Properties

Label 3.23.aw_ir_acam
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 8 x + 23 x^{2} )( 1 - 14 x + 90 x^{2} - 322 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0869454733845$, $\pm0.186011988595$, $\pm0.334554373298$
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 it is unknown whether it contains a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4544 139010048 1817511950912 21974468178477056 266689032350853700544 3244152252081269342019584 39472180178332293828683799616 480254677475099551401650832801792 5843221972145488345017783228569415104 71094359362063254822390494808856716320768

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 496 12278 280604 6437642 148035952 3404876862 78311623420 1801156029554 41426517373296

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.ai $\times$ 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.ag_b_cy$2$(not in LMFDB)
3.23.g_b_acy$2$(not in LMFDB)
3.23.w_ir_cam$2$(not in LMFDB)