Properties

Label 3.23.aw_ir_acal
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 85 x^{2} - 299 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.166921904620$, $\pm0.337099187115$
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
$A(\F_{q^r})$ 4545 139036095 1818038596140 21981448813532175 266742709730253471600 3244429883396733155158320 39473235136455346558249073235 480257711767160190726785430108975 5843228343266986326257979405330678780 71094366742695305772458221652309737593600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 496 12281 280692 6438937 148048621 3404967862 78312118196 1801157993429 41426521673971

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.an_dh 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.ae_aj_gl$2$(not in LMFDB)
3.23.e_aj_agl$2$(not in LMFDB)
3.23.w_ir_cal$2$(not in LMFDB)