Global number field search results

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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
4.0.318059997625.2	x^4 - x^3 + 11691x^2 + 9x + 34142796	\( 5^{3}\cdot 17^{2}\cdot 19^{2}\cdot 29^{3} \)	$C_4$ (as 4T1)	$[2, 2, 2, 13192]$
4.0.1373656048625.1	x^4 - x^3 + 1301x^2 - 11311x + 834106	\( 5^{3}\cdot 7\cdot 83\cdot 89\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 30176]$
4.0.1470055574225.1	x^4 - x^3 + 343x^2 - 8527x + 182904	\( 5^{2}\cdot 7\cdot 29^{2}\cdot 47\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[2, 73952]$
4.0.1706927328793.2	x^4 - x^3 + 12285x^2 - 74187x + 32180814	\( 17^{3}\cdot 41^{3}\cdot 71^{2} \)	$C_4$ (as 4T1)	$[2, 2, 58812]$
4.0.1918133542217.1	x^4 - 2x^3 + 1751x^2 - 1750x + 745976	\( 401^{2}\cdot 2099\cdot 5683 \)	$D_{4}$ (as 4T3)	$[5, 20750]$
4.0.2113257976393.1	x^4 - x^3 + 13679x^2 + 137701x + 17966196	\( 17^{3}\cdot 41^{3}\cdot 79^{2} \)	$C_4$ (as 4T1)	$[2, 2, 38028]$
4.0.2134683011825.1	x^4 - x^3 - 503x^2 - 3559x + 259086	\( 5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 67^{2}\cdot 2297 \)	$D_{4}$ (as 4T3)	$[2, 2, 26096]$
4.0.2195420073025.1	x^4 + 1647x^2 + 1048576	\( 5^{2}\cdot 401^{2}\cdot 739^{2} \)	$C_2^2$ (as 4T2)	$[2, 90, 720]$
4.0.2258721005225.1	x^4 - x^3 + 403x^2 + 5273x + 225204	\( 5^{2}\cdot 41\cdot 461^{2}\cdot 10369 \)	$D_{4}$ (as 4T3)	$[2, 87264]$
4.0.2444555695025.1	x^4 - x^3 - 287x^2 + 7273x + 242854	\( 5^{2}\cdot 17^{2}\cdot 61^{2}\cdot 79\cdot 1151 \)	$D_{4}$ (as 4T3)	$[4, 25760]$
4.0.2667398888225.1	x^4 - x^3 + 433x^2 + 2953x + 249334	\( 5^{2}\cdot 89\cdot 461^{2}\cdot 5641 \)	$D_{4}$ (as 4T3)	$[4, 32736]$
4.0.2676487143193.1	x^4 - x^3 + 47861x^2 - 95735x + 502488786	\( 43^{2}\cdot 61^{2}\cdot 73^{3} \)	$C_4$ (as 4T1)	$[2, 2, 30292]$
4.0.2872012728585.1	x^4 + 1531x^2 + 582660	\( 3\cdot 5\cdot 7^{2}\cdot 11^{2}\cdot 13\cdot 83\cdot 173^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 26260]$
4.0.3112244760937.1	x^4 - x^3 + 15563x^2 - 219215x + 5781636	\( 13^{3}\cdot 61^{3}\cdot 79^{2} \)	$C_4$ (as 4T1)	$[2, 2, 2, 21320]$
4.0.3129592943529.1	x^4 - x^3 + 226x^2 + 5664x + 235680	\( 3^{2}\cdot 13^{2}\cdot 79^{2}\cdot 439\cdot 751 \)	$D_{4}$ (as 4T3)	$[16, 7920]$
4.0.3296499325657.4	x^4 - x^3 + 53117x^2 - 106247x + 618861882	\( 41^{2}\cdot 71^{2}\cdot 73^{3} \)	$C_4$ (as 4T1)	$[2, 2, 4, 7556]$
4.0.3468687365897.1	x^4 - x^3 + 103x^2 - 5903x + 243400	\( 13^{2}\cdot 277^{2}\cdot 267497 \)	$D_{4}$ (as 4T3)	$[5, 26600]$
4.0.3517510775833.1	x^4 - x^3 + 54869x^2 - 109751x + 660343986	\( 31^{2}\cdot 73^{3}\cdot 97^{2} \)	$C_4$ (as 4T1)	$[2, 2, 27514]$
4.0.3517558883225.1	x^4 - x^3 - 275x^2 - 3103x + 259314	\( 5^{2}\cdot 17^{2}\cdot 61^{2}\cdot 130841 \)	$D_{4}$ (as 4T3)	$[2, 2, 28020]$
4.0.3637089707025.1	x^4 - x^3 + 1394x^2 - 7900x + 949480	\( 3\cdot 5^{2}\cdot 173\cdot 461^{2}\cdot 1319 \)	$D_{4}$ (as 4T3)	$[8, 16672]$
4.0.3641893267257.1	x^4 - x^3 + 232x^2 - 3636x + 253920	\( 3^{2}\cdot 7^{2}\cdot 17\cdot 149^{2}\cdot 21881 \)	$D_{4}$ (as 4T3)	$[2, 58440]$
4.0.3668421791097.1	x^4 - x^3 + 295x^2 + 945x + 260904	\( 3^{2}\cdot 7\cdot 151\cdot 409\cdot 971^{2} \)	$D_{4}$ (as 4T3)	$[2, 50820]$
4.0.3681619771617.1	x^4 - 2x^3 + 1689x^2 - 1688x + 691564	\( 3^{2}\cdot 577^{2}\cdot 709\cdot 1733 \)	$D_{4}$ (as 4T3)	$[2, 2, 30730]$
4.0.3707906289945.1	x^4 - x^3 + 848x^2 - 22480x + 634240	\( 3\cdot 5\cdot 11\cdot 13^{2}\cdot 277^{2}\cdot 1733 \)	$D_{4}$ (as 4T3)	$[2, 4, 19320]$
4.0.3709261838625.1	x^4 - x^3 + 1406x^2 + 5924x + 961336	\( 3\cdot 5^{3}\cdot 7\cdot 61\cdot 109\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 13024]$
4.0.3738806623225.1	x^4 - x^3 + 84x^2 + 14480x + 989120	\( 5^{2}\cdot 157\cdot 397\cdot 1549^{2} \)	$D_{4}$ (as 4T3)	$[3, 33528]$
4.0.3855998171025.1	x^4 - x^3 + 1074x^2 - 15040x + 463360	\( 3^{3}\cdot 5^{2}\cdot 7^{3}\cdot 11\cdot 13^{2}\cdot 17^{2}\cdot 31 \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 4, 3464]$
4.0.3898760997033.1	x^4 - x^3 + 1630x^2 - 5472x + 895872	\( 3^{2}\cdot 7\cdot 47\cdot 1033\cdot 1129^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 14706]$
4.0.3915194687625.1	x^4 - 2x^3 + 799x^2 - 798x + 46256	\( 3\cdot 5^{3}\cdot 13\cdot 461^{2}\cdot 3779 \)	$D_{4}$ (as 4T3)	$[2, 8, 7520]$
4.0.3925004187777.1	x^4 - 2x^3 + 1729x^2 - 1728x + 737264	\( 3\cdot 17\cdot 271\cdot 577^{2}\cdot 853 \)	$D_{4}$ (as 4T3)	$[2, 2, 26320]$
4.0.4011195510729.1	x^4 - 2x^3 + 1743x^2 - 1742x + 753448	\( 3^{2}\cdot 11\cdot 131\cdot 577^{2}\cdot 929 \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 14000]$
4.0.4094410850993.1	x^4 - x^3 + 16x^2 + 3500x + 255072	\( 19^{2}\cdot 211^{2}\cdot 254753 \)	$D_{4}$ (as 4T3)	$[102520]$
4.0.4151177088929.1	x^4 - x^3 + 121x^2 - 2311x + 259710	\( 13^{2}\cdot 113\cdot 277^{2}\cdot 2833 \)	$D_{4}$ (as 4T3)	$[10, 26200]$
4.0.4189202798129.1	x^4 - x^3 - 59x^2 - 2671x + 259530	\( 29^{2}\cdot 89\cdot 149^{2}\cdot 2521 \)	$D_{4}$ (as 4T3)	$[5, 22460]$
4.0.4198910222625.1	x^4 - x^3 + 911x^2 + 18849x + 386256	\( 3\cdot 5^{3}\cdot 19\cdot 47\cdot 59\cdot 461^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 14944]$
4.0.4208417581689.1	x^4 - x^3 + 1471x^2 - 8031x + 766272	\( 3^{2}\cdot 233\cdot 1193\cdot 1297^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 38544]$
4.0.4235082476625.2	x^4 - x^3 + 63806x^2 + 4x + 1002641656	\( 3^{2}\cdot 5^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{3}\cdot 17^{2} \)	$C_4$ (as 4T1)	$[2, 2, 2, 2, 4, 1700]$
4.0.4274244766857.1	x^4 - x^3 - 311x^2 - 24039x + 935406	\( 3\cdot 13^{2}\cdot 31\cdot 541\cdot 709^{2} \)	$D_{4}$ (as 4T3)	$[6, 18972]$
4.0.4358204042225.1	x^4 - x^3 - 62x^2 - 512x + 262144	\( 5^{2}\cdot 11^{2}\cdot 79^{2}\cdot 230849 \)	$D_{4}$ (as 4T3)	$[4, 28536]$
4.0.4452303944289.1	x^4 - 2x^3 + 1573x^2 - 1572x + 573188	\( 3\cdot 17^{2}\cdot 41^{2}\cdot 1607\cdot 1901 \)	$D_{4}$ (as 4T3)	$[4, 25320]$
4.0.4478865411825.1	x^4 - x^3 + 1738x^2 + 1248x + 1015584	\( 3^{2}\cdot 5^{2}\cdot 7\cdot 23\cdot 97\cdot 1129^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 2, 2, 6, 1170]$
4.0.4596570331225.1	x^4 - x^3 + 1734x^2 + 1280x + 1015520	\( 5^{2}\cdot 19\cdot 127\cdot 229^{2}\cdot 1453 \)	$D_{4}$ (as 4T3)	$[2, 50616]$
4.0.4791323186697.1	x^4 - 2x^3 + 1159x^2 - 1158x + 178304	\( 3\cdot 19\cdot 107\cdot 467\cdot 1297^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 27060]$
4.0.4954159284945.1	x^4 - x^3 - 247x^2 - 31635x + 836490	\( 3\cdot 5\cdot 13\cdot 331\cdot 8761^{2} \)	$D_{4}$ (as 4T3)	$[2, 2, 27270]$
4.0.4974898952025.1	x^4 - x^3 + 697x^2 - 13959x + 960606	\( 3^{2}\cdot 5^{2}\cdot 17^{2}\cdot 29\cdot 61^{2}\cdot 709 \)	$D_{4}$ (as 4T3)	$[2, 4, 13140]$
4.0.5072491218345.1	x^4 - 2x^3 + 1243x^2 - 1242x + 249032	\( 3\cdot 5\cdot 127\cdot 1129^{2}\cdot 2089 \)	$D_{4}$ (as 4T3)	$[2, 2, 26640]$
4.0.5104071276025.1	x^4 - x^3 + 1344x^2 + 4400x + 1009280	\( 5^{2}\cdot 17\cdot 37\cdot 541^{2}\cdot 1109 \)	$D_{4}$ (as 4T3)	$[2, 54096]$
4.0.5141489021625.1	x^4 - x^3 - 869x^2 + 4809x + 1044636	\( 3\cdot 5^{3}\cdot 11\cdot 229\cdot 2333^{2} \)	$D_{4}$ (as 4T3)	$[2, 4, 19920]$
4.0.5193995281025.1	x^4 - 2x^3 + 1397x^2 - 1396x + 396704	\( 5^{2}\cdot 181^{2}\cdot 1031\cdot 6151 \)	$D_{4}$ (as 4T3)	$[2, 4, 13080]$
4.0.5207620368225.1	x^4 - x^3 + 1559x^2 + 5105x + 870520	\( 3\cdot 5^{2}\cdot 11\cdot 83\cdot 269^{2}\cdot 1051 \)	$D_{4}$ (as 4T3)	$[2, 6, 9228]$

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