Properties

Label 2.19.am_cs
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:  $( 1 - 8 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$
Frobenius angles:  $\pm0.130073469147$, $\pm0.348268167089$
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
$A(\F_{q^r})$ 192 129024 47791296 17020846080 6129255605952 2213192742598656 799047672711483072 288449268959839518720 104127999873776666133696 37589992898409852999727104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 358 6968 130606 2475368 47043286 893917592 16984025566 322689710792 6131069428678

Decomposition

1.19.ai $\times$ 1.19.ae

Base change

This is a primitive isogeny class.