Properties

Label 2.13.ah_bk
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$
Frobenius angles:  $\pm0.256122854178$, $\pm0.410543812489$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 108 32832 5143824 821193984 137699760348 23293210300416 3937502388759516 665399771295667200 112452896477996048016 19004886538871760447552

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 193 2338 28753 370867 4825798 62750527 815710081 10604262634 137857931593

Decomposition

1.13.af $\times$ 1.13.ac

Base change

This is a primitive isogeny class.