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

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Degree	Signature	Ramified prime count	Ramified	Unramified primes

Galois group	Field is	Intermediate field	Class group structure	Class number

Discriminant	Root discriminant	Galois root discriminant	CM field	Relative class number

Regulator	$p$ -adic completions	Monogenic	Index	Ines. $p$

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Results (3 matches)

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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
20.2.217...704.1	$x^{20} - 4 x + 2$	$20$	[2,9]	$-\,2^{40}\cdot 31\cdot 127\cdot 137\cdot 173\cdot 1073393\cdot 19752251119$	$7$	$65.5956988623$				✓	$S_{20}$ (as 20T1117)	trivial	$2$	$10$	$34634743019.0$
28.0.617...208.1	$x^{28} - 2 x + 5$	$28$	[0,14]	$2^{26}\cdot 53\cdot 137\cdot 5167\cdot 182453\cdot 1981277\cdot 67\!\cdots\!51$	$7$	$125.79479702$	$7.425367777949566e+25$			?	$S_{28}$ (as 28T1854)	trivial	$2$	$13$	$7257941571662790000$
37.1.124...256.1	$x^{37} + 2 x - 4$	$37$	[1,18]	$2^{70}\cdot 13\cdot 137\cdot 195791\cdot 10489284688357\cdot 5723750340436657\cdot 504174169295944373011$	$7$	$137.314984457$				?	$S_{37}$ (as 37T11)	not computed	$2$	$18$

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