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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	Narrow class group	Narrow class number

CM field	Relative class number	Regulator	$p$-adic completions	Monogenic

Index	Ines. \(p\)	Minimal sibling

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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	Narrow class group	Unit group torsion	Unit group rank	Regulator
17.1.232...865.1	$x^{17} - 7 x - 7$	$17$	(1, 8)	$5\cdot 7^{16}\cdot 40829\cdot 3419692147103137$	$4$	$105.07506577$	$164948841578.08176$			✓	$S_{17}$ (as 17T10)	trivial	trivial	$2$	$8$	$41100396946.0$
17.1.274...377.1	$x^{17} - 7$	$17$	(1, 8)	$7^{16}\cdot 17^{17}$	$2$	$106.129302988$	$124.07690477638815$			✓	$F_{17}$ (as 17T5)	trivial	trivial	$2$	$8$	$70086534327.5$
17.1.317...889.1	$x^{17} + 7 x - 7$	$17$	(1, 8)	$3\cdot 7^{16}\cdot 318789156800767875163$	$3$	$107.038691241$	$193062883561.7909$			✓	$S_{17}$ (as 17T10)	trivial	trivial	$2$	$8$	$51547035300.5$

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