Properties

Label 2.13.ag_t
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:  $( 1 - 7 x + 13 x^{2} )( 1 + x + 13 x^{2} )$
Frobenius angles:  $\pm0.0772104791556$, $\pm0.544284357238$
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
$A(\F_{q^r})$ 105 28665 4596480 802190025 137990339025 23309890007040 3936680352813705 665412853037812425 112458736342523370240 19005059294898370518825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 172 2090 28084 371648 4829254 62737424 815726116 10604813330 137859184732

Decomposition

1.13.ah $\times$ 1.13.b

Base change

This is a primitive isogeny class.