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
4.0.3905625025.1	x^4 + 143x^2 + 20736	\( 5^{2}\cdot 29^{2}\cdot 431^{2} \)	$C_2^2$ (as 4T2)	$[2, 6, 840]$
4.0.6558307225.1	x^4 - 2x^3 + 355x^2 - 354x + 19584	\( 5^{2}\cdot 29^{2}\cdot 73\cdot 4273 \)	$D_{4}$ (as 4T3)	$[10872]$
4.0.6850975225.1	x^4 - x^3 + 653x^2 - 2447x + 88194	\( 5^{2}\cdot 29^{2}\cdot 325849 \)	$D_{4}$ (as 4T3)	$[15080]$
4.0.9176172025.1	x^4 - x^3 + 707x^2 + 1441x + 115356	\( 5^{2}\cdot 17\cdot 29^{2}\cdot 25673 \)	$D_{4}$ (as 4T3)	$[13288]$
4.0.10612263625.4	x^4 - x^3 + 2121x^2 + 9x + 1155006	\( 5^{3}\cdot 29^{3}\cdot 59^{2} \)	$C_4$ (as 4T1)	$[2, 2, 2, 2, 680]$
4.0.11200953025.1	x^4 - x^3 + 383x^2 + 1513x + 58584	\( 5^{2}\cdot 101^{2}\cdot 167\cdot 263 \)	$D_{4}$ (as 4T3)	$[10728]$
4.0.11606830225.1	x^4 + 299x^2 + 49284	\( 5^{2}\cdot 29^{2}\cdot 743^{2} \)	$C_2^2$ (as 4T2)	$[3, 4536]$
4.0.11809386241.1	x^4 - 65x^2 + 28224	\( 271^{2}\cdot 401^{2} \)	$C_2^2$ (as 4T2)	$[5, 2805]$
4.0.12161514225.2	x^4 - x^3 - 96x^2 - 240x + 57600	\( 3\cdot 5^{2}\cdot 7\cdot 109\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[8, 1696]$
4.0.13135175505.1	x^4 - x^3 + 622x^2 - 4968x + 186240	\( 3^{2}\cdot 5\cdot 229\cdot 1129^{2} \)	$D_{4}$ (as 4T3)	$[2, 18, 324]$
4.0.13530567489.1	x^4 - 2x^3 + 783x^2 - 782x + 23056	\( 3\cdot 19\cdot 23\cdot 31\cdot 577^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 3080]$
4.0.14194419025.1	x^4 - x^3 + 815x^2 - 1223x + 176664	\( 5^{2}\cdot 17\cdot 29^{2}\cdot 151\cdot 263 \)	$D_{4}$ (as 4T3)	$[8, 1792]$
4.0.14244220025.1	x^4 - 2x^3 + 619x^2 - 618x + 37856	\( 5^{2}\cdot 7\cdot 383\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[10016]$
4.0.15078478225.1	x^4 - x^3 + 833x^2 + 73x + 187014	\( 5^{2}\cdot 29^{2}\cdot 127\cdot 5647 \)	$D_{4}$ (as 4T3)	$[22648]$
4.0.15539969441.1	x^4 - x^3 + 652x^2 - 3584x + 115712	\( 241\cdot 401^{3} \)	$D_{4}$ (as 4T3)	$[10010]$
4.0.15552833521.1	x^4 - 45x^2 + 31684	\( 311^{2}\cdot 401^{2} \)	$C_2^2$ (as 4T2)	$[12160]$
4.0.15717245161.1	x^4 - x^3 + 275x^2 - 3383x + 26436	\( 17\cdot 577^{2}\cdot 2777 \)	$D_{4}$ (as 4T3)	$[15904]$
4.0.16244777025.1	x^4 + 367x^2 + 65536	\( 3^{2}\cdot 5^{2}\cdot 29^{2}\cdot 293^{2} \)	$C_2^2$ (as 4T2)	$[4, 8, 352]$
4.0.16591834777.1	x^4 - x^3 + 1133x^2 + 12241x + 188514	\( 7^{2}\cdot 17^{3}\cdot 41^{3} \)	$C_4$ (as 4T1)	$[2, 2, 3900]$
4.0.16766197025.1	x^4 - 2x^3 + 561x^2 - 560x + 49980	\( 5^{2}\cdot 29^{2}\cdot 113\cdot 7057 \)	$D_{4}$ (as 4T3)	$[3, 3816]$
4.0.16898402225.1	x^4 - x^3 + 883x^2 - 967x + 209364	\( 5^{2}\cdot 29^{2}\cdot 803729 \)	$D_{4}$ (as 4T3)	$[12728]$
4.0.17698520889.1	x^4 - x^3 + 391x^2 + 8073x + 73008	\( 3^{2}\cdot 7\cdot 167\cdot 1297^{2} \)	$D_{4}$ (as 4T3)	$[2, 22, 264]$
4.0.17794403625.1	x^4 - 2x^3 + 1389x^2 - 1388x + 476416	\( 3\cdot 5^{3}\cdot 17\cdot 29^{2}\cdot 3319 \)	$D_{4}$ (as 4T3)	$[2, 4, 1720]$
4.0.17941210881.2	x^4 - x^3 + 1324x^2 + 420x + 536448	\( 3\cdot 11\cdot 23\cdot 71\cdot 577^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 3514]$
4.0.18096659025.1	x^4 - 2x^3 + 1395x^2 - 1394x + 484504	\( 3\cdot 5^{2}\cdot 29^{2}\cdot 113\cdot 2539 \)	$D_{4}$ (as 4T3)	$[2, 5240]$
4.0.19026468625.1	x^4 - x^3 + 2846x^2 + 11464x + 927936	\( 5^{3}\cdot 29^{3}\cdot 79^{2} \)	$C_4$ (as 4T1)	$[2, 2, 8, 680]$
4.0.19338143225.1	x^4 - x^3 + 943x^2 - 127x + 238704	\( 5^{2}\cdot 29^{2}\cdot 919769 \)	$D_{4}$ (as 4T3)	$[12952]$
4.0.19699268625.1	x^4 - 2x^3 + 1539x^2 - 1538x + 527416	\( 3^{2}\cdot 5^{3}\cdot 29^{2}\cdot 47\cdot 443 \)	$D_{4}$ (as 4T3)	$[2, 2, 8, 360]$
4.0.19858217625.1	x^4 - 2x^3 + 1059x^2 - 1058x + 59296	\( 3^{2}\cdot 5^{3}\cdot 29^{2}\cdot 139\cdot 151 \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 1400]$
4.0.19906068497.1	x^4 - x^3 + 736x^2 + 620x + 257952	\( 7\cdot 23\cdot 97\cdot 1129^{2} \)	$D_{4}$ (as 4T3)	$[6, 1854]$
4.0.20614781225.1	x^4 - x^3 + 973x^2 - 287x + 254194	\( 5^{2}\cdot 29^{2}\cdot 980489 \)	$D_{4}$ (as 4T3)	$[15800]$
4.0.20724193681.1	x^4 - 21x^2 + 36100	\( 359^{2}\cdot 401^{2} \)	$C_2^2$ (as 4T2)	$[11305]$
4.0.20833169569.3	x^4 + 1559x^2 + 571536	\( 37^{2}\cdot 47^{2}\cdot 83^{2} \)	$C_2^2$ (as 4T2)	$[2, 6080]$
4.0.21001977625.2	x^4 - x^3 + 2991x^2 + 9x + 2274696	\( 5^{3}\cdot 29^{3}\cdot 83^{2} \)	$C_4$ (as 4T1)	$[2, 2, 2, 2248]$
4.0.21394849185.1	x^4 - x^3 + 637x^2 + 105x + 210858	\( 3^{2}\cdot 5\cdot 373\cdot 1129^{2} \)	$D_{4}$ (as 4T3)	$[2, 18, 306]$
4.0.21773658481.4	x^4 + 1779x^2 + 828100	\( 41^{2}\cdot 59^{2}\cdot 61^{2} \)	$C_2^2$ (as 4T2)	$[2, 6, 858]$
4.0.22705667856.1	x^4 + 6277x^2 + 9859600	\( 2^{4}\cdot 3^{2}\cdot 29^{2}\cdot 433^{2} \)	$C_2^2$ (as 4T2)	$[2, 2, 2726]$
4.0.22872572625.1	x^4 - 2x^3 + 449x^2 - 448x + 13296	\( 3\cdot 5^{3}\cdot 7\cdot 41\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 4320]$
4.0.23025115024.2	x^4 + 1129x^2 + 112900	\( 2^{4}\cdot 1129^{3} \)	$C_4$ (as 4T1)	$[2, 5202]$
4.0.23410265225.1	x^4 - 2x^3 + 615x^2 - 614x + 69744	\( 5^{2}\cdot 17\cdot 29^{2}\cdot 65497 \)	$D_{4}$ (as 4T3)	$[10296]$
4.0.24082224225.1	x^4 - 2x^3 + 1647x^2 - 1646x + 644704	\( 3\cdot 5^{2}\cdot 17\cdot 29^{2}\cdot 37\cdot 607 \)	$D_{4}$ (as 4T3)	$[2, 8, 1120]$
4.0.24093248400.1	x^4 + 3873x^2 + 3779136	\( 2^{4}\cdot 3^{2}\cdot 5^{2}\cdot 13^{2}\cdot 199^{2} \)	$C_2^2$ (as 4T2)	$[2, 48, 144]$
4.0.24205213729.1	x^4 - x^3 + 1893x^2 - 1999x + 990506	\( 109\cdot 401^{2}\cdot 1381 \)	$D_{4}$ (as 4T3)	$[5, 2380]$
4.0.24435185593.1	x^4 - x^3 + 1289x^2 - 19379x + 114858	\( 7^{2}\cdot 13^{3}\cdot 61^{3} \)	$C_4$ (as 4T1)	$[2, 2, 3016]$
4.0.24570553601.1	x^4 - x^3 + 742x^2 - 1624x + 173632	\( 11\cdot 29\cdot 401^{2}\cdot 479 \)	$D_{4}$ (as 4T3)	$[10, 1290]$
4.0.24826548793.2	x^4 - x^3 + 357x^2 - 1231x + 49706	\( 181\cdot 401^{2}\cdot 853 \)	$D_{4}$ (as 4T3)	$[13510]$
4.0.24884847225.1	x^4 - 2x^3 + 775x^2 - 774x + 141264	\( 3^{2}\cdot 5^{2}\cdot 7^{3}\cdot 89\cdot 3623 \)	$D_{4}$ (as 4T3)	$[2, 5004]$
4.0.25315971225.1	x^4 - x^3 + 1109x^2 - 2095x + 311770	\( 3\cdot 5^{2}\cdot 29^{2}\cdot 71\cdot 5653 \)	$D_{4}$ (as 4T3)	$[2, 5320]$
4.0.25792776625.1	x^4 + 415x^2 + 24640	\( 5^{3}\cdot 7\cdot 11\cdot 1637^{2} \)	$D_{4}$ (as 4T3)	$[4, 2828]$
4.0.25977664657.1	x^4 - x^3 + 152x^2 - 860x + 25872	\( 7\cdot 17^{2}\cdot 41^{2}\cdot 7639 \)	$D_{4}$ (as 4T3)	$[3, 6468]$

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