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 (10 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
22.0.747...779.1	$x^{22} - 5 x + 6$	$22$	[0,11]	$-\,3^{21}\cdot 31\cdot 61\cdot 67\cdot 181\cdot 143137\cdot 217732675899704637585877$	$7$	$121.665283278$				✓	$S_{22}$ (as 22T59)	trivial	$2$	$10$	$2404518202930000$
22.0.748...515.1	$x^{22} - 3 x + 6$	$22$	[0,11]	$-\,3^{21}\cdot 5\cdot 47\cdot 67\cdot 240033317\cdot 189458757487545844247197$	$6$	$121.675578385$	$2.414895616392203e+18$			✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$10$	$518995826970000$
22.0.748...483.1	$x^{22} - x + 6$	$22$	[0,11]	$-\,3^{21}\cdot 67\cdot 10\!\cdots\!83$	$3$	$121.675578521$				✓	$S_{22}$ (as 22T59)	trivial	$2$	$10$	$1018165466990000$
22.2.423...440.1	$x^{22} - 8 x + 6$	$22$	[2,10]	$2^{43}\cdot 3^{21}\cdot 5\cdot 67\cdot 43223\cdot 317963629399156207$	$6$	$146.171405779$				✓	$S_{22}$ (as 22T59)	$[2]$	$2$	$11$	$2419229210220000$
22.2.574...997.1	$x^{22} - 9 x + 6$	$22$	[2,10]	$3^{21}\cdot 67\cdot 54631\cdot 398887\cdot 3137422219\cdot 119919973547835079$	$6$	$164.564143046$	$6.688798124490173e+19$			✓	$S_{22}$ (as 22T59)	trivial	$2$	$11$	$26906527131600000$
23.1.322...336.1	$x^{23} + 3 x - 2$	$23$	[1,11]	$-\,2^{23}\cdot 17\cdot 43\cdot 67\cdot 971821\cdot 15873405731\cdot 5085469520371$	$7$	$57.7070814215$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$407641553662$
23.1.274...080.1	$x^{23} + 3 x - 6$	$23$	[1,11]	$-\,2^{23}\cdot 3^{22}\cdot 5\cdot 67\cdot 7457\cdot 701609\cdot 5956705599335914343$	$7$	$127.657526001$				✓	$S_{23}$ (as 23T7)	trivial	$2$	$11$	$4214765620360000$
26.2.212...232.1	$x^{26} - 2 x - 2$	$26$	[2,12]	$2^{26}\cdot 3\cdot 67\cdot 107\cdot 5867\cdot 10536636742939\cdot 2381953897662043$	$7$	$50.6874484196$				✓	$S_{26}$ (as 26T96)	trivial	$2$	$13$	$1482708296476.7107$
26.2.405...768.1	$x^{26} - 4 x - 3$	$26$	[2,12]	$2^{26}\cdot 67\cdot 373\cdot 24\!\cdots\!57$	$4$	$88.399434024$				✓	$S_{26}$ (as 26T96)	trivial	$2$	$13$	$2741919708088632.0$
36.0.314...416.1	$x^{36} - 2 x + 4$	$36$	[0,18]	$2^{34}\cdot 67\cdot 28429\cdot 40984105163\cdot 8661963725601919\cdot 27\!\cdots\!19$	$6$	$133.325958569$	$2.650843439265746e+33$			?	$S_{36}$ (as 36T121279)	not computed	$2$	$17$