Number field search results

Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

Results (1-50 of 2949 matches)

 

Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
4.0.318059997625.2	$x^{4} - x^{3} + 11691 x^{2} + 9 x + 34142796$	$4$	[0,2]	$5^{3}\cdot 17^{2}\cdot 19^{2}\cdot 29^{3}$	$4$	$750.978083633$	$750.9780836334288$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 2, 13192]$	$2$	$1$	$6.359570875399758$
4.0.1373656048625.1	$x^{4} - x^{3} + 1301 x^{2} - 11311 x + 834106$	$4$	[0,2]	$5^{3}\cdot 7\cdot 83\cdot 89\cdot 461^{2}$	$5$	$1082.60368421$	$16325.294913320155$	✓			$D_{4}$ (as 4T3)	$[2, 2, 30176]$	$2$	$1$	$9.128913361511804$
4.0.1470055574225.1	$x^{4} - x^{3} + 343 x^{2} - 8527 x + 182904$	$4$	[0,2]	$5^{2}\cdot 7\cdot 29^{2}\cdot 47\cdot 461^{2}$	$5$	$1101.11692545$	$4689.563412515071$	✓			$D_{4}$ (as 4T3)	$[2, 73952]$	$2$	$1$	$9.128913361511804$
4.0.1706927328793.2	$x^{4} - x^{3} + 12285 x^{2} - 74187 x + 32180814$	$4$	[0,2]	$17^{3}\cdot 41^{3}\cdot 71^{2}$	$3$	$1143.01981156$	$1143.0198115577966$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 58812]$	$2$	$1$	$11.151926901726478$
4.0.1918133542217.1	$x^{4} - 2 x^{3} + 1751 x^{2} - 1750 x + 745976$	$4$	[0,2]	$401^{2}\cdot 2099\cdot 5683$	$3$	$1176.84620166$	$69161.95064484517$	✓			$D_{4}$ (as 4T3)	$[5, 20750]$	$2$	$1$	$7.379007737977811$
4.0.2113257976393.1	$x^{4} - x^{3} + 13679 x^{2} + 137701 x + 17966196$	$4$	[0,2]	$17^{3}\cdot 41^{3}\cdot 79^{2}$	$3$	$1205.69685817$	$1205.6968581676895$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 38028]$	$2$	$1$	$11.151926901726478$
4.0.2134683011825.1	$x^{4} - x^{3} - 503 x^{2} - 3559 x + 259086$	$4$	[0,2]	$5^{2}\cdot 7^{2}\cdot 13^{2}\cdot 67^{2}\cdot 2297$	$5$	$1208.74126449$	$8368.03710555827$	✓			$D_{4}$ (as 4T3)	$[2, 2, 26096]$	$2$	$1$	$15.071660356100303$
4.0.2195420073025.1	$x^{4} + 1647 x^{2} + 1048576$	$4$	[0,2]	$5^{2}\cdot 401^{2}\cdot 739^{2}$	$3$	$1217.24894742$	$1217.2489474220135$	✓	✓		$C_2^2$ (as 4T2)	$[2, 90, 720]$	$2$	$1$	$7.379007737977811$
4.0.2258721005225.1	$x^{4} - x^{3} + 403 x^{2} + 5273 x + 225204$	$4$	[0,2]	$5^{2}\cdot 41\cdot 461^{2}\cdot 10369$	$4$	$1225.92992879$	$31303.711361434445$	✓			$D_{4}$ (as 4T3)	$[2, 87264]$	$2$	$1$	$9.128913361511804$
4.0.2444555695025.1	$x^{4} - x^{3} - 287 x^{2} + 7273 x + 242854$	$4$	[0,2]	$5^{2}\cdot 17^{2}\cdot 61^{2}\cdot 79\cdot 1151$	$5$	$1250.40293409$	$21713.287751973443$	✓			$D_{4}$ (as 4T3)	$[4, 25760]$	$2$	$1$	$9.939723042792991$
4.0.2667398888225.1	$x^{4} - x^{3} + 433 x^{2} + 2953 x + 249334$	$4$	[0,2]	$5^{2}\cdot 89\cdot 461^{2}\cdot 5641$	$4$	$1277.97392095$	$34017.97973131268$	✓			$D_{4}$ (as 4T3)	$[4, 32736]$	$2$	$1$	$9.128913361511804$
4.0.2676487143193.1	$x^{4} - x^{3} + 47861 x^{2} - 95735 x + 502488786$	$4$	[0,2]	$43^{2}\cdot 61^{2}\cdot 73^{3}$	$3$	$1279.06109829$	$1279.061098286417$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 30292]$	$2$	$1$	$15.333380838516575$
4.0.2872012728585.1	$x^{4} + 1531 x^{2} + 582660$	$4$	[0,2]	$3\cdot 5\cdot 7^{2}\cdot 11^{2}\cdot 13\cdot 83\cdot 173^{2}$	$7$	$1301.80696286$	$14683.33698448687$	✓			$D_{4}$ (as 4T3)	$[2, 2, 26260]$	$2$	$1$	$15.853204937705078$
4.0.3112244760937.1	$x^{4} - x^{3} + 15563 x^{2} - 219215 x + 5781636$	$4$	[0,2]	$13^{3}\cdot 61^{3}\cdot 79^{2}$	$3$	$1328.21516993$	$1328.2151699277294$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 2, 21320]$	$2$	$1$	$18.16182962316263$
4.0.3129592943529.1	$x^{4} - x^{3} + 226 x^{2} + 5664 x + 235680$	$4$	[0,2]	$3^{2}\cdot 13^{2}\cdot 79^{2}\cdot 439\cdot 751$	$5$	$1330.06223787$	$31871.175205818814$	✓			$D_{4}$ (as 4T3)	$[16, 7920]$	$2$	$1$	$19.413728414653708$
4.0.3296499325657.4	$x^{4} - x^{3} + 53117 x^{2} - 106247 x + 618861882$	$4$	[0,2]	$41^{2}\cdot 71^{2}\cdot 73^{3}$	$3$	$1347.45182767$	$1347.4518276699955$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 4, 7556]$	$2$	$1$	$15.333380838516575$
4.0.3468687365897.1	$x^{4} - x^{3} + 103 x^{2} - 5903 x + 243400$	$4$	[0,2]	$13^{2}\cdot 277^{2}\cdot 267497$	$3$	$1364.71287758$	$31036.376995390427$	✓			$D_{4}$ (as 4T3)	$[5, 26600]$	$2$	$1$	$9.57512235998762$
4.0.3517510775833.1	$x^{4} - x^{3} + 54869 x^{2} - 109751 x + 660343986$	$4$	[0,2]	$31^{2}\cdot 73^{3}\cdot 97^{2}$	$3$	$1369.4899803$	$1369.48998029865$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 27514]$	$2$	$1$	$15.333380838516575$
4.0.3517558883225.1	$x^{4} - x^{3} - 275 x^{2} - 3103 x + 259314$	$4$	[0,2]	$5^{2}\cdot 17^{2}\cdot 61^{2}\cdot 130841$	$4$	$1369.49466275$	$26046.316150273535$	✓			$D_{4}$ (as 4T3)	$[2, 2, 28020]$	$2$	$1$	$9.939723042792991$
4.0.3637089707025.1	$x^{4} - x^{3} + 1394 x^{2} - 7900 x + 949480$	$4$	[0,2]	$3\cdot 5^{2}\cdot 173\cdot 461^{2}\cdot 1319$	$5$	$1380.9835431$	$39722.95438408377$	✓			$D_{4}$ (as 4T3)	$[8, 16672]$	$2$	$1$	$9.128913361511804$
4.0.3641893267257.1	$x^{4} - x^{3} + 232 x^{2} - 3636 x + 253920$	$4$	[0,2]	$3^{2}\cdot 7^{2}\cdot 17\cdot 149^{2}\cdot 21881$	$5$	$1381.43928899$	$34116.21363809296$	✓			$D_{4}$ (as 4T3)	$[2, 58440]$	$2$	$1$	$14.979941173469065$
4.0.3668421791097.1	$x^{4} - x^{3} + 295 x^{2} + 945 x + 260904$	$4$	[0,2]	$3^{2}\cdot 7\cdot 151\cdot 409\cdot 971^{2}$	$5$	$1383.94813942$	$35487.008453798975$	✓			$D_{4}$ (as 4T3)	$[2, 50820]$	$2$	$1$	$16.530271127433164$
4.0.3681619771617.1	$x^{4} - 2 x^{3} + 1689 x^{2} - 1688 x + 691564$	$4$	[0,2]	$3^{2}\cdot 577^{2}\cdot 709\cdot 1733$	$4$	$1385.1912305$	$46118.04968773072$	✓			$D_{4}$ (as 4T3)	$[2, 2, 30730]$	$2$	$1$	$7.743269512775463$
4.0.3707906289945.1	$x^{4} - x^{3} + 848 x^{2} - 22480 x + 634240$	$4$	[0,2]	$3\cdot 5\cdot 11\cdot 13^{2}\cdot 277^{2}\cdot 1733$	$6$	$1387.65718089$	$32088.751066378387$	✓			$D_{4}$ (as 4T3)	$[2, 4, 19320]$	$2$	$1$	$9.57512235998762$
4.0.3709261838625.1	$x^{4} - x^{3} + 1406 x^{2} + 5924 x + 961336$	$4$	[0,2]	$3\cdot 5^{3}\cdot 7\cdot 61\cdot 109\cdot 461^{2}$	$6$	$1387.78398958$	$26826.609022160876$	✓			$D_{4}$ (as 4T3)	$[2, 2, 2, 13024]$	$2$	$1$	$9.128913361511804$
4.0.3738806623225.1	$x^{4} - x^{3} + 84 x^{2} + 14480 x + 989120$	$4$	[0,2]	$5^{2}\cdot 157\cdot 397\cdot 1549^{2}$	$4$	$1390.53924639$	$21971.301850368356$	✓			$D_{4}$ (as 4T3)	$[3, 33528]$	$2$	$1$	$10.341032553065643$
4.0.3855998171025.1	$x^{4} - x^{3} + 1074 x^{2} - 15040 x + 463360$	$4$	[0,2]	$3^{3}\cdot 5^{2}\cdot 7^{3}\cdot 11\cdot 13^{2}\cdot 17^{2}\cdot 31$	$7$	$1401.30994704$	$6021.7510849830505$	✓			$D_{4}$ (as 4T3)	$[2, 2, 2, 4, 3464]$	$2$	$1$	$11.646074284346346$
4.0.3898760997033.1	$x^{4} - x^{3} + 1630 x^{2} - 5472 x + 895872$	$4$	[0,2]	$3^{2}\cdot 7\cdot 47\cdot 1033\cdot 1129^{2}$	$5$	$1405.17900786$	$33927.80068026809$	✓			$D_{4}$ (as 4T3)	$[2, 2, 2, 14706]$	$2$	$1$	$11.634240035110537$
4.0.3915194687625.1	$x^{4} - 2 x^{3} + 799 x^{2} - 798 x + 46256$	$4$	[0,2]	$3\cdot 5^{3}\cdot 13\cdot 461^{2}\cdot 3779$	$5$	$1406.65741763$	$27561.2376216004$	✓			$D_{4}$ (as 4T3)	$[2, 8, 7520]$	$2$	$1$	$9.128913361511804$
4.0.3925004187777.1	$x^{4} - 2 x^{3} + 1729 x^{2} - 1728 x + 737264$	$4$	[0,2]	$3\cdot 17\cdot 271\cdot 577^{2}\cdot 853$	$5$	$1407.53768423$	$82476.86706586278$	✓			$D_{4}$ (as 4T3)	$[2, 2, 26320]$	$2$	$1$	$7.743269512775463$
4.0.4011195510729.1	$x^{4} - 2 x^{3} + 1743 x^{2} - 1742 x + 753448$	$4$	[0,2]	$3^{2}\cdot 11\cdot 131\cdot 577^{2}\cdot 929$	$5$	$1415.20207815$	$48138.037548283995$	✓			$D_{4}$ (as 4T3)	$[2, 2, 2, 14000]$	$2$	$1$	$7.743269512775463$
4.0.4094410850993.1	$x^{4} - x^{3} + 16 x^{2} + 3500 x + 255072$	$4$	[0,2]	$19^{2}\cdot 211^{2}\cdot 254753$	$3$	$1422.48552206$	$31957.859393269755$	✓			$D_{4}$ (as 4T3)	$[102520]$	$2$	$1$	$17.87128063285087$
4.0.4151177088929.1	$x^{4} - x^{3} + 121 x^{2} - 2311 x + 259710$	$4$	[0,2]	$13^{2}\cdot 113\cdot 277^{2}\cdot 2833$	$4$	$1427.3905434$	$33952.6807336328$	✓			$D_{4}$ (as 4T3)	$[10, 26200]$	$2$	$1$	$9.57512235998762$
4.0.4189202798129.1	$x^{4} - x^{3} - 59 x^{2} - 2671 x + 259530$	$4$	[0,2]	$29^{2}\cdot 89\cdot 149^{2}\cdot 2521$	$4$	$1430.64817844$	$31136.770047646238$	✓			$D_{4}$ (as 4T3)	$[5, 22460]$	$2$	$1$	$23.612652309719678$
4.0.4198910222625.1	$x^{4} - x^{3} + 911 x^{2} + 18849 x + 386256$	$4$	[0,2]	$3\cdot 5^{3}\cdot 19\cdot 47\cdot 59\cdot 461^{2}$	$6$	$1431.47625111$	$28542.38951215586$	✓			$D_{4}$ (as 4T3)	$[2, 2, 2, 14944]$	$2$	$1$	$9.128913361511804$
4.0.4208417581689.1	$x^{4} - x^{3} + 1471 x^{2} - 8031 x + 766272$	$4$	[0,2]	$3^{2}\cdot 233\cdot 1193\cdot 1297^{2}$	$4$	$1432.28586702$	$32887.34375105414$	✓			$D_{4}$ (as 4T3)	$[2, 2, 38544]$	$2$	$1$	$8.553717928916416$
4.0.4235082476625.2	$x^{4} - x^{3} + 63806 x^{2} + 4 x + 1002641656$	$4$	[0,2]	$3^{2}\cdot 5^{3}\cdot 7^{2}\cdot 11^{2}\cdot 13^{3}\cdot 17^{2}$	$6$	$1434.54926773$	$1434.5492677290474$	✓	✓		$C_4$ (as 4T1)	$[2, 2, 2, 2, 4, 1700]$	$2$	$1$	$5.55294456145$
4.0.4274244766857.1	$x^{4} - x^{3} - 311 x^{2} - 24039 x + 935406$	$4$	[0,2]	$3\cdot 13^{2}\cdot 31\cdot 541\cdot 709^{2}$	$5$	$1437.85418947$	$21534.50535768119$	✓			$D_{4}$ (as 4T3)	$[6, 18972]$	$2$	$1$	$10.51504499532034$
4.0.4358204042225.1	$x^{4} - x^{3} - 62 x^{2} - 512 x + 262144$	$4$	[0,2]	$5^{2}\cdot 11^{2}\cdot 79^{2}\cdot 230849$	$4$	$1444.86373184$	$31670.789459689822$	✓			$D_{4}$ (as 4T3)	$[4, 28536]$	$2$	$1$	$14.73288949752545$
4.0.4452303944289.1	$x^{4} - 2 x^{3} + 1573 x^{2} - 1572 x + 573188$	$4$	[0,2]	$3\cdot 17^{2}\cdot 41^{2}\cdot 1607\cdot 1901$	$5$	$1452.60053954$	$79923.77954651543$	✓			$D_{4}$ (as 4T3)	$[4, 25320]$	$2$	$1$	$11.151926901726478$
4.0.4478865411825.1	$x^{4} - x^{3} + 1738 x^{2} + 1248 x + 1015584$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 7\cdot 23\cdot 97\cdot 1129^{2}$	$6$	$1454.76218353$	$16262.65338129052$	✓			$D_{4}$ (as 4T3)	$[2, 2, 2, 2, 6, 1170]$	$2$	$1$	$11.634240035110537$
4.0.4565098917225.1	$x^{4} - 2 x^{3} + 1107 x^{2} - 1106 x + 89824$	$4$	[0,2]	$3^{3}\cdot 5^{2}\cdot 7^{2}\cdot 11^{2}\cdot 17^{2}\cdot 3947$	$6$	$1461.7144763005422$	$11585.888101190561$	✓			$D_{4}$ (as 4T3)	$[2, 4, 8, 2408]$	$2$	$1$	$11.646074284346346$
4.0.4596570331225.1	$x^{4} - x^{3} + 1734 x^{2} + 1280 x + 1015520$	$4$	[0,2]	$5^{2}\cdot 19\cdot 127\cdot 229^{2}\cdot 1453$	$5$	$1464.22722424$	$63359.86036127289$	✓			$D_{4}$ (as 4T3)	$[2, 50616]$	$2$	$1$	$15.651289783418354$
4.0.4791323186697.1	$x^{4} - 2 x^{3} + 1159 x^{2} - 1158 x + 178304$	$4$	[0,2]	$3\cdot 19\cdot 107\cdot 467\cdot 1297^{2}$	$5$	$1479.49624253$	$60779.58704203246$	✓			$D_{4}$ (as 4T3)	$[2, 2, 27060]$	$2$	$1$	$8.553717928916416$
4.0.4954159284945.1	$x^{4} - x^{3} - 247 x^{2} - 31635 x + 836490$	$4$	[0,2]	$3\cdot 5\cdot 13\cdot 331\cdot 8761^{2}$	$5$	$1491.90954137$	$23779.79699240513$	✓			$D_{4}$ (as 4T3)	$[2, 2, 27270]$	$2$	$1$	$13.683233235806123$
4.0.4974898952025.1	$x^{4} - x^{3} + 697 x^{2} - 13959 x + 960606$	$4$	[0,2]	$3^{2}\cdot 5^{2}\cdot 17^{2}\cdot 29\cdot 61^{2}\cdot 709$	$6$	$1493.46849665$	$17883.6896360902$	✓			$D_{4}$ (as 4T3)	$[2, 4, 13140]$	$2$	$1$	$9.939723042792991$
4.0.5072491218345.1	$x^{4} - 2 x^{3} + 1243 x^{2} - 1242 x + 249032$	$4$	[0,2]	$3\cdot 5\cdot 127\cdot 1129^{2}\cdot 2089$	$5$	$1500.73954314$	$67029.14519073028$	✓			$D_{4}$ (as 4T3)	$[2, 2, 26640]$	$2$	$1$	$11.634240035110537$
4.0.5104071276025.1	$x^{4} - x^{3} + 1344 x^{2} + 4400 x + 1009280$	$4$	[0,2]	$5^{2}\cdot 17\cdot 37\cdot 541^{2}\cdot 1109$	$5$	$1503.06991653$	$43438.491053442456$	✓			$D_{4}$ (as 4T3)	$[2, 54096]$	$2$	$1$	$9.28896668388649$
4.0.5141489021625.1	$x^{4} - x^{3} - 869 x^{2} + 4809 x + 1044636$	$4$	[0,2]	$3\cdot 5^{3}\cdot 11\cdot 229\cdot 2333^{2}$	$5$	$1505.81711227$	$14039.756762853563$	✓			$D_{4}$ (as 4T3)	$[2, 4, 19920]$	$2$	$1$	$10.750599680931229$
4.0.5193995281025.1	$x^{4} - 2 x^{3} + 1397 x^{2} - 1396 x + 396704$	$4$	[0,2]	$5^{2}\cdot 181^{2}\cdot 1031\cdot 6151$	$4$	$1509.64692831$	$75757.64849175296$	✓			$D_{4}$ (as 4T3)	$[2, 4, 13080]$	$2$	$1$	$13.164046441094415$