 - 86x^15 + 66x^14 + 156x^13 - 181x^12 - 144x^11 + 266x^10 + 38x^9 - 198x^8 - 16x^7 + 92x^6 + 46x^5 - 34x^4 - 30x^3 + 8x^2 + 8x + 1	\( 2^{30}\cdot 89^{8} \)	20T555	Trivial (GRH)
20.0.4226880044572534053535744.4	x^20 + 4x^18 + 2x^16 + 18x^14 - 3x^12 + 20x^10 - 3x^8 + 18x^6 + 2x^4 + 4x^2 + 1	\( 2^{30}\cdot 89^{8} \)	20T555	$[2]$
20.8.270520322852642179426287616.1	x^20 - 10x^18 + 21x^16 + 42x^14 - 118x^12 - 72x^10 + 189x^8 + 104x^6 - 148x^4 + 24x^2 + 4	\( 2^{36}\cdot 89^{8} \)	20T555	Trivial (GRH)
20.0.2363431422578463908630533729.1	x^20 + 19x^18 + 116x^16 + 194x^14 - 498x^12 - 1778x^10 + 97x^8 + 4847x^6 + 4182x^4 + 892x^2 + 9	\( 36497^{6} \)	20T555	$[3]$ (GRH)
20.0.5550973666685307776998047744.2	x^20 + 4x^18 + 21x^16 + 33x^14 + 36x^12 + 33x^10 + 36x^8 + 33x^6 + 21x^4 + 4x^2 + 1	\( 2^{20}\cdot 3^{16}\cdot 223^{6} \)	20T555	Trivial (GRH)
20.0.14567038657959705229319471104.1	x^20 + x^18 + 12x^16 + 18x^14 + 98x^12 + 56x^10 + 275x^8 - 15x^6 + 762x^4 - 400x^2 + 625	\( 2^{20}\cdot 4903^{6} \)	20T555	Trivial (GRH)
20.0.294978023461273318901285601961.1	x^20 - 4x^19 + 6x^18 + 16x^17 - 31x^16 - 111x^15 + 618x^14 - 509x^13 - 1353x^12 + 3273x^11 + 5434x^10 - 23902x^9 + 32513x^8 - 6308x^7 + 727x^6 - 46451x^5 + 136687x^4 - 185194x^3 + 189809x^2 - 81196x + 44944	\( 83^{6}\cdot 983^{6} \)	20T555	$[4]$ (GRH)
20.4.294978023461273318901285601961.1	x^20 - 6x^18 - 39x^16 + 468x^14 - 222x^12 - 6203x^10 + 12362x^8 + 7637x^6 - 37869x^4 + 27159x^2 + 4	\( 83^{6}\cdot 983^{6} \)	20T555	Trivial (GRH)
20.4.511117286455166049253968832369.1	x^20 - 39x^18 + 573x^16 - 4413x^14 + 19359x^12 - 50028x^10 + 78205x^8 - 96693x^6 + 159319x^4 - 212082x^2 + 112225	\( 89417^{6} \)	20T555	Trivial (GRH)
20.0.654253297161106870378547679969.2	x^20 - 8x^18 + 42x^16 - 109x^14 + 245x^12 - 282x^10 + 830x^8 - 550x^6 - 8148x^4 + 10951x^2 + 3481	\( 3^{28}\cdot 7^{6}\cdot 79^{6} \)	20T555	$[2, 4]$ (GRH)
20.4.750553614330423255547227138649.1	x^20 - 3x^19 - 2x^18 + 13x^17 - 25x^16 - 66x^15 + 155x^14 - 21x^13 - 603x^12 + 99x^11 + 1022x^10 - 3360x^9 - 1705x^8 + 5750x^7 - 605x^6 - 4724x^5 + 3057x^4 + 19x^3 - 485x^2 + 55x + 1	\( 61^{8}\cdot 397^{6} \)	20T555	Trivial (GRH)
20.4.1477144639111539942894083580625.1	x^20 + 35x^18 + 372x^16 - 266x^14 - 32626x^12 - 242662x^10 - 728339x^8 - 759137x^6 + 382590x^4 + 860968x^2 + 19881	\( 5^{4}\cdot 36497^{6} \)	20T555	Trivial (GRH)
20.4.10031136353027322365301951711681.1	x^20 - 6x^19 + 42x^18 - 204x^17 + 769x^16 - 2685x^15 + 7178x^14 - 17815x^13 + 36830x^12 - 68376x^11 + 113765x^10 - 161759x^9 + 217139x^8 - 240305x^7 + 248504x^6 - 225324x^5 + 149057x^4 - 118439x^3 + 21318x^2 - 136x - 1241	\( 3^{4}\cdot 17^{6}\cdot 4153^{6} \)	20T555	Trivial (GRH)
20.4.30243788970849950224000000000000.1	x^20 - 2x^19 + 13x^18 - 24x^17 - 3x^16 - 8x^15 - 199x^14 + 708x^13 + 1259x^12 + 886x^11 + 1357x^10 - 2484x^9 - 3166x^8 - 2612x^7 - 6214x^6 + 3292x^5 + 2592x^4 + 3916x^3 + 5228x^2 - 1112x - 1264	\( 2^{16}\cdot 5^{12}\cdot 17^{6}\cdot 23^{8} \)	20T555	$[2]$ (GRH)
20.12.97182738115842943341316071817216.1	x^20 - 10x^19 + 17x^18 + 132x^17 - 500x^16 - 284x^15 + 3466x^14 - 2360x^13 - 9656x^12 + 11604x^11 + 13604x^10 - 19846x^9 - 15802x^8 + 23414x^7 + 7869x^6 - 10780x^5 - 2861x^4 - 498x^3 + 1546x^2 + 944x + 109	\( 2^{16}\cdot 33769^{6} \)	20T555	Trivial (GRH)
20.0.115464362371968140967058305099481.1	x^20 + 31x^18 + 392x^16 + 3031x^14 + 24669x^12 + 220501x^10 + 1326559x^8 + 4244282x^6 + 6538225x^4 + 5314268x^2 + 3534400	\( 149^{6}\cdot 1481^{6} \)	20T555	Trivial (GRH)
20.8.115464362371968140967058305099481.1	x^20 - 4x^19 + 5x^18 - 45x^17 - 53x^16 + 483x^15 + 210x^14 + 4293x^13 + 1470x^12 - 35376x^11 - 47202x^10 - 46028x^9 + 51083x^8 + 238054x^7 + 78465x^6 - 28625x^5 - 71574x^4 - 20169x^3 - 2093x^2 + 2581x + 193	\( 149^{6}\cdot 1481^{6} \)	20T555	Trivial (GRH)
20.8.128962918343732771112194751258889.1	x^20 - 31x^18 - 9x^17 + 403x^16 + 360x^15 - 3612x^14 - 2007x^13 + 21199x^12 - 7999x^11 - 66951x^10 + 106939x^9 + 49995x^8 - 336218x^7 + 279990x^6 + 187238x^5 - 379608x^4 + 185738x^3 + 33663x^2 - 116850x + 36100	\( 53^{6}\cdot 4241^{6} \)	20T555	Trivial (GRH)
20.12.211505645444809969257911648518144.1	x^20 - 26x^18 + 203x^16 - 847x^14 + 2742x^12 - 7949x^10 + 17944x^8 - 28927x^6 + 33011x^4 - 23628x^2 + 7225	\( 2^{20}\cdot 61^{6}\cdot 397^{6} \)	20T555	Trivial (GRH)
20.4.2478237467361635371456170535419904.1	x^20 + 12x^18 - 87x^16 - 1126x^14 - 1245x^12 - 7650x^10 + 9968x^8 - 3580x^6 + 20333x^4 + 4432x^2 + 29929	\( 2^{20}\cdot 36497^{6} \)	20T555	$[3]$ (GRH)
20.12.19331679745558008227514653210116096.1	x^20 + 3x^18 - 107x^16 - 1309x^14 + 14986x^12 - 49704x^10 + 109085x^8 - 262652x^6 + 326736x^4 - 26944x^2 + 256	\( 2^{16}\cdot 83^{6}\cdot 983^{6} \)	20T555	Trivial (GRH)
20.4.19331679745558008227514653210116096.1	x^20 - 16x^18 - 74x^16 + 243x^14 + 6324x^12 + 46739x^10 + 205833x^8 + 613178x^6 + 1220345x^4 + 1372716x^2 + 719104	\( 2^{16}\cdot 83^{6}\cdot 983^{6} \)	20T555	$[4]$ (GRH)
20.12.19331679745558008227514653210116096.2	x^20 - 25x^18 - 129x^16 + 690x^14 + 4301x^12 - 646x^10 - 39270x^8 - 24898x^6 + 156737x^4 - 62716x^2 + 4624	\( 2^{16}\cdot 83^{6}\cdot 983^{6} \)	20T555	Trivial (GRH)
20.20.535945319762012195262529622370156544.1	x^20 - 52x^18 + 1105x^16 - 12690x^14 + 87180x^12 - 371452x^10 + 975653x^8 - 1501478x^6 + 1191833x^4 - 346822x^2 + 2401	\( 2^{20}\cdot 89417^{6} \)	20T555	Trivial (GRH)
20.20.1548898417101022107160106584637440000.1	x^20 - 72x^18 + 2140x^16 - 33996x^14 + 312519x^12 - 1685443x^10 + 5186361x^8 - 8500822x^6 + 6400608x^4 - 1581254x^2 + 19881	\( 2^{20}\cdot 5^{4}\cdot 36497^{6} \)	20T555	Trivial (GRH)