Number field search results

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

Results (28 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
15.1.977...323.1	$x^{15} - 62 x^{12} - 651 x^{9} + 66712 x^{6} + 311488 x^{3} + 428544$	$15$	[1,7]	$-\,3^{17}\cdot 31^{14}$	$2$	$85.6396735085572$	$88.83396458771315$				$D_{15}$ (as 15T2)	$[3, 3, 15]$	$2$	$7$	$87591483.71466897$
15.1.104...032.1	$x^{15} - 3 x^{14} - 33 x^{13} + 124 x^{12} + 483 x^{11} - 2319 x^{10} - 2706 x^{9} + 25551 x^{8} + 2529 x^{7} - 143204 x^{6} + 31821 x^{5} + 278535 x^{4} + 68827 x^{3} + 31542 x^{2} - 285666 x - 612462$	$15$	[1,7]	$-\,2^{10}\cdot 3^{17}\cdot 31^{12}$	$3$	$86.00296832962381$	$89.21081001398987$				$D_{15}$ (as 15T2)	$[15, 15]$	$2$	$7$	$14870825.28920645$
15.1.100...752.1	$x^{15} - 124 x^{12} - 2604 x^{9} + 533696 x^{6} + 4983808 x^{3} + 13713408$	$15$	[1,7]	$-\,2^{10}\cdot 3^{17}\cdot 31^{14}$	$3$	$135.94450781769683$	$141.01512883704163$				$D_{15}$ (as 15T2)	$[3, 3, 3, 15]$	$2$	$7$	$255791278.6064881$
15.1.467...723.1	$x^{15} - 3 x^{14} - 2 x^{13} + 10 x^{12} + 1234 x^{11} - 2708 x^{10} - 7364 x^{9} + 21436 x^{8} + 142132 x^{7} - 818166 x^{6} - 1239170 x^{5} + 17611188 x^{4} - 4641981 x^{3} - 117043497 x^{2} + 64960110 x + 322857900$	$15$	[1,7]	$-\,3^{7}\cdot 7^{10}\cdot 31^{14}$	$3$	$150.65822963546339$	$156.2776606679498$				$D_{15}$ (as 15T2)	$[3, 45]$	$2$	$7$	$45692282010.76435$
15.1.127...883.1	$x^{15} - 122 x^{12} - 1220 x^{9} + 791170 x^{6} + 31455931 x^{3} + 310395328$	$15$	[1,7]	$-\,3^{17}\cdot 61^{14}$	$2$	$161.08135271294557$	$167.08955786961192$				$D_{15}$ (as 15T2)	$[3, 3, 30]$	$2$	$7$	$5240656099.233523$
15.1.252...347.1	$x^{15} - 6 x^{14} + 71 x^{13} + 708 x^{12} - 9630 x^{11} + 133026 x^{10} - 824449 x^{9} + 4611324 x^{8} - 10911485 x^{7} - 723492 x^{6} + 271409820 x^{5} - 1328274288 x^{4} + 3021383088 x^{3} + 24795072 x^{2} - 36616748544 x + 88119373824$	$15$	[1,7]	$-\,3^{7}\cdot 271^{14}$	$2$	$311.4783917781079$	$323.0962857686453$				$D_{15}$ (as 15T2)	$[3, 3, 45]$	$2$	$7$	$4216988041825.0723$
15.1.297...483.1	$x^{15} - 3 x^{14} - 8 x^{13} + 865 x^{12} + 3568 x^{11} + 9637 x^{10} + 844830 x^{9} + 6649711 x^{8} + 5405568 x^{7} + 223416675 x^{6} + 2013610536 x^{5} - 901747161 x^{4} + 10699701561 x^{3} + 487825736544 x^{2} + 1798362956448 x - 95121251640$	$15$	[1,7]	$-\,3^{7}\cdot 13^{10}\cdot 61^{14}$	$3$	$428.147421735145$	$444.1169768931938$				$D_{15}$ (as 15T2)	$[3, 45]$	$2$	$7$	$122626209213368.53$
15.1.223...056.1	$x^{15} - 2 x^{14} + 254 x^{13} - 1646 x^{12} + 48397 x^{11} - 268124 x^{10} + 4851472 x^{9} - 28394144 x^{8} + 351300576 x^{7} - 1427698176 x^{6} + 7649749760 x^{5} - 35334150144 x^{4} + 102643653888 x^{3} - 184778966016 x^{2} + 191206490112 x - 98107490304$	$15$	[1,7]	$-\,2^{14}\cdot 13^{10}\cdot 61^{14}$	$3$	$489.6638882502056$	$512.8221123219365$				$D_{15}$ (as 15T2)	$[3, 60]$	$2$	$7$	$714737732523037.0$
15.5.464...375.1	$x^{15} - 1870 x^{12} - 32010 x^{11} + 777876 x^{10} - 6851625 x^{9} + 30190710 x^{8} - 74603760 x^{7} + 2486105930 x^{6} - 13069638582 x^{5} - 50184822600 x^{4} - 124388611655 x^{3} + 1660824701580 x^{2} + 7902686294580 x + 5476184846968$	$15$	[5,5]	$-\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7}$	$4$	$599.497873717$				?	$C_5^3:D_6$ (as 15T40)	$[5, 5, 5]$	$2$	$9$	$20411798198200$
15.5.464...375.2	$x^{15} - 330 x^{13} - 4620 x^{12} + 12650 x^{11} + 1106633 x^{10} + 4277350 x^{9} - 70074125 x^{8} - 1077527385 x^{7} + 10086284725 x^{6} + 100194176808 x^{5} + 168219899100 x^{4} - 16147355822675 x^{3} - 69620528681495 x^{2} + 79865978259705 x + 368982332191957$	$15$	[5,5]	$-\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7}$	$4$	$599.497873717$				?	$C_5^3:D_6$ (as 15T40)	$[5, 5, 5]$	$2$	$9$	$15044332102100$
15.5.464...375.3	$x^{15} - 165 x^{13} - 5060 x^{12} - 38940 x^{11} + 448382 x^{10} + 4734125 x^{9} + 55321200 x^{8} - 126490375 x^{7} - 3623768500 x^{6} - 28815296950 x^{5} - 158435585000 x^{4} - 533034720625 x^{3} - 1167814408750 x^{2} - 1433453725000 x - 462103235000$	$15$	[5,5]	$-\,3^{6}\cdot 5^{24}\cdot 11^{12}\cdot 23^{7}$	$4$	$599.4978737170752$				?	$C_5^3:D_6$ (as 15T40)	$[5, 5, 5]$	$2$	$9$	$14994406703732.422$
15.3.881...000.1	$x^{15} - 25377 x^{10} + 370293 x^{5} + 1185921$	$15$	[3,6]	$2^{10}\cdot 3^{13}\cdot 5^{17}\cdot 11^{13}\cdot 29^{5}$	$5$	$625.697014205$	$1335.5578789528886$			?	$F_5 \times S_3$ (as 15T11)	$[5, 30]$	$2$	$8$	$44165670046597.32$
15.1.197...363.1	$x^{15} - 6 x^{14} + 47 x^{13} + 895 x^{12} + 15234 x^{11} + 5759 x^{10} + 645209 x^{9} + 5729370 x^{8} + 33028813 x^{7} + 139087385 x^{6} + 1227903666 x^{5} + 5153540557 x^{4} + 29562837870 x^{3} + 140928486312 x^{2} + 229415202360 x + 119995194096$	$15$	[1,7]	$-\,3^{7}\cdot 7^{10}\cdot 151^{14}$	$3$	$660.3392260062253$	$684.9693490839093$				$D_{15}$ (as 15T2)	$[3, 45]$	$2$	$7$	$3949880626343237.0$
15.1.262...000.1	$x^{15} - 5 x^{14} + 20 x^{12} + 25 x^{11} + 10769 x^{10} - 36230 x^{9} + 180490 x^{8} + 505680 x^{7} - 1263140 x^{6} + 40460928 x^{5} - 62922700 x^{4} + 648860840 x^{3} - 1694606600 x^{2} + 1630311940 x + 46251096148$	$15$	[1,7]	$-\,2^{23}\cdot 5^{27}\cdot 19^{13}$	$3$	$672.94327177$	$1218.5033880377791$			?	$F_5 \times S_3$ (as 15T11)	$[2, 10, 20]$	$2$	$7$	$9655767972734.52$
15.3.140...000.1	$x^{15} - 5 x^{14} - 80 x^{13} + 460 x^{12} + 2265 x^{11} - 15553 x^{10} - 24090 x^{9} + 392310 x^{8} - 976120 x^{7} + 1638320 x^{6} - 2453272 x^{5} + 68720 x^{4} - 5194480 x^{3} + 231378160 x^{2} + 420777040 x - 520184176$	$15$	[3,6]	$2^{23}\cdot 5^{17}\cdot 89^{13}$	$3$	$877.438468387$	$1424.0410311070943$			?	$F_5 \times S_3$ (as 15T11)	$[4, 40]$	$2$	$8$	$308642886210973.75$
15.1.776...000.1	$x^{15} + 10 x^{13} - 850 x^{12} + 2070 x^{11} + 30349 x^{10} - 183910 x^{9} - 3083670 x^{8} - 13206720 x^{7} + 473102930 x^{6} + 2772478367 x^{5} - 8431068230 x^{4} - 57993380220 x^{3} + 184194250760 x^{2} + 2061802323020 x + 4449241879687$	$15$	[1,7]	$-\,2^{10}\cdot 5^{17}\cdot 7^{13}\cdot 29^{13}$	$4$	$983.292141349$	$1272.1771858163766$			?	$F_5 \times S_3$ (as 15T11)	$[2, 2, 30]$	$2$	$7$	$817223481214211.9$
15.1.898...000.1	$x^{15} - 17028 x^{10} + 265060026 x^{5} - 41497747632$	$15$	[1,7]	$-\,2^{23}\cdot 3^{13}\cdot 5^{9}\cdot 11^{13}\cdot 251^{5}$	$5$	$992.88279312$	$4599.2170077172$			?	$F_5 \times S_3$ (as 15T11)	$[5, 85]$	$2$	$7$	$606628696626962.5$
15.1.923...000.1	$x^{15} - 5 x^{14} + 25 x^{13} - 95 x^{12} + 285 x^{11} + 19844 x^{10} - 66945 x^{9} - 175530 x^{8} + 3169175 x^{7} - 5716705 x^{6} + 145166318 x^{5} - 219639400 x^{4} - 2382376375 x^{3} - 3290217500 x^{2} + 6382037500 x + 325852261250$	$15$	[1,7]	$-\,2^{10}\cdot 5^{27}\cdot 11^{12}\cdot 131^{5}$	$4$	$994.727027595$	$2853.8291401938136$			?	$F_5 \times S_3$ (as 15T11)	$[5, 40]$	$2$	$7$	$411098018557015.94$
15.1.618...000.1	$x^{15} - 5 x^{13} - 160 x^{12} + 10 x^{11} + 376 x^{10} + 10230 x^{9} - 2280 x^{8} - 284155 x^{7} - 328800 x^{6} + 11711 x^{5} - 11509040 x^{4} + 5331200 x^{3} - 5059000 x^{2} - 48405120 x - 35925416$	$15$	[1,7]	$-\,2^{12}\cdot 5^{15}\cdot 11^{12}\cdot 6911^{5}$	$4$	$1129.15903349$	$6273.705036586494$				$F_5 \times S_3$ (as 15T11)	$[5, 5, 5]$	$2$	$7$	$3869041310693481.0$
15.1.373...000.1	$x^{15} - 5 x^{14} - 15 x^{13} - 25 x^{12} + 565 x^{11} + 794 x^{10} - 1125 x^{9} - 29310 x^{8} - 139405 x^{7} + 309215 x^{6} + 186450 x^{5} - 3565970 x^{4} + 4878805 x^{3} - 4003430 x^{2} - 19039100 x - 9329068$	$15$	[1,7]	$-\,2^{10}\cdot 5^{28}\cdot 11^{12}\cdot 199^{5}$	$4$	$1273.0022721$	$3517.376507077087$			?	$F_5 \times S_3$ (as 15T11)	$[5, 30]$	$2$	$7$	$3549486217575014.5$
15.1.748...000.1	$x^{15} - 85701 x^{10} + 18380656217 x^{5} - 28950040844263$	$15$	[1,7]	$-\,2^{10}\cdot 5^{17}\cdot 7^{13}\cdot 11^{13}\cdot 31^{5}$	$5$	$1333.31222701$	$2960.217818666064$			?	$F_5 \times S_3$ (as 15T11)	$[5, 30]$	$2$	$7$	$4911429110107489.0$
15.1.244...000.1	$x^{15} - 5 x^{14} + 145 x^{13} - 370 x^{12} + 7385 x^{11} + 377 x^{10} + 165195 x^{9} + 114930 x^{8} + 88155 x^{7} + 27605475 x^{6} + 15925923 x^{5} + 438449760 x^{4} - 1007584920 x^{3} + 5251526460 x^{2} - 2872916100 x + 13217245308$	$15$	[1,7]	$-\,2^{12}\cdot 3^{12}\cdot 5^{15}\cdot 7^{13}\cdot 2069^{5}$	$5$	$1442.65605501$	$6995.278130958687$			?	$F_5 \times S_3$ (as 15T11)	$[5, 40]$	$2$	$7$	$16856432353285514$
15.3.204...000.1	$x^{15} - 5 x^{14} - 65 x^{13} + 265 x^{12} + 1905 x^{11} - 4006 x^{10} - 34875 x^{9} + 124650 x^{8} + 377075 x^{7} + 1279775 x^{6} - 2527180 x^{5} - 9127000 x^{4} + 68380625 x^{3} - 20459750 x^{2} + 244074250 x - 401691100$	$15$	[3,6]	$2^{15}\cdot 5^{28}\cdot 73^{13}$	$3$	$1662.08724181$	$3101.18072540463$			?	$F_5 \times S_3$ (as 15T11)	$[6, 30]$	$2$	$8$	$55268394954893130$
15.1.219...000.1	$x^{15} - 33759 x^{10} + 715190553 x^{5} + 163598974587$	$15$	[1,7]	$-\,2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 31^{13}\cdot 71^{5}$	$5$	$1670.17254298$	$5032.293895753155$			?	$F_5 \times S_3$ (as 15T11)	$[5, 45]$	$2$	$7$	$28227301138879788$
15.1.284...000.1	$x^{15} - 39711 x^{10} - 288331 x^{5} - 923521$	$15$	[1,7]	$-\,2^{10}\cdot 5^{15}\cdot 31^{13}\cdot 1301^{5}$	$4$	$1699.27069694$	$8014.313768421478$			?	$F_5 \times S_3$ (as 15T11)	$[5, 10, 10]$	$2$	$7$	$4645373618587904.0$
15.1.561...000.1	$x^{15} - 145860 x^{10} - 243079056 x^{5} - 4696791102432$	$15$	[1,7]	$-\,2^{10}\cdot 3^{12}\cdot 5^{9}\cdot 11^{13}\cdot 10889^{5}$	$5$	$1778.15110187$	$11544.060292982782$			?	$F_5 \times S_3$ (as 15T11)	$[165]$	$2$	$7$	$49247044495643600$
15.1.110...000.1	$x^{15} - 47157 x^{10} - 348513 x^{5} - 1185921$	$15$	[1,7]	$-\,2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 11^{13}\cdot 1451^{5}$	$5$	$1860.33527103$	$8953.615099393597$			?	$F_5 \times S_3$ (as 15T11)	$[15, 45]$	$2$	$7$	$16321354555659744$
15.1.353...000.1	$x^{15} - 2 x^{14} - 623 x^{13} + 956 x^{12} + 148616 x^{11} + 1678622 x^{10} - 22740148 x^{9} - 945266382 x^{8} + 4164671679 x^{7} + 68139475134 x^{6} + 2607605182191 x^{5} - 47700853439788 x^{4} + 481533826058428 x^{3} - 5829949369516366 x^{2} + 57762542818688054 x - 294690202775308898$	$15$	[1,7]	$-\,2^{23}\cdot 5^{10}\cdot 19^{13}\cdot 29^{13}$	$4$	$2010.12955275$	$3657.8082405082237$				$F_5 \times S_3$ (as 15T11)	$[5, 5, 10]$	$2$	$7$	$447144440989138750$
15.3.152...000.1	$x^{15} - 199629 x^{10} + 1618399683 x^{5} + 500575083867$	$15$	[3,6]	$2^{10}\cdot 3^{13}\cdot 5^{15}\cdot 11^{5}\cdot 29^{5}\cdot 41^{13}$	$6$	$3511.59691684$	$13718.673197748421$			?	$F_5 \times S_3$ (as 15T11)	$[5, 5, 5]$	$2$	$8$	$41608561817458170000$