Properties

Label 2.23.aq_ee
Base field $\F_{23}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
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:  $2$
Isomorphism classes:  2

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $254$ $259588$ $147834350$ $78392460944$ $41427442113454$

Point counts of the curve

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

Jacobians and polarizations

This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.10496.2.

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)