Properties

Label 3.23.aw_il_abyj
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 79 x^{2} - 299 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0326071920932$, $\pm0.112386341891$, $\pm0.382576753817$
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
$A(\F_{q^r})$ 4455 135400815 1783198341540 21817987023088575 266290481393365532400 3243673368503450417692080 39472342624913945550597719145 480255052723877579508676433177775 5843216031655719281393437880977393380 71094338887917438648797169764002520851200

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 484 12047 278604 6428017 148014097 3404890876 78311684612 1801154198417 41426505443059

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.an_db 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_ap_ej$2$(not in LMFDB)
3.23.e_ap_aej$2$(not in LMFDB)
3.23.w_il_byj$2$(not in LMFDB)