Properties

Label 2.13.al_ce
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $( 1 - 6 x + 13 x^{2} )( 1 - 5 x + 13 x^{2} )$
Frobenius angles:  $\pm0.187167041811$, $\pm0.256122854178$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 72 27360 5025888 832291200 138591237672 23315295467520 3937143790280808 665370955154880000 112452955480771954272 19004889181346053336800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 161 2286 29137 373263 4830374 62744811 815674753 10604268198 137857950761

Decomposition

1.13.ag $\times$ 1.13.af

Base change

This is a primitive isogeny class.