Properties

Label 2.13.aj_br
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:  $1 - 9 x + 43 x^{2} - 117 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.161492811255$, $\pm0.37797305228$
Angle rank:  $2$ (numerical)
Number field:  4.0.92781.3
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 87 29493 5008851 819698949 137804618832 23305056711525 3938728027833483 665491412853217989 112456388771410123359 19004848787538456323328

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 175 2279 28699 371150 4828255 62770055 815822419 10604591957 137857657750

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.