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)

 

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
32.2.316...495.1	$x^{32} - 3 x + 1$	$32$	[2,15]	$-\,5\cdot 43\cdot 653\cdot 13933\cdot 79810093778148091175287\cdot 202599589222390924962441257111$	$6$	$83.5368116685$	$5.624013181995244e+30$			✓	$S_{32}$ (as 32T2801324)	trivial	$2$	$16$	$1316142683122737200$
32.2.314...520.1	$x^{32} - 4 x + 1$	$32$	[2,15]	$-\,2^{64}\cdot 3\cdot 5\cdot 11\cdot 149\cdot 45481\cdot 35147261\cdot 434330976903076049484620989627$	$8$	$111.382415558$				✓	$S_{32}$ (as 32T2801324)	not computed	$2$	$16$
32.2.168...720.1	$x^{32} - 2 x - 4$	$32$	[2,15]	$-\,2^{30}\cdot 5\cdot 40163\cdot 133680241488339708940699\cdot 58456903283190320429286378563$	$5$	$117.37651753$	$7.747631187804111e+28$			?	$S_{32}$ (as 32T2801324)	not computed	$2$	$16$
32.2.673...735.1	$x^{32} - x - 4$	$32$	[2,15]	$-\,5\cdot 19\cdot 50555657\cdot 14\!\cdots\!09$	$4$	$122.573219929$	$2.596148429267414e+33$			✓	$S_{32}$ (as 32T2801324)	trivial	$2$	$16$	$1794404961520178200000$
47.1.277...320.1	$x^{47} + 2 x - 2$	$47$	[1,23]	$-\,2^{46}\cdot 5\cdot 13\cdot 17\cdot 89\cdot 361179289\cdot 582997712425903553\cdot 19\!\cdots\!87$	$8$	$92.6548218769$	$3.911414135180125e+39$			✓	$S_{47}$ (as 47T6)	not computed	$2$	$23$