$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (8 matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
19.10.0.1	x^10 + x^2 - 2x + 14	$19$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$ [\ ]^{10}$
19.10.5.1	x^10 - 722x^6 + 130321x^2 - 61902475	$19$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$ [\ ]_{2}^{5}$
19.10.5.2	x^10 - 130321x^2 + 12380495	$19$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$ [\ ]_{2}^{5}$
19.10.8.1	x^10 - 209x^5 + 11552	$19$	$5$	$2$	$8$	$D_5$ (as 10T2)	$ [\ ]_{5}^{2}$
19.10.8.2	x^10 - 19x^5 + 722	$19$	$5$	$2$	$8$	$D_5\times C_5$ (as 10T6)	$ [\ ]_{5}^{10}$
19.10.8.3	x^10 + 57x^5 + 1444	$19$	$5$	$2$	$8$	$D_5\times C_5$ (as 10T6)	$ [\ ]_{5}^{10}$
19.10.9.1	x^10 - 19	$19$	$10$	$1$	$9$	$D_{10}$ (as 10T3)	$ [\ ]_{10}^{2}$
19.10.9.2	x^10 + 76	$19$	$10$	$1$	$9$	$D_{10}$ (as 10T3)	$ [\ ]_{10}^{2}$