Properties

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

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Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 19 x^{2} )( 1 - 3 x + 19 x^{2} )$
Frobenius angles:  $\pm0.203259864187$, $\pm0.388176076177$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 221 137241 48439664 17046567369 6131185293701 2213482610416896 799053232013574941 288443891852288625609 104127042519008111932784 37589914962904844325667401

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 380 7060 130804 2476150 47049446 893923810 16983708964 322686743980 6131056717100

Decomposition

1.19.ah $\times$ 1.19.ad

Base change

This is a primitive isogeny class.