Number field search results

Note: Search results may be incomplete. Given $p$-adic completions contain an unramified field and completions are only searched for ramified primes.

Results (1-50 of 226 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
9.1.37086373.1	$x^{9} + x^{7} - x^{3} - x - 1$	$9$	[1,4]	$23\cdot 1612451$	$2$	$6.934638365839786$	$6089.858208529982$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$0.7901849778796387$
9.3.120155887.1	$x^{9} - 2 x^{8} + 2 x^{7} - 6 x^{5} + 11 x^{4} - 13 x^{3} + 10 x^{2} - 5 x + 1$	$9$	[3,3]	$-\,23\cdot 5224169$	$2$	$7.902226077812687$	$10961.564076353337$			✓	$S_9$ (as 9T34)	trivial	$2$	$5$	$2.050524505530881$
9.1.1338983180.1	$x^{9} - 2 x^{8} + x^{7} + x^{6} - 3 x^{5} + 3 x^{3} - 2 x - 1$	$9$	[1,4]	$2^{2}\cdot 5\cdot 23\cdot 2910833$	$4$	$10.3296623222$	$36592.11909687659$			✓	$S_9$ (as 9T34)	trivial	$2$	$4$	$12.175494282$
9.7.2794474079.1	$x^{9} - 3 x^{8} + 4 x^{6} + 3 x^{4} - 4 x^{3} - 5 x^{2} + 2 x + 1$	$9$	[7,1]	$-\,23\cdot 5569\cdot 21817$	$3$	$11.2095685817$	$52862.78538821048$			✓	$S_9$ (as 9T34)	trivial	$2$	$7$	$22.822475055385944$
9.9.29297320489.1	$x^{9} - 3 x^{8} - 5 x^{7} + 19 x^{6} + 4 x^{5} - 36 x^{4} + 9 x^{3} + 18 x^{2} - 9 x + 1$	$9$	[9,0]	$23\cdot 1273796543$	$2$	$14.5539499805$	$171164.6005720809$			✓	$S_9$ (as 9T34)	trivial	$2$	$8$	$127.371942561$
10.0.643869199.1	$x^{10} + x^{8} - x^{7} - 2 x^{5} - x^{3} + 2 x^{2} + 1$	$10$	[0,5]	$-\,23\cdot 27994313$	$2$	$7.60115808759$	$25374.577809295664$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.1758205716653927$
10.2.898547141.1	$x^{10} - 4 x^{9} + 9 x^{8} - 13 x^{7} + 14 x^{6} - 10 x^{5} + 4 x^{4} + x^{3} - 3 x^{2} + 3 x - 1$	$10$	[2,4]	$23\cdot 61\cdot 197\cdot 3251$	$4$	$7.85876109813$	$29975.77590321892$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$1.7693093670729252$
10.2.1045543936.1	$x^{10} - 2 x^{9} + 4 x^{8} - 4 x^{7} + 5 x^{6} - 4 x^{5} + 4 x^{4} - 2 x^{3} - 1$	$10$	[2,4]	$2^{10}\cdot 23\cdot 103\cdot 431$	$4$	$7.97873844995$	$3870.4974176860615$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$1.9466491998307853$
10.0.1176103183.1	$x^{10} - 2 x^{8} - x^{7} + 4 x^{6} - x^{5} - x^{4} + x^{3} + 2 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,23\cdot 51134921$	$2$	$8.07317826922$	$34294.36080465708$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.7141737757352025$
10.0.1189886623.1	$x^{10} - x^{8} - x^{7} + 3 x^{6} + 4 x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,23\cdot 53\cdot 976117$	$3$	$8.08259016771$	$34494.7332646594$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.789725083735533$
10.0.1264682899.1	$x^{10} - x^{9} + 3 x^{8} - 4 x^{7} + 5 x^{6} - 5 x^{5} + 5 x^{4} - 3 x^{3} + 2 x^{2} - x + 1$	$10$	[0,5]	$-\,23\cdot 54986213$	$2$	$8.13201487939$	$35562.38038995703$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.1436873451319682$
10.0.1288851667.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 4 x^{6} - 4 x^{5} + 2 x^{4} - 3 x^{3} + x^{2} + 1$	$10$	[0,5]	$-\,23\cdot 56037029$	$2$	$8.147423545$	$35900.58031564392$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.804235425189463$
10.0.1311615779.1	$x^{10} - 3 x^{9} + 5 x^{8} - 7 x^{7} + 8 x^{6} - 7 x^{5} + 6 x^{4} - 5 x^{3} + 4 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,23\cdot 1279\cdot 44587$	$3$	$8.16170067505$	$36216.236400266665$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.8271553045219913$
10.2.1585388597.1	$x^{10} - x^{9} + 3 x^{8} - 3 x^{7} + 4 x^{6} - 5 x^{5} + 4 x^{4} - 3 x^{3} - 1$	$10$	[2,4]	$13\cdot 23\cdot 61\cdot 86923$	$4$	$8.31789766646$	$39816.93856890557$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.542274249164089$
10.0.1591663043.1	$x^{10} - x^{9} - x^{7} + 2 x^{6} + x^{5} - 3 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,23\cdot 5519\cdot 12539$	$3$	$8.3211837683$	$39895.651931006214$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$1.924794492254434$
10.2.1694257717.1	$x^{10} - x^{9} - 2 x^{6} + 4 x^{5} - 3 x^{4} + 2 x^{3} - x^{2} + 1$	$10$	[2,4]	$23\cdot 73663379$	$2$	$8.373324983$	$41161.36194296782$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.6738573822184706$
10.0.1741268567.1	$x^{10} - 2 x^{9} + 4 x^{8} - 6 x^{7} + 7 x^{6} - 6 x^{5} + 6 x^{4} - 8 x^{3} + 10 x^{2} - 7 x + 2$	$10$	[0,5]	$-\,23^{2}\cdot 367\cdot 8969$	$3$	$8.39627348438$	$14673.158251578248$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.4013681734163086$
10.2.1772527637.1	$x^{10} - x^{9} + 2 x^{7} - 5 x^{6} + 6 x^{5} - 7 x^{4} + 5 x^{3} - 4 x^{2} + 3 x - 1$	$10$	[2,4]	$23\cdot 2531\cdot 30449$	$3$	$8.41122598856$	$42101.39709083299$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.6995560847117055$
10.0.1817313812.1	$x^{10} - 2 x^{9} + 3 x^{7} - 2 x^{6} - 3 x^{5} + 4 x^{4} + x^{3} - 2 x^{2} + x + 1$	$10$	[0,5]	$-\,2^{2}\cdot 23\cdot 191\cdot 103421$	$4$	$8.43224065467$	$42629.963781359234$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.5157294942148996$
10.2.1837369421.1	$x^{10} - x^{9} - x^{8} - 2 x^{7} + 2 x^{6} + 4 x^{5} + x^{4} - x^{3} - 3 x^{2} + 1$	$10$	[2,4]	$23\cdot 37\cdot 1303\cdot 1657$	$4$	$8.44150045903$	$42864.54736725911$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.777341822378834$
10.2.1837466297.1	$x^{10} - 2 x^{9} + x^{8} - x^{7} - x^{6} + 3 x^{5} + x^{3} - 2 x - 1$	$10$	[2,4]	$23\cdot 71\cdot 1125209$	$3$	$8.4415449661$	$42865.67737712773$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.820623624863861$
10.0.1889475323.1	$x^{10} - x^{9} - x^{7} - x^{6} + 2 x^{5} - x^{4} - 2 x^{3} + 2 x^{2} + 3 x + 1$	$10$	[0,5]	$-\,23^{2}\cdot 3571787$	$2$	$8.46513955916$	$15284.855363802135$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.737673691337467$
10.2.1896532229.1	$x^{10} - 4 x^{9} + 5 x^{8} - 8 x^{6} + 12 x^{5} - 7 x^{4} - x^{3} + 5 x^{2} - 3 x + 1$	$10$	[2,4]	$23\cdot 31\cdot 677\cdot 3929$	$4$	$8.46829586029$	$43549.19320722257$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.9100766934031683$
10.2.2008003937.1	$x^{10} - 3 x^{8} - 2 x^{7} + 4 x^{6} + 3 x^{5} - 2 x^{4} - x^{3} + x^{2} - x - 1$	$10$	[2,4]	$23\cdot 87304519$	$2$	$8.51680014058$	$44810.75693402199$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$2.926017882046041$
10.0.2121277879.1	$x^{10} - 3 x^{9} + 6 x^{8} - 9 x^{7} + 11 x^{6} - 10 x^{5} + 9 x^{4} - 7 x^{3} + 5 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,7\cdot 23\cdot 3191\cdot 4129$	$4$	$8.56366670406$	$46057.33252154319$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.9272366163664376$
10.2.2212334672.1	$x^{10} - 3 x^{9} + 3 x^{8} - x^{7} - 2 x^{6} + 4 x^{5} - 4 x^{4} + x^{3} + 2 x^{2} - x + 1$	$10$	[2,4]	$2^{4}\cdot 23\cdot 6011779$	$3$	$8.59973527452$	$23517.730927961566$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.50403828655027$
10.2.2253497749.1	$x^{10} - 3 x^{9} + 6 x^{8} - 6 x^{7} + 4 x^{6} - 3 x^{4} + 6 x^{3} - 7 x^{2} + 4 x - 1$	$10$	[2,4]	$23\cdot 1789\cdot 54767$	$3$	$8.61560367541$	$47471.0200964757$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.1245749196817325$
10.0.2350065572.1	$x^{10} - x^{9} - x^{8} + 2 x^{6} + x^{5} - x^{4} - 2 x^{3} + 2 x + 1$	$10$	[0,5]	$-\,2^{2}\cdot 23^{2}\cdot 1110617$	$3$	$8.65183041103$	$17046.322924539654$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.575569671640329$
10.2.2384536477.1	$x^{10} - x^{9} - 3 x^{8} + 2 x^{7} + 5 x^{6} - 5 x^{4} - 2 x^{3} + x^{2} + 2 x + 1$	$10$	[2,4]	$23\cdot 103675499$	$2$	$8.66443797293$	$48831.71589244023$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.238532109500859$
10.0.2424560939.1	$x^{10} - 2 x^{8} + 2 x^{6} - x^{4} - x^{3} + x + 1$	$10$	[0,5]	$-\,23^{2}\cdot 1091\cdot 4201$	$3$	$8.67887254309$	$17314.39310171944$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.4648929438328615$
10.0.2429220739.1	$x^{10} - 3 x^{9} + 4 x^{8} - 5 x^{6} + 6 x^{5} - x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1$	$10$	[0,5]	$-\,11\cdot 23\cdot 9601663$	$3$	$8.68053910776$	$49287.12548932023$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$2.538811022758741$
10.2.2584327909.1	$x^{10} - 2 x^{7} + 3 x^{6} + 2 x^{5} - 2 x^{4} - 2 x^{3} - x^{2} + 3 x - 1$	$10$	[2,4]	$23\cdot 112362083$	$2$	$8.73443388441$	$50836.28535799995$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.466142174370157$
10.0.2664772364.1	$x^{10} - x^{9} + x^{7} - x^{6} - x^{5} + 2 x^{4} - x^{2} + x + 1$	$10$	[0,5]	$-\,2^{2}\cdot 23\cdot 28964917$	$3$	$8.7612487609$	$40971.95867042313$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.711786850995665$
10.0.2707274179.1	$x^{10} - 3 x^{9} + 5 x^{8} - 8 x^{7} + 12 x^{6} - 13 x^{5} + 11 x^{4} - 8 x^{3} + 5 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,23\cdot 89\cdot 1322557$	$3$	$8.7751232318$	$52031.472965888635$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.7663997888577874$
10.2.2826767045.1	$x^{10} - 2 x^{9} - x^{8} + 6 x^{7} - 4 x^{6} - 5 x^{5} + 9 x^{4} - 2 x^{3} - 4 x^{2} + 4 x - 1$	$10$	[2,4]	$5\cdot 23^{2}\cdot 1068721$	$3$	$8.81310616863$	$18695.441735781576$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.924411844833808$
10.0.2848953259.1	$x^{10} - x^{9} + x^{8} + 2 x^{7} - x^{6} + 4 x^{4} - 6 x^{3} + 5 x^{2} - 3 x + 1$	$10$	[0,5]	$-\,23\cdot 123867533$	$2$	$8.81999892928$	$53375.58673213813$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.6220957044496886$
10.0.2850882292.1	$x^{10} - 2 x^{9} + 5 x^{8} - 7 x^{7} + 8 x^{6} - 8 x^{5} + 5 x^{4} - 4 x^{3} + 3 x^{2} - 2 x + 2$	$10$	[0,5]	$-\,2^{2}\cdot 23\cdot 30987851$	$3$	$8.82059595161$	$53393.654042404705$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.58041195997292$
10.2.2916915821.1	$x^{10} - 3 x^{9} + 3 x^{8} - 5 x^{6} + 6 x^{5} - x^{4} - 4 x^{3} + 3 x^{2} - 1$	$10$	[2,4]	$23\cdot 126822427$	$2$	$8.84081676785$	$54008.4791583692$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.79852825328065$
10.0.3012288679.1	$x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} + x^{5} - 3 x^{3} + 4 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,23\cdot 5701\cdot 22973$	$3$	$8.86930641267$	$54884.320884930334$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$3.7529210697147266$
10.0.3034260487.1	$x^{10} - 2 x^{9} + 2 x^{8} - x^{7} - 2 x^{6} + 2 x^{5} - x^{3} + 3 x^{2} - x + 1$	$10$	[0,5]	$-\,17\cdot 23\cdot 7760257$	$3$	$8.87575459926$	$55084.121913669456$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.712251485605574$
10.2.3118581293.1	$x^{10} - 3 x^{7} - 2 x^{5} + 4 x^{4} - x^{3} + 2 x^{2} - 3 x + 1$	$10$	[2,4]	$23\cdot 135590491$	$2$	$8.900116817$	$55844.259266284476$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.138286800311635$
10.0.3126857452.1	$x^{10} - x^{9} + 2 x^{8} - 2 x^{7} + 3 x^{6} - 4 x^{5} + 4 x^{4} - 3 x^{3} + 3 x^{2} - 2 x + 1$	$10$	[0,5]	$-\,2^{2}\cdot 23\cdot 33987581$	$3$	$8.90247593346$	$44382.392476045316$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.748603544586397$
10.2.3216663873.1	$x^{10} - 2 x^{8} - 3 x^{7} - x^{6} + 5 x^{5} + 6 x^{4} + 2 x^{3} - 4 x^{2} - 4 x - 1$	$10$	[2,4]	$3^{3}\cdot 23\cdot 241\cdot 21493$	$4$	$8.92772014617$	$18905.21348728969$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.9426250687366156$
10.0.3232158536.1	$x^{10} - 2 x^{9} + 5 x^{8} - 6 x^{7} + 7 x^{6} - 5 x^{5} + 3 x^{4} + x^{2} - x + 1$	$10$	[0,5]	$-\,2^{3}\cdot 23\cdot 191\cdot 91969$	$4$	$8.93201133347$	$56852.075916363865$			?	$S_{10}$ (as 10T45)	trivial	$2$	$4$	$4.869834607752987$
10.2.3261564841.1	$x^{10} - 2 x^{9} + 4 x^{8} - 9 x^{7} + 9 x^{6} - 12 x^{5} + 12 x^{4} - 8 x^{3} + 6 x^{2} - 3 x + 1$	$10$	[2,4]	$23^{2}\cdot 6165529$	$2$	$8.94010463248$	$20081.85050580739$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.029238489501814$
10.2.3286499509.1	$x^{10} - x^{8} - x^{7} + 5 x^{5} - 4 x^{4} + 2 x^{3} - 4 x^{2} + 4 x - 1$	$10$	[2,4]	$23\cdot 142891283$	$2$	$8.94691594388$	$57327.99934586938$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$3.94324229082789$
10.2.3374835977.1	$x^{10} - 4 x^{9} + 8 x^{8} - 12 x^{7} + 15 x^{6} - 16 x^{5} + 15 x^{4} - 13 x^{3} + 8 x^{2} - 4 x + 1$	$10$	[2,4]	$23\cdot 8389\cdot 17491$	$3$	$8.9706779782$	$58093.33849074264$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.129835433875135$
10.2.3386243057.1	$x^{10} - 4 x^{9} + 6 x^{8} - 5 x^{7} + 4 x^{6} - 3 x^{5} + 2 x^{4} - 2 x^{3} + x^{2} - 2 x + 1$	$10$	[2,4]	$23\cdot 31\cdot 4749289$	$3$	$8.97370550101$	$58191.43456729693$			?	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.1168151391424646$
10.2.3390947477.1	$x^{10} - x^{9} + 2 x^{7} - x^{5} - 3 x^{4} + 8 x^{3} - 8 x^{2} + 4 x - 1$	$10$	[2,4]	$23\cdot 147432499$	$2$	$8.97495141602$	$58231.842466128444$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.064964287233693$
10.2.3435605749.1	$x^{10} - x^{9} - 2 x^{8} + x^{7} + x^{6} + 2 x^{4} + x^{3} - x^{2} - 2 x - 1$	$10$	[2,4]	$23\cdot 2137\cdot 69899$	$3$	$8.98670182209$	$58614.04054490699$			✓	$S_{10}$ (as 10T45)	trivial	$2$	$5$	$4.0168237884815925$