Properties

Label 2.13.aj_bt
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:  $1 - 9 x + 45 x^{2} - 117 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.215685987913$, $\pm0.344616475996$
Angle rank:  $2$ (numerical)
Number field:  4.0.20725.1
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
$A(\F_{q^r})$ 89 30349 5131829 828193861 138005338064 23290133646901 3937075508657429 665419951329961509 112455333921596387681 19004890815397948493824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 5 179 2333 28995 371690 4825163 62743721 815734819 10604492489 137857962614

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.