# Properties

 Label 2.19.al_ck Base Field $\F_{19}$ Dimension $2$ $p$-rank $2$ Principally polarizable Contains a Jacobian

## Invariants

 Base field: $\F_{19}$ Dimension: $2$ Weil polynomial: $( 1 - 8 x + 19 x^{2} )( 1 - 3 x + 19 x^{2} )$ Frobenius angles: $\pm0.130073469147$, $\pm0.388176076177$ Angle rank: $2$ (numerical)

## Newton polygon

This isogeny class is ordinary.

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

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 204 131376 47655216 16974304704 6126953978724 2213482610416896 799091751465814164 288449990483531192064 104127672854620178665776 37589962955782452689708976

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 9 365 6948 130249 2474439 47049446 893966901 16984068049 322688697372 6131064544925

## Decomposition

1.19.ai $\times$ 1.19.ad

## Base change

This is a primitive isogeny class.