Properties

Label 2.13.ah_bl
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:  $1 - 7 x + 37 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.278766070715$, $\pm0.392843588800$
Angle rank:  $2$ (numerical)
Number field:  4.0.35525.3
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
$A(\F_{q^r})$ 109 33245 5191561 822647525 137557260544 23277947169605 3937096540195081 665423657339063525 112455224289323433109 19004944405616091648000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 195 2359 28803 370482 4822635 62744059 815739363 10604482147 137858351350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
The endomorphism algebra of this simple isogeny class is 4.0.35525.3.
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_bl$2$2.169.z_qr