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 (5 matches)

  Download displayed columns for results to

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
21.3.211...304.1	$x^{21} + 15 x^{19} - 10 x^{18} + 99 x^{17} - 132 x^{16} + 449 x^{15} - 810 x^{14} + 1512 x^{13} - 2712 x^{12} + 3564 x^{11} - 4392 x^{10} + 4512 x^{9} - 2880 x^{8} - 1227 x^{7} + 10078 x^{6} - 20412 x^{5} + 22680 x^{4} - 15120 x^{3} + 6048 x^{2} - 1344 x + 128$	$21$	[3,9]	$-\,2^{14}\cdot 3^{21}\cdot 47\cdot 59^{3}\cdot 10859^{3}$	$5$	$38.6324178312$				?	$C_3^7.(C_2^7.S_7)$ (as 21T152)	trivial	$2$	$11$	$150713525.554$
21.9.293...281.1	$x^{21} - 63 x^{19} - 4 x^{18} + 1683 x^{17} + 216 x^{16} - 24877 x^{15} - 5346 x^{14} + 221076 x^{13} + 76086 x^{12} - 1185372 x^{11} - 647136 x^{10} + 3493272 x^{9} + 3080592 x^{8} - 3545727 x^{7} - 6328004 x^{6} - 4869576 x^{5} - 126336 x^{4} + 2790672 x^{3} + 1272384 x^{2} - 282752$	$21$	[9,6]	$3^{28}\cdot 47^{4}\cdot 59^{3}\cdot 10859^{3}$	$4$	$60.8382574825$				?	$C_3^6.S_7$ (as 21T130)	trivial	$2$	$14$	$64859089096.9$
21.9.834...152.1	$x^{21} - 26208 x^{19} - 195536 x^{18} + 291973068 x^{17} + 4409577342 x^{16} - 1795665131924 x^{15} - 41002370088498 x^{14} + 6572542654341105 x^{13} + 203858863109865284 x^{12} - 14213279062376569485 x^{11} - 582361703119054694040 x^{10} + 16275661558142313035035 x^{9} + 945745018043095393911180 x^{8} - 5646302360560715152043103 x^{7} - 792530253662409376623342416 x^{6} - 4726551871709798292359565120 x^{5} + 266740346394447654507510010344 x^{4} + 2440298711745375561122234921808 x^{3} - 44488899123058840085730493001568 x^{2} - 315068960394756661920290849696640 x + 3724414958441731059478927509146752$	$21$	[9,6]	$2^{14}\cdot 3^{21}\cdot 37^{12}\cdot 59^{3}\cdot 109^{12}\cdot 10859^{3}$	$6$	$3695.61878548$				?	$C_3^6.(C_2\times S_7)$ (as 21T138)	not computed	$2$	$14$
32.2.314...048.1	$x^{32} - 4 x + 2$	$32$	[2,15]	$-\,2^{64}\cdot 59\cdot 9796937\cdot 29\!\cdots\!41$	$4$	$111.382415523$				✓	$S_{32}$ (as 32T2801324)	not computed	$2$	$16$
43.1.174...571.1	$x^{43} + x - 1$	$43$	[1,21]	$-\,59\cdot 397\cdot 877\cdot 935899\cdot 2402649604770175349\cdot 37\!\cdots\!51$	$6$	$43.0086198004$	$1.3226452398347625e+35$			✓	$S_{43}$ (as 43T10)	not computed	$2$	$21$

  Download displayed columns for results to