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 )

Label	Polynomial	Discriminant	Galois group	Class group
4.0.40389025.4	x^4 - x^3 + 74x^2 - 200x + 2880	\( 5^{2}\cdot 17\cdot 29^{2}\cdot 113 \)	$D_{4}$ (as 4T3)	$[1064]$
4.0.94381225.3	x^4 + 95x^2 + 14400	\( 5^{2}\cdot 29^{2}\cdot 67^{2} \)	$C_2^2$ (as 4T2)	$[2, 576]$
4.0.105987025.1	x^4 - 37x^2 + 2916	\( 5^{2}\cdot 29^{2}\cdot 71^{2} \)	$C_2^2$ (as 4T2)	$[2, 2, 448]$
4.0.112254025.8	x^4 - x^3 + 359x^2 + 1145x + 7840	\( 5^{2}\cdot 13^{2}\cdot 163^{2} \)	$C_2^2$ (as 4T2)	$[1020]$
4.0.116704809.3	x^4 + 435x^2 + 39204	\( 3^{2}\cdot 13^{2}\cdot 277^{2} \)	$C_2^2$ (as 4T2)	$[2, 2, 280]$
4.0.125498225.2	x^4 - x^3 + 133x^2 + 713x + 2754	\( 5^{2}\cdot 29^{2}\cdot 47\cdot 127 \)	$D_{4}$ (as 4T3)	$[1128]$
4.0.128142400.4	x^4 + 278x^2 + 20736	\( 2^{6}\cdot 5^{2}\cdot 283^{2} \)	$C_2^2$ (as 4T2)	$[1020]$
4.0.130841097.1	x^4 - x^3 + 18x^2 + 496x + 5984	\( 3\cdot 131\cdot 577^{2} \)	$D_{4}$ (as 4T3)	$[1036]$
4.0.133837305.2	x^4 - 2x^3 + 83x^2 - 82x + 552	\( 3\cdot 5\cdot 7\cdot 1129^{2} \)	$D_{4}$ (as 4T3)	$[2, 522]$
4.0.139393600.1	x^4 - 2x^3 + 167x^2 + 104x + 5784	\( 2^{6}\cdot 5^{2}\cdot 87121 \)	$D_{4}$ (as 4T3)	$[2, 574]$
4.0.149382625.1	x^4 - x^3 + 236x^2 + 1024x + 9216	\( 5^{3}\cdot 7^{2}\cdot 29^{3} \)	$C_4$ (as 4T1)	$[2, 4, 4, 52]$
4.0.150798400.4	x^4 + 302x^2 + 24336	\( 2^{6}\cdot 5^{2}\cdot 307^{2} \)	$C_2^2$ (as 4T2)	$[1292]$
4.0.154529761.2	x^4 - 185x^2 + 11664	\( 31^{2}\cdot 401^{2} \)	$C_2^2$ (as 4T2)	$[1155]$
4.0.154753600.2	x^4 - 2x^3 + 137x^2 - 136x + 7734	\( 2^{6}\cdot 5^{2}\cdot 311^{2} \)	$C_2^2$ (as 4T2)	$[2, 2, 304]$
4.0.163174273.1	x^4 + 115x^2 + 388	\( 97\cdot 1297^{2} \)	$D_{4}$ (as 4T3)	$[1661]$
4.0.167314225.2	x^4 + 67x^2 + 4356	\( 5^{2}\cdot 13^{2}\cdot 199^{2} \)	$C_2^2$ (as 4T2)	$[2, 18, 36]$
4.0.170678025.1	x^4 - 2x^3 + 67x^2 - 66x + 984	\( 3^{2}\cdot 5^{2}\cdot 7^{2}\cdot 113\cdot 137 \)	$D_{4}$ (as 4T3)	$[2, 576]$
4.0.174108025.5	x^4 - x^3 + 449x^2 + 1425x + 11790	\( 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2$ (as 4T2)	$[4, 4, 64]$
4.0.174108025.7	x^4 + 155x^2 + 22500	\( 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 29^{2} \)	$C_2^2$ (as 4T2)	$[2, 4, 320]$
4.0.175117225.2	x^4 - 2x^3 + 223x^2 - 222x + 576	\( 5^{2}\cdot 29^{2}\cdot 8329 \)	$D_{4}$ (as 4T3)	$[2, 720]$
4.0.175790025.1	x^4 - 2x^3 + 87x^2 - 86x + 544	\( 3^{2}\cdot 5^{2}\cdot 29^{2}\cdot 929 \)	$D_{4}$ (as 4T3)	$[2, 552]$
4.0.176119441.1	x^4 - 277x^2 + 22500	\( 23^{2}\cdot 577^{2} \)	$C_2^2$ (as 4T2)	$[3, 462]$
4.0.183873025.1	x^4 - x^3 + 18x^2 - 72x + 5184	\( 5^{2}\cdot 7\cdot 101^{2}\cdot 103 \)	$D_{4}$ (as 4T3)	$[1128]$
4.0.186773169.2	x^4 - x^3 - 24x^2 - 60x + 3600	\( 3\cdot 11\cdot 17\cdot 577^{2} \)	$D_{4}$ (as 4T3)	$[14, 84]$
4.0.193374025.1	x^4 - x^3 + 239x^2 - 615x + 12600	\( 5^{2}\cdot 13^{2}\cdot 37\cdot 1237 \)	$D_{4}$ (as 4T3)	$[1020]$
4.0.195248689.1	x^4 - x^3 + 829x^2 - 663x + 169898	\( 17^{2}\cdot 675601 \)	$D_{4}$ (as 4T3)	$[1001]$
4.0.200179025.2	x^4 - x^3 + 184x^2 - 400x + 11520	\( 5^{2}\cdot 29^{2}\cdot 9521 \)	$D_{4}$ (as 4T3)	$[4, 364]$
4.0.206209600.2	x^4 - 2x^3 + 161x^2 - 160x + 9990	\( 2^{6}\cdot 5^{2}\cdot 359^{2} \)	$C_2^2$ (as 4T2)	$[2, 2, 266]$
4.0.206928225.1	x^4 - x^3 + 364x^2 - 1980x + 7680	\( 3^{2}\cdot 5^{2}\cdot 7^{2}\cdot 137^{2} \)	$C_2^2$ (as 4T2)	$[2, 504]$
4.0.212457625.1	x^4 - x^3 + 101x^2 - 431x + 3786	\( 5^{3}\cdot 29^{2}\cdot 43\cdot 47 \)	$D_{4}$ (as 4T3)	$[8, 280]$
4.0.213580537.1	x^4 - 2x^3 + 459x^2 - 458x + 46304	\( 17^{2}\cdot 587\cdot 1259 \)	$D_{4}$ (as 4T3)	$[1014]$
4.0.221664625.1	x^4 - x^3 + 321x^2 - 1111x + 14726	\( 5^{3}\cdot 7\cdot 13^{2}\cdot 1499 \)	$D_{4}$ (as 4T3)	$[4, 276]$
4.0.225450225.7	x^4 + 83x^2 + 5476	\( 3^{2}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 13^{2} \)	$C_2^2$ (as 4T2)	$[4, 12, 24]$
4.0.226426009.1	x^4 - 2x^3 + 483x^2 - 482x + 49088	\( 17^{2}\cdot 421\cdot 1861 \)	$D_{4}$ (as 4T3)	$[1098]$
4.0.227376241.1	x^4 + 435x^2 + 51076	\( 17^{2}\cdot 887^{2} \)	$C_2^2$ (as 4T2)	$[1131]$
4.0.229825600.6	x^4 + 374x^2 + 36864	\( 2^{6}\cdot 5^{2}\cdot 379^{2} \)	$C_2^2$ (as 4T2)	$[1056]$
4.0.230180841.1	x^4 - x^3 + 481x^2 + 201x + 53766	\( 3^{2}\cdot 11^{2}\cdot 211369 \)	$D_{4}$ (as 4T3)	$[1024]$
4.0.230892025.1	x^4 - x^3 + 243x^2 - 487x + 14804	\( 5^{2}\cdot 7\cdot 13^{2}\cdot 37\cdot 211 \)	$D_{4}$ (as 4T3)	$[4, 276]$
4.0.231770176.7	x^4 - 2x^3 + 949x^2 - 948x + 228482	\( 2^{6}\cdot 11^{2}\cdot 173^{2} \)	$C_2^2$ (as 4T2)	$[1100]$
4.0.238801225.1	x^4 - 2x^3 + 271x^2 - 270x + 3600	\( 5^{2}\cdot 13^{2}\cdot 29\cdot 1949 \)	$D_{4}$ (as 4T3)	$[2, 2, 280]$
4.0.239308225.2	x^4 - 2x^3 + 177x^2 - 176x + 3584	\( 5^{2}\cdot 13^{3}\cdot 4357 \)	$D_{4}$ (as 4T3)	$[1388]$
4.0.239537529.8	x^4 + 687x^2 + 129600	\( 3^{2}\cdot 7^{2}\cdot 11^{2}\cdot 67^{2} \)	$C_2^2$ (as 4T2)	$[4, 264]$
4.0.239727705.1	x^4 - 2x^3 - 137x^2 + 138x + 6272	\( 3\cdot 5\cdot 7\cdot 1511^{2} \)	$D_{4}$ (as 4T3)	$[1274]$
4.0.239847169.1	x^4 + 447x^2 + 53824	\( 17^{2}\cdot 911^{2} \)	$C_2^2$ (as 4T2)	$[1085]$
4.0.241958025.11	x^4 - x^3 - 257x^2 + 2073x + 268584	\( 3^{2}\cdot 5^{2}\cdot 17^{2}\cdot 61^{2} \)	$C_2^2$ (as 4T2)	$[2, 2, 260]$
4.0.243609664.6	x^4 - 2x^3 + 973x^2 - 972x + 240098	\( 2^{6}\cdot 1951^{2} \)	$C_2^2$ (as 4T2)	$[1056]$
4.0.244078129.1	x^4 + 451x^2 + 54756	\( 17^{2}\cdot 919^{2} \)	$C_2^2$ (as 4T2)	$[1064]$
4.0.244578321.1	x^4 - 181x^2 + 12100	\( 3^{2}\cdot 13^{2}\cdot 401^{2} \)	$C_2^2$ (as 4T2)	$[1160]$
4.0.244612201.1	x^4 - x^3 + 921x^2 - 607x + 212678	\( 17^{2}\cdot 829\cdot 1021 \)	$D_{4}$ (as 4T3)	$[1068]$
4.0.247041600.1	x^4 - 2x^3 + 507x^2 + 984x + 10314	\( 2^{6}\cdot 3\cdot 5^{2}\cdot 13\cdot 37\cdot 107 \)	$D_{4}$ (as 4T3)	$[2, 4, 144]$

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