Properties

Label 2.19.ao_di
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:  $( 1 - 8 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$
Frobenius angles:  $\pm0.130073469147$, $\pm0.258380448083$
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
$A(\F_{q^r})$ 168 122304 47532744 17083422720 6139358981448 2213711304831936 799013955490370088 288441475423798394880 104127474329448490192104 37589999149034860983559104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 338 6930 131086 2479446 47054306 893879874 16983566686 322688082150 6131070448178

Decomposition

1.19.ai $\times$ 1.19.ag

Base change

This is a primitive isogeny class.