# Properties

 Label 2.19.ap_dq Base Field $\F_{19}$ Dimension $2$ $p$-rank $2$ Principally polarizable Does not contain a Jacobian

## Invariants

 Base field: $\F_{19}$ Dimension: $2$ Weil polynomial: $( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )$ Frobenius angles: $\pm0.130073469147$, $\pm0.203259864187$ Angle rank: $1$ (numerical)

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 156 117936 47056464 17068169664 6142403868276 2214310804183296 799070872855699236 288444096418094233344 104127350297602681851984 37589961044115088796272176

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 325 6860 130969 2480675 47067046 893943545 16983721009 322687697780 6131064233125

## Decomposition

1.19.ai $\times$ 1.19.ah

## Base change

This is a primitive isogeny class.