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 matches 1-50 of 1004)

Label	Polynomial	Discriminant	Galois group	Class group
5.5.14641.1	x^5 - x^4 - 4x^3 + 3x^2 + 3x - 1	\( 11^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.390625.1	x^5 - 10x^3 - 5x^2 + 10x - 1	\( 5^{8} \)	$C_5$ (as 5T1)	Trivial
5.5.923521.1	x^5 - x^4 - 12x^3 + 21x^2 + x - 5	\( 31^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.2825761.1	x^5 - x^4 - 16x^3 - 5x^2 + 21x + 9	\( 41^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.13845841.1	x^5 - x^4 - 24x^3 + 17x^2 + 41x + 13	\( 61^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.25411681.1	x^5 - x^4 - 28x^3 - 37x^2 + 25x - 1	\( 71^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.104060401.1	x^5 - x^4 - 40x^3 - 93x^2 - 21x + 17	\( 101^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.294499921.1	x^5 - x^4 - 52x^3 + 89x^2 + 109x - 193	\( 131^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.519885601.1	x^5 - x^4 - 60x^3 + 12x^2 + 784x - 128	\( 151^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.1073283121.1	x^5 - x^4 - 72x^3 + 123x^2 + 223x + 49	\( 181^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.1330863361.1	x^5 - x^4 - 76x^3 + 359x^2 - 437x + 155	\( 191^{4} \)	$C_5$ (as 5T1)	$[11]$
5.5.1982119441.1	x^5 - x^4 - 84x^3 + 59x^2 + 1661x - 269	\( 211^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.3373402561.1	x^5 - x^4 - 96x^3 + 212x^2 + 1232x - 512	\( 241^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.3969126001.1	x^5 - x^4 - 100x^3 + 20x^2 + 1504x - 1024	\( 251^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.5393580481.1	x^5 - x^4 - 108x^3 + 401x^2 - 13x - 845	\( 271^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.5719140625.1	x^5 - 110x^3 - 605x^2 - 990x - 451	\( 5^{8}\cdot 11^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.5719140625.2	x^5 - 110x^3 - 495x^2 - 440x - 99	\( 5^{8}\cdot 11^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.5719140625.3	x^5 - 110x^3 - 55x^2 + 660x + 649	\( 5^{8}\cdot 11^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.5719140625.4	x^5 - 110x^3 - 220x^2 + 1485x + 1276	\( 5^{8}\cdot 11^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.6234839521.1	x^5 - x^4 - 112x^3 + 191x^2 + 2257x - 967	\( 281^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.9354951841.1	x^5 - x^4 - 124x^3 - 535x^2 - 413x + 539	\( 311^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.12003612721.1	x^5 - x^4 - 132x^3 + 887x^2 - 1843x + 1027	\( 331^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.13521270961.1	x^5 - x^4 - 136x^3 + 300x^2 + 2016x - 3136	\( 11^{4}\cdot 31^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.13521270961.2	x^5 - x^4 - 136x^3 - 41x^2 + 3039x - 1431	\( 11^{4}\cdot 31^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.13521270961.3	x^5 - x^4 - 136x^3 - 723x^2 - 1053x - 67	\( 11^{4}\cdot 31^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.13521270961.4	x^5 - x^4 - 136x^3 + 641x^2 - 371x - 67	\( 11^{4}\cdot 31^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.25856961601.1	x^5 - x^4 - 160x^3 - 369x^2 + 879x + 29	\( 401^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.31414372081.1	x^5 - x^4 - 168x^3 - 219x^2 + 3853x + 3517	\( 421^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.34507149121.1	x^5 - x^4 - 172x^3 + 724x^2 + 1824x - 1728	\( 431^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.41371966801.1	x^5 - x^4 - 180x^3 + 1389x^2 - 3341x + 2551	\( 11^{4}\cdot 41^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.41371966801.2	x^5 - x^4 - 180x^3 - 415x^2 + 1169x + 2551	\( 11^{4}\cdot 41^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.41371966801.3	x^5 - x^4 - 180x^3 - 415x^2 + 3875x + 2551	\( 11^{4}\cdot 41^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.41371966801.4	x^5 - x^4 - 180x^3 + 36x^2 + 3424x + 3904	\( 11^{4}\cdot 41^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.45165175441.1	x^5 - x^4 - 184x^3 + 129x^2 + 4551x - 5419	\( 461^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.58120048561.1	x^5 - x^4 - 196x^3 - 59x^2 + 2019x - 1377	\( 491^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.73680216481.1	x^5 - x^4 - 208x^3 + 771x^2 + 4143x - 2083	\( 521^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.85662167761.1	x^5 - x^4 - 216x^3 - 1147x^2 - 805x + 2629	\( 541^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.106302733681.1	x^5 - x^4 - 228x^3 - 868x^2 + 3056x + 7552	\( 571^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.130466162401.1	x^5 - x^4 - 240x^3 - 1755x^2 - 3731x - 2399	\( 601^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.158532181921.1	x^5 - x^4 - 252x^3 - 2095x^2 - 5785x - 5069	\( 631^{4} \)	$C_5$ (as 5T1)	$[11]$
5.5.168823196161.1	x^5 - x^4 - 256x^3 + 564x^2 + 5328x + 5120	\( 641^{4} \)	$C_5$ (as 5T1)	$[11]$
5.5.190899960241.1	x^5 - x^4 - 264x^3 + 185x^2 + 16837x - 4851	\( 661^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.202716958081.1	x^5 - x^4 - 268x^3 - 1020x^2 + 4128x - 1024	\( 11^{4}\cdot 61^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.202716958081.2	x^5 - x^4 - 268x^3 + 2335x^2 - 5937x + 2331	\( 11^{4}\cdot 61^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.202716958081.3	x^5 - x^4 - 268x^3 - 349x^2 + 3457x + 5015	\( 11^{4}\cdot 61^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.202716958081.4	x^5 - x^4 - 268x^3 - 349x^2 + 7483x + 13067	\( 11^{4}\cdot 61^{4} \)	$C_5$ (as 5T1)	$[5]$
5.5.227988105361.1	x^5 - x^4 - 276x^3 + 1299x^2 + 5329x - 15581	\( 691^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.241474942801.1	x^5 - x^4 - 280x^3 - 2047x^2 - 3791x - 1699	\( 701^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.318097128001.1	x^5 - x^4 - 300x^3 + 2313x^2 - 3761x + 571	\( 751^{4} \)	$C_5$ (as 5T1)	Trivial
5.5.335381132641.1	x^5 - x^4 - 304x^3 - 2831x^2 - 8925x - 8775	\( 761^{4} \)	$C_5$ (as 5T1)	Trivial