Properties

Label 3.23.ax_jf_acdy
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0869454733845$, $\pm0.112386341891$, $\pm0.334554373298$
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
$A(\F_{q^r})$ 4260 134394480 1795477893840 21903902642476800 266524621004524446300 3243931737075909398280960 39472452504325828128485815860 480257810448077398389124518604800 5843235203242345487203360003355776560 71094399794614202139325727325839828300400

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 479 12130 279703 6433671 148025888 3404900353 78312134287 1801160107990 41426540933239

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.ao_dm 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.af_an_gk$2$(not in LMFDB)
3.23.f_an_agk$2$(not in LMFDB)
3.23.x_jf_cdy$2$(not in LMFDB)