Properties

Label 2.23.aq_ee
Base Field $\F_{23}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-polynomial:  $1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.0613235619868$, $\pm0.259095524151$
Angle rank:  $2$ (numerical)
Number field:  4.0.10496.2
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 254 259588 147834350 78392460944 41427442113454 21912558187788100 11592417567558781886 6132566431072158715904 3244149258226861236480350 1716156167378259126439823428

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 490 12152 280134 6436488 148021930 3404702456 78310423614 1801151744456 41426519325450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.10496.2.
All geometric endomorphisms are defined over $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.23.q_ee$2$(not in LMFDB)