Properties

Label 2.13.ah_bg
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:  $( 1 - 6 x + 13 x^{2} )( 1 - x + 13 x^{2} )$
Frobenius angles:  $\pm0.187167041811$, $\pm0.455715642762$
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
$A(\F_{q^r})$ 104 31200 4954976 814320000 138011646344 23331990988800 3938757157931336 665396405968320000 112452136652458719584 19004887894305550380000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 185 2254 28513 371707 4833830 62770519 815705953 10604190982 137857941425

Decomposition

1.13.ag $\times$ 1.13.ab

Base change

This is a primitive isogeny class.