Properties

Label 3.13.ar_fa_awr
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 3 x + 13 x^{2} )( 1 - 7 x + 13 x^{2} )^{2}$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.0772104791556$, $\pm0.363422825076$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 539 4040883 10360942592 23029384182651 50927936696817719 112345575772777611264 247088949485721000382571 542864656551803925290156667 1192575188601264731387374874624 2620011162605555917374724132443243

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 141 2148 28229 369417 4822092 62754717 815826725 10604871924 137859308421

Decomposition

1.13.ah 2 $\times$ 1.13.ad

Base change

This is a primitive isogeny class.