Properties

Label 2.13.al_cd
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:  $1 - 11 x + 55 x^{2} - 143 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.129998747777$, $\pm0.292104599859$
Angle rank:  $2$ (numerical)
Number field:  4.0.6725.1
Galois group:  $D_{4}$
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 71 26909 4949339 824733941 138120708816 23299305353501 3937346592497291 665439985622292389 112458147667396136951 19005123190067808033024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 159 2253 28875 371998 4827063 62748045 815759379 10604757819 137859648214

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The endomorphism algebra of this simple isogeny class is 4.0.6725.1.
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.l_cd$2$2.169.al_ij