Properties

Label 2.13.ai_bm
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:  $( 1 - 6 x + 13 x^{2} )( 1 - 2 x + 13 x^{2} )$
Frobenius angles:  $\pm0.187167041811$, $\pm0.410543812489$
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
$A(\F_{q^r})$ 96 30720 5025888 818380800 137854828896 23315295467520 3938851984386912 665446208805273600 112452955480771954272 19004772804678878361600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 182 2286 28654 371286 4830374 62772030 815767006 10604268198 137857106582

Decomposition

1.13.ag $\times$ 1.13.ac

Base change

This is a primitive isogeny class.