Properties

Label 2.13.ah_be
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:  $1 - 7 x + 30 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.15506067089$, $\pm0.47225635523$
Angle rank:  $2$ (numerical)
Number field:  4.0.640332.1
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
$A(\F_{q^r})$ 102 30396 4861728 810235776 138012101742 23337188957952 3938904764517342 665414807044689408 112454567999145347616 19005013455302895068316

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 181 2212 28369 371707 4834906 62772871 815728513 10604420260 137858852221

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.