Properties

Label 3.23.ax_jj_acfk
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 7 x + 23 x^{2} )( 1 - 16 x + 108 x^{2} - 368 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0613235619868$, $\pm0.239612957690$, $\pm0.259095524151$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4318 136802876 1819545179800 22019736747021104 266812073826110743018 3243948787556459503774400 39469443190034239532520905702 480244003529391045774537458429952 5843200394530446652676150204822883400 71094355630649454237829073958243677685596

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 487 12292 281183 6440611 148026664 3404640765 78309882895 1801149378316 41426515199007

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ah $\times$ 2.23.aq_ee and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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
3.23.aj_t_u$2$(not in LMFDB)
3.23.j_t_au$2$(not in LMFDB)
3.23.x_jj_cfk$2$(not in LMFDB)