Properties

Label 2.13.ag_v
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:  $1 - 6 x + 21 x^{2} - 78 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.115489212201$, $\pm0.532795966182$
Angle rank:  $2$ (numerical)
Number field:  4.0.1056832.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 107 29425 4674188 805803625 138191347547 23327470051600 3937539395235203 665430236259215625 112459321594157760812 19005106939521087834625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 176 2126 28212 372188 4832894 62751116 815747428 10604868518 137859530336

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The endomorphism algebra of this simple isogeny class is 4.0.1056832.1.
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.g_v$2$2.169.g_agb