Properties

Label 2.13.ag_u
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:  $1 - 6 x + 20 x^{2} - 78 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.0978612922159$, $\pm0.538629668498$
Angle rank:  $2$ (numerical)
Number field:  4.0.878400.4
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
$A(\F_{q^r})$ 106 29044 4635274 804054096 138102032266 23319664860436 3937175737938346 665426473200497664 112459378287178054426 19005101711592935851924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 174 2108 28150 371948 4831278 62745320 815742814 10604873864 137859492414

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.