Local Number Field Search Results

Degree		Discriminant exponent $c$		Galois group
Prime $p$		Ramification index $e$		Top slope

Results (displaying all 8 matches)

Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
x^8 - x + 2	19	1	8	0	$C_8$ (as 8T1)	$ [\ ]^{8}$
x^8 + 7220x^4 - 27436x^2 + 13032100	19	2	4	4	$C_4\times C_2$ (as 8T2)	$ [\ ]_{2}^{4}$
x^8 - 13718x^2 + 1303210	19	2	4	4	$C_8$ (as 8T1)	$ [\ ]_{2}^{4}$
x^8 + 57x^4 + 1444	19	4	2	6	$Q_8$ (as 8T5)	$ [\ ]_{4}^{2}$
x^8 - 19x^4 + 5776	19	4	2	6	$D_4$ (as 8T4)	$ [\ ]_{4}^{2}$
x^8 - 19x^4 + 722	19	4	2	6	$C_8:C_2$ (as 8T7)	$ [\ ]_{4}^{4}$
x^8 + 76	19	8	1	7	$QD_{16}$ (as 8T8)	$ [\ ]_{8}^{2}$
x^8 - 19	19	8	1	7	$QD_{16}$ (as 8T8)	$ [\ ]_{8}^{2}$

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