Properties

Label 2.13.ah_be
Base Field $\F_{13}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{13}$
Dimension:  $2$
L-polynomial:  $1 - 7 x + 30 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.155060670890$, $\pm0.472256355230$
Angle rank:  $2$ (numerical)
Number field:  4.0.640332.1
Galois group:  $D_{4}$
Jacobians:  4

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 4 curves, 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 and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The endomorphism algebra of this simple isogeny class is 4.0.640332.1.
All geometric endomorphisms are defined over $\F_{13}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.13.h_be$2$2.169.l_abk